10 Pages. Due in 36 hours. No Plagiarism. 

 This is an article to be written in conjunction with the content of the intermediate econ class and the information. Here are notes about what we have learned so far in class, which are basically classic models and keysian models, solow models, IS / LM models. For example, there are Monetary and Fiscal policy in which model is effective and so on. Combining this knowledge with the information checked.  

ECON

1

110 Lectu

r

e Notes 7

ECON 1110 Intermed

i

ate Macroeconomics

James R. Maloy

Spring 2020

Lecture Notes for Topic 7: Keynesian Macroeconomics (III)

Readings: Froyen Ch. 7 (8th Ed. Ch. 8)

In this section, we will discuss the role of demand management in the Keynesian system, i.e. the use of fiscal/monetary policies to adjust aggregate demand and output. The overall goal of such policies in the Keynesian system is to sta

b

ilize output, employment and prices—i.e. keep AD stable—by counterbalancing any AD shifts (due primarily to volatile investment), thus eradicating the business cycle. Note that this is IS/LM analysis, which assumes prices are fixed—more on price volatility in a later topic.
I. Monetary Policy in the IS

–

LM Model

In the last topic we discussed factors that cause a shift in the LM curve—changes in money supply or money demand. Monetary policy is the manipulation of the money supply to change equilibrium income. Suppose the central bank wants to increase equilibrium income. They will increase the money supply (the methods and tools of the central bank will be discussed in the spring term), thus shifting the LM curve to the right. At the new equilibrium, output has increased and the interest rate has fallen.

How does monetary policy work? Why does increasing the money supply increase output? There is some disagreement about how monetary policy actually works. In the Keynesian system, monetary policy works through what is known as the indirect transmission process. In economic terms, the increase in the money supply creates an excess supply of money at the current interest rate, which causes the interest rate to fall. (Remember the money market analysis from the last chapter.) As the interest rate falls, investment will increase, and thus income will rise. The rise in income will boost consumption through the multiplier effect. Both of these factors will then boost the quantity of money demanded, since money demand is a positive function of income. At the new equilibrium, income is higher and interest rates are lower. This is where the new LM curve intersects the IS curve. Hence the indirect transmission process—changes in money yield changes in interest rates, which in turn cause changes in consumption, investment, and output. Monetary policy works indirectly via the interest rate.

A monetary contraction is a decrease in the money supply, and has the opposite effects.

II. Fiscal Policy in the IS-LM Model

Fiscal policy is the manipulation of government spending and taxes to change the level of equilibrium income. An increase in government spending and/or a decrease in taxes will shift the IS curve to the right, and a decrease in government spending and/or an increase in taxes will shift the IS curve left. For an expansionary government policy (G up and/or T down), a new equilibrium will be attained with increased output and higher interest rates.

The economic reason for this occurrence is also straightforward. Since government spending adds to aggregate demand (

Y

=

C + I + G), an increase in government spending will place upward pressure on output. Likewise, a decrease in taxes will boost consumption. If the interest rate remains unchanged, output will increase by the amount of the expansion times the multiplier, just as in the simple Keynesian model from Topic 4. However, the simple Keynesian model did not include the money market. The increase in income from the fiscal expansion will increase the quantity of money demanded. As the quantity of money demanded increases, the interest rate will rise. The increase in the interest rate will in turn cause a decrease in investment. The decrease in investment will partially offset the fiscal expansion. Therefore, the equilibrium output is at a lower level than in the simple Keynesian model—there is partial crowding out because the increase in government spending drives up interest rates. Note that this result is between the two extremes of the Classical model and the simple Keynesian model. In the Classical model there was complete crowding out and the fiscal policy was useless. In the simple Keynesian model without the money market there was no crowding out at all. In the complete Keynesian model the fiscal policy is partially effective. Again, the new equilibrium occurs where the new IS curve intersects the LM curve.

III. Policy Effectiveness and the Slope of the IS Schedule

Recall that we calculated the slope of the IS schedule to be

1
i
b
1
Y
r
–
–
=

¶

¶
. Therefore, the higher the value of (1 – b), which you should recall is the marginal propensity to save (MPS), the steeper the IS curve. (Alternatively, you could say that the lower the value of the marginal propensity to consume, b, the steeper the IS curve.) Also, the lower the absolute value of the interest elasticity of investment (i1), the steeper the IS curve. A low value of b (i.e. a high value of 1 – b) and/or a low value of i1 will make a steep IS curve, and vice versa. The interest rate sensitivity of investment demand (i1) is the more interesting case, and is the source of much disagreement among economists over the slope of the IS curve.

So what are the policy effects of having a steep IS curve because of low interest rate sensitivity of investment? Assuming a “normal” upward-sloping LM curve, we can easily show that fiscal policy will be relatively more effective than monetary policy in changing output. What is the economic intuition for this result? If investment is not very sensitive to changes in the interest rate, it will take a large change in interest rates to change investment. An increase in G, for example, will cause a rise in the interest rate, but since investment is not sensitive to this change, the increase in interest rates will not cause a large fall in investment—there is very little crowding out. Therefore, fiscal policy is very effective. Monetary policy, remember, works by influencing investment via the interest rate, but since investment is not very sensitive to the interest rate, monetary policy will not work very well.

Conversely for a flat IS curve, due to high interest rate sensitivity of investment, monetary policy will be relatively more effective than fiscal policy, for the exact opposite reason as the low interest rate elasticity case. These results can easily be viewed graphically. It is also possible to demonstrate this mathematically. The homework will show some examples of economies with different values of i1 and b, and your assignment will be to calculate the effect of monetary and fiscal policies for these economies using the same procedures from the previous homework. Consult the appendix to chapter 7 if you need help on this before the seminars.

IV. Policy Effectiveness and the Slope of the LM Schedule

Recall that we calculated the slope of the LM schedule to be

2
1
c
c
Y
r
=
¶
¶
. Therefore, the higher the value of c1, (the increase in money demand from an increase in income, i.e. the percentage of income that is demanded as money), the steeper the LM curve. Likewise, the lower the value of c2, (the interest elasticity of money demand), the steeper the LM curve, and vice versa. Again, the more interesting case is the interest rate sensitivity of money demand, c2. Keynesians typically believe that c2 is relatively high and thus the LM curve is relatively flat.

The policy implications for LM curves of different slopes can be seen graphically. For a flat LM curve, we can easily see that fiscal policy will be relatively more effective than monetary policy for changing equilibrium output. Why?

If there is an expansionary fiscal policy, for example an increase in G, output will increase, thus boosting transactions demand for money and throwing the money market out of equilibrium at the current interest rate (more money demanded, same quantity of money). Interest rates will therefore rise. If money demand is very sensitive to changes in the interest rate, it will not take much an increase in interest rates to restore equilibrium (very small change in interest rates will cause a big change in money demand and thus equilibrium quickly restored). Since interest rates only rise by a small amount, there is not much crowding out and the policy is very effective.

Monetary policy with a flat LM curve will not be very effective because the increase in the money supply will only yield a small fall in interest rates (again, it only takes a small change in interest rates to cause money demand to match the larger money supply). Since interest rates only fall a little, there will not be much increase in investment and thus only a small change in output.

Conversely, monetary policy will be relatively more effective than fiscal policy for a steep LM curve. Keynesians typically believe the previous case to be true, i.e. fiscal policy more effective.

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ECON

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110 Lectu

r

e Notes 6

ECON 1110

I

ntermed

i

ate Macroeconomics

James R. Maloy

Spring 2020

Lecture Notes for Topic 6: Keynesian Macroeconomics (II)

Readings: Froyen Ch. 6 (8th Ed. Ch. 7)

I. Interest Rates and Aggregate Demand

Recall that in the Classical system interest rates were determined by the interaction of the supply of and demand for loanable funds. Interest rates were seen to be the mechanism that ensures the stability of aggregate demand. The Classical economists theorised that a change in one component of aggregate demand would generate a change in the interest rate, and that the change in the interest rate would generate a change in other components of aggregate demand that would cancel out the initial change, thus keeping aggregate demand at the original level. Money, since it did not bear interest, was not a factor in determining interest rates, nor did money affect the real level of income or output (neutrality of money).

Keynes had a different way of looking at the situation. He argued that changes in the interest rate would indeed cause a change in aggregate demand, since the classical theory ignored factors such as a direct link between consumption and the interest rate. He also derived the interest rate not as a function of demand and supply of bonds, but rather demand and supply of money. This is Keynes’ attack on the classical system—changes in money yield changes in the interest rate, which in turns yield changes in aggregate demand. Recalling that in the Keynesian system output and income was demand

–

determined, we see that changes in the demand and supply of money will generate changes in income.

We have already discussed how aggregate demand affects income in the last chapter. We now must see how interest rates affect aggregate demand, and how money affects the interest rate, to have a full picture of the Keynesian model.

Keynes, like the classical economists, saw a negative relationship between investment and the interest rate. However, he also saw that a decrease in the interest rate could have a positive impact on consumption as well. Many consumer durable goods, such as cars, are purchased on credit. A decrease in interest rates will reduce financing costs and will boost consumption. Likewise, the lower mortgage costs will boost demand for homes, which will increase new housing starts, a component of investment. Keynesians also argue that lower interest rates might boost government expenditures that require financing, especially for local governments with lower funds. Therefore, the forces causing increases in aggregate demand from a decline in the interest rate outweigh the forces causing decreases in aggregate demand—and thus self-correction does not occur.

I. The Keynesian Theory of the Interest Rate

To develop the Keynesian interest rate, some assumptions will be used. First, assume that all financial assets are classified as either money or bonds. Money consists of currency and demand deposit accounts. Money is assumed to not bear interest (if we adjust the model to allow interest on money accounts, we get a similar result as money earns less interest than other assets). Bonds are homogenous perpetuities, which pay a fixed amount at fixed intervals with no repayment on the principle.

Keynes hypothesised that wealth (Wh) could be divided into holdings of bonds (B) and money (M).

Wh

=

B + M

The equilibrium interest rate is the rate where the demand and supply of bonds are equal. This implies that the bond market is in equilibrium—since the person is satisfied with how much he is holding in bonds at the current rate of interest, there is no excess supply of or demand for bonds. However, if a person is satisfied with the percentage of wealth held as bonds, he must also be satisfied with the percentage held as money. Using the same logic, it is evident that money supply and demand are at equilibrium too. If the person is happy with their bond-money combination, so there can be no excess demand or supply of money. This can be proven by contradiction: suppose that the bond market is in equilibrium but there is excess demand for money. This means people want to hold more money than they currently hold, which means that they want to sell bonds, so there is excess supply of bonds at the current interest rate—which implies that the bond market could not be in equilibrium! When one market is in equilibrium, so is the other. Keynes wanted to emphasise the role of money in the system, so he uses the money market rather than the bond market for determining interest rates.

II. The Keynesian Theory of Money Demand

Since bonds bear interest and money does not, there is obviously an opportunity cost of holding money. So why would someone want to hold any money at all when interest-bearing bonds are available? What factors determine how much of the non-interest bearing asset, money, a person chooses to hold?

Keynes listed three motives for money demand: transactions, precautionary, and speculative demand for money. The transactions motive is essentially the same as in the classical model. Money is a liquid asset and can be easily converted into other goods. Changing back and forth from bonds to money has associated transaction costs, and it makes little sense to incur them for short-run interest gains if the wealth is going to be spent soon anyway. Like the classical economists, Keynes expected the transactions demand for money to increase as income increases.

Keynes’ second motive, precautionary demand, is similar to transactions motive. Keynes felt people would keep some wealth as money in case of unexpected events, such as unemployment or injury. Again, Keynes expected precautionary demand to be directly related to income. One can think of precautionary demand as simply the demand for unexpected transactions.

The third motive, speculative, is more original. Bonds command a price on the open market, and it is a fact of finance that the price of bonds is inversely related to the interest rate (this relationship can be proven rather easily but it is not particularly relevant to the course so it will not be taken up further). Therefore, when interest rates increase, the value of the bond declines, which is a capital loss for the bondholder (and vice versa). Keynes theorised that people formed some judgment as to what was the “normal” rate of interest. If interest rates are above this level, they are expected to fall and the value of the bonds is expected to increase, thus generating both interest and a capital gain for the bondholder. If interest rates are below this level, they are expected to rise, generating a capital loss. Since the net return on a bond is the interest payment plus the capital gain or loss, there is some critical value below the normal rate of interest such that for any point below the critical value, the capital loss outweighs the interest gain and the net return on the bond is negative. Above the normal rate, the expected return is positive since there is a capital gain as well as the interest payment. Between the normal and critical value, the interest payment outweighs the expected capital loss, and the net return is positive. Therefore, speculative demand for money is zero above the critical value, since there is a positive return from bondholding. (Money, remember, bears no interest.) The only money that will be held will be for transactions or precautionary purposes. Below the critical value, people will hold only money and no bonds, since the expected return on bonds is negative.

The aggregate speculative demand for money is the compilation of the individual curves. It is downward sloping since at low interest rates people expect rates to start increasing and will hold more money to prevent a capital loss. The curve is smooth since each person has their own idea of a “normal” interest rate.

Total Money Demand in the Keynesian System

Therefore, we have three motives for money demand. Keynes’ first two (transactions and precautionary) give money demand as a function of income, while speculative demand is assumed to be a function of the interest rate and income. These concepts were later revised by other economists. William Baumol demonstrated that transactions demand is also inversely related to the interest rate, while James Tobin improved Keynes’ speculative demand theory.

Using all of these ideas, we can now express the Keynesian demand for money as

Md = L (Y, r)

Money demand for transactions is positively related to income and negatively related to interest rates. The money demand curve, when plotted against the interest rate, is a downward sloping function.

A typical linear version of this function is:

Md = c0 + c1Y – c2r
c1 > 0,
c2 > 0

The parameter c1 is the sensitivity of money demand to changes in income, and c2 is the sensitivity of money demand to changes in the interest rate.

Money Supply and Equilibrium: The Liquidity Preference Model

Again, we are assuming that the money supply is fixed by the central bank and is independent of the interest rate; i.e. a vertical line at the fixed money supply (this assumption is actually not correct, and is the topic of a later lecture on the money supply process). Equilibrium in the money market and the equilibrium interest rate are determined by the intersection of money demand and supply. Note that income (Y) is held constant when deriving the demand curve; an increase (decrease) in Y will lead to an increase (decrease) in money demand; the curve will shift right (left) and interest rates will increase (decrease). Interest rates are thus procyclical: they move with the business cycle. Note also that monetary policy (changes in the money supply) will shift the curve; a monetary expansion leads to lower interest rates while a monetary contraction leads to higher rates.

However, what is the relationship between the money market and the goods market (for output)? How do changes in the money market affect the goods market, and vice versa? The IS/LM model shows these ideas by combining the simple Keynesian model with the Keynesian liquidity preference model. Note: The IS/LM model is a demand-side model; both the simple Keynesian model and liquidity preference model are AD-side concepts. The IS/LM model thus assumes that firms automatically supply whatever level of output is demanded at a fixed price (essentially, a horizontal AS curve whereby AD determines Y*). This will be discussed in more detail in a later topic.

III. Money Market Equilibrium: The LM Curve

We have said that money demand is a function of the interest rate and income:

Md = L(Y, r)

or in linear form:

Md = c0 + c1Y – c2r
c1 > 0,
c2 > 0

The signs indicate that money demand increases as income increases (due to the transactions/precautionary motives) and is negatively related to the interest rate. We have seen that the money demand schedule is downward sloping when plotted against the interest rate. A change in income causes a shift in the money demand schedule (not the money demand function). Why? As income increases, you are demanding more money for transactions at any given interest rate. An increase in the quantity of money demanded for a fixed money supply will naturally cause a rise in the equilibrium interest rate (think of the interest rate as the price of money). Therefore, we note that there is a positive relationship between interest rates and income. This positive relationship is called the LM curve. The LM curve shows all combinations of the interest rate and income that generate equilibrium in the money market, i.e. money supply equals money demand.

The LM curve can be derived graphically by calculating the interest rate for different levels of income (and thus money demand) and plotting this relationship.

The LM curve can also be derived algebraically. The LM curve shows money market equilibrium where money supply and demand are equal. This can be calculated by setting money demand and supply equal and solving for r (alternatively, you can solve for Y but solving for the interest rate is the more common method).

Ms = Md = c0 + c1Y – c2r

r = c0/ c2 – Ms/ c2 + (c1/c2)Y

IV. The Slope of the LM Curve

The slope of the LM curve can be calculated by calculating the change in interest rates from a change in income. This partial derivative is:

∂r/∂Y = c1/c2

Therefore, two things influence the slope of the LM curve. c1 measures the increase in money demand from an increase in income. The higher the value of c1, the steeper the curve. c2 measures the interest elasticity of money demand. The higher the interest elasticity of money demand, the flatter the money demand curve. There is little disagreement about the value of c1 but there is considerable argument about the value of c2.

V. Factors That Shift the LM Schedule

There are two factors that cause a shift in the LM curve. The first is a change in money supply. An increase in money supply will shift the LM curve to the right. The second is a change in the money demand function itself, i.e. a change in the c0 parameter. Basically, this change in anything that affects money demand other than changes in income or interest rates. A shift in the variables of money demand—income and interest rates—does not shift in the LM curve—it causes a movement along the curve, but a change in anything else that affects money demand does shift the LM curve. (Remember your rules of graphing—r and Y are endogenous changes.) An increase in money demand for a given interest rate and income will shift the LM curve to the left, and vice versa.

VI. Product Market Equilibrium: The IS Curve

We have stated two equivalent ways to describe product market equilibrium:

Y = C + I + G

or

I + G = S + T

The IS curve can be derived from either of these equations. The second one will be used to derive the IS curve graphically.

First, ignore the government sector, i.e. G and T are zero. Now that we have developed the Keynesian interest rate, we can express investment as a function of the interest rate. Again, this is a negative relationship. Again, saving is a positive function of income.

Now add the government sector. The government is assumed to not be concerned about the interest it has to pay for its borrowing. Therefore, adding government spending to the investment function and taxes to the saving function will be a parallel shift of these functions. Adding government spending will shift the investment function to the right, and the saving function will shift to the left since taxes will decrease the level of disposable income and thus savings. Combining these two functions will give us the IS curve. The IS curve shows all possible combinations of output and the interest rate that generate equilibrium in the product market. It shows an inverse relationship between interest rates and output.

The IS curve can also be derived algebraically, using either of the two conditions for equilibrium. From the first condition,

I + G = S + T

we can express investment as a linear function of the interest rate

r
i
I
I
1
–
=

0
1
>
i

The savings function is again:

)
)(
1
(
T
Y
b
a
s
–
–
+
–
=

Taking government spending and taxes as exogenous, we have

T
T
Y
b
a
G
r
i
I
+
–
–
+
=
+
–
)
)(
1
(
1

Rearranging and solving for Y yields an expression for the IS curve: (Usually, the LM curve is solved for r. The IS curve is solved for Y.)

[
]
b
r
i
bT
G
I
a
b
Y
–
–
–
+
+
–
=
1
1
1
1

We can also find the IS curve by using Y = C + I + G. Substituting our equations for investment and consumption and solving for Y gives an identical expression for equilibrium.

Factors That Determine the Slope of the IS Curve
As for the LM curve, the slope of the IS schedule is calculated by taking the partial derivative of the IS curve equation, ∂r/∂Y. This yields:

∂r/∂Y = – (1-b)/i1
This slope is negative, as previously mentioned. Two factors influence the slope of the IS curve. 1 – b is the marginal propensity to save (MPS), which is the slope of the savings function. The IS curve is steeper the higher the MPS. We will not consider saving in more detail until next term.

The second factor that influences the slope of the IS curve is i1, the slope of the investment function and more commonly called the interest elasticity of investment. The higher the interest elasticity of investment, the flatter the investment function. In this case, there are large changes in investment with small changes in interest rates, and since investment is a component of income, small changes in interest rates therefore yield large changes in income; thus the flatter the IS curve. Conversely, low interest elasticity of investment will yield a steep IS curve.
VII. Factors That Shift the IS Curve

The factors that shift the IS curve are the same factors that cause a shift in the simple Keynesian model from the last chapter. Changes in government spending, taxes, and autonomous investment and consumption will shift the position of the IS curve. The magnitude of this change can again be calculated by using the multiplier, which are again calculated by taking partial derivatives. These multipliers are unchanged from the last section—the multiplier is 1/(1 – b) for changes in G, I, and a; and –b/(1 – b) for changes in T.

We can graphically show the effects of changes in government spending, investment, consumption, and taxes. An increase in autonomous investment or government spending will shift the IS curve to the right.
An increase in autonomous consumption will shift the savings function and thus the IS curve will shift right. An increase in taxes, again, reduces aggregate demand and the IS curve will shift left. Decreases in any of these factors will yield opposite effects. Note that if the interest rate is unchanged, output will change by the full amount of multiplier, as in the simple Keynesian model. If the interest rate changes at all, output will not increase by the full amount.
VIII. The IS and LM Curves Combined

The point of intersection between the IS and LM curves gives the interest rate and output level at which the money market and product market are simultaneously in equilibrium.
Again, the equilibrium values of the interest rate and income can be calculated algebraically. Since in equilibrium Y and r must be the same in both the IS and LM curves, substituting the LM curve into the equation for the IS curve and solving for Y gives equilibrium income:
Substituting this value of Y into the equation of either the IS or LM curve and solving for r yields:
The point of the IS/LM model is to improve the simple Keynesian model by acknowledging the fact that money and interest will affect output levels and vice versa—the goods market and money market are interrelated. For example, suppose that there is an increase in autonomous investment, which shifts the IS curve to the right. The new equilibrium occurs at higher interest rates and higher output levels. We know what causes the higher output—higher investment means higher AD which means higher output, as in the Keynesian cross diagram. However, more output (income) leads to more money demanded for transactions and as a store of wealth—the money demand curve shifts upward and to the right, hence higher interest rates. IS/LM shows both of these effects on a single diagram. A similar thing occurs due to LM shifts. An increase in the money supply lowers interest rates; lower interest rates boost I, and thus AD and output, Y, as shown by IS/LM.
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ECON

1

110 Lecture Notes 3

ECON 1110 Intermediate Macroeconomics

James R. Maloy

Spring 2019

Lecture Notes for Topic 3: Classical Macroeconomics (II)

Readings: Froyen Ch. 4

This section discusses the determination of prices in the classical model. The roles of money and the classical quantity theory of money are discussed. The classical aggregate demand curve is derived and equilibrium prices and output are determined by the intersection of aggregate demand and aggregate supply. The determination of interest rates and the role of interest rates in stabilisation are analysed, as well as the role of government policy.

I. The Quantity Theory of Money

There are two main versions of the classical quantity theory of money—Fisher’s quantity theory and the Cambridge quantity theory. Both models are similar and draw basically the same conclusions, but the techniques and analysis are a bit different.

One of the oldest economic theories still in use today, the quantity theory of money traces its origins to theorists who were trying to determine the effects of an increase in the gold supply.
At that time, most of the world was on a gold standard, so the quantity of gold in the nation determined the quantity of money. When new gold supplies were discovered (i.e. in the New World) it increased the quantity of money in the economy. Under mercantilist theory, the increase in gold would make the country more affluent, but theorists such as David Hume and some of his contemporaries disagreed. They developed a theory which is familiar today—the idea that increases the money supply only cause inflation. The quantity theory shows a relationship between the quantity of money (the independent variable) and the price level (the dependent variable). Hume wrote that in the long run the absolute size of the money stock was insignificant because the price level would eventually adjust to match it. This idea became known as the neutrality of money, as mentioned in the last topic. If the money stock were to double, for example, prices would eventually double and employment would be at the normal level. The classical economists argued that monetary policy would only cause inflation in the long run, although there was some room for short-run non-neutrality due to lags in the adjustment process. Therefore, early quantity theorists suggested that in the short run it may be possible to experience an increase in output as a result of an increase in the money supply, but this would be a transitory effect. Hume even suggested that output could be continually increased, but at the cost of ever-increasing inflation.

Fisher’s Quantity Theory

Fisher greatly advanced the quantity theory by coupling it with the equation of exchange
.

MV = PY

M is the money supply, V is the velocity of money, P is the price level, and Y is the real level of output. PY is of course nominal output. Velocity measures the turnover rate of money (money being currency and demand deposits) in the economy, i.e. how many times on average a pound coin changed hands in a year. For example, if nominal output PY was $100 and the money supply M was $20, it means that each dollar was used an average of 5 times.

The equation of exchange is true by definition, but Fisher and other quantity theorists went further by attempting to explain the determination of each component. The equilibrium level of output Y is determined exogenously by the factors considered in the previous chapter; a change in the money supply is not a factor that affects equilibrium output. Velocity is dependent on the paying habits of society. An increase in credit transactions, for example, would increase velocity, since things could be bought immediately without needing up-front payment. Shorter pay periods yield smaller paychecks, which would cause a decrease in the amount of money held at any given time and therefore increase velocity. These factors, however, are assumed to be relatively stable in the short run and would therefore generate constant velocity. It is important to note that many classical economists did not believe that velocity was necessarily stable; they only believed that in equilibrium, velocity (like output) was independent of the money supply, and could therefore be treated as an exogenously-given constant. In other words, a change in the money supply would not affect equilibrium velocity. Therefore, for simplicity, we will treat velocity as a constant. In summary, the changes in the money supply do not affect equilibrium values of V and Y.

The equation of exchange can be used to determine the price level. Holding Y and V constant, an increase in the money supply must be met by an equal increase in the price level for the identity to hold, ceteris paribus. Fisher wrote in his work The Purchasing Power of Money that doubling the quantity of money will initially decrease velocity by fifty percent, and the person will be left with “double the amount of money and deposits which his convenience had taught him to keep on hand…and there cannot be surplus money and deposits without a desire to spend it, and there cannot be a desire to spend it without a rise in prices.” P will therefore double and V will return to its original level. In other words, an increase in the money supply increases demand for goods, but does not increase the productive capacity of the economy to produce more goods—it is demand without production to match it; prices simply increase. Thus Fisher’s quantity theory of money (sometimes called the transactions quantity theory): the quantity of money determines the price level. Note that in the short run, before prices double, there may be some non-neutrality of money, and velocity and output can be affected. Thus we have an important conclusion: although the economy can move away from full employment output, any change in output is only temporary and the economy, through natural behaviour in the “perfect system,” will correct itself. Laissez-faire should be maintained because firstly, any fluctuation in output will correct itself without government interference and secondly, any attempts to use monetary policy to artificially increase output will only cause inflation.

The Cambridge Quantity Theory

The Cambridge approach is named for two famous classical economists from Cambridge University, A.C. Pigou and Alfred Marshall. They arrived at the same conclusion as Fisher, but unlike the Fisher version, which said that by definition changes in the money supply generate changes in prices, the Cambridge economists developed a model of money demand to analyse how people decide how much money to hold, and therefore how changes in the money supply will affect their optimum money holdings. They thus generated an economic rationale for the link between money and prices.

The Cambridge economists argued that people would hold money for transactions or for unexpected expenses. But, holding wealth in the form of money would entail an opportunity cost, namely the foregone interest that could be obtained from holding bonds. There is therefore an optimum level between the desire to hold money for transactions or emergencies and the desire to not hold money and hold interest-bearing bonds instead. Interestingly they veer towards the foundation of Keynes’ monetary theory—their model treats money as an asset rather than just a means of transactions, but they do not explore the full implications. Marshall and Pigou theorized that the demand for money (MD) would be a proportion, k, of nominal income (PY):

MD = kPY

Since in equilibrium money demand must be equal to money supply (M), we have:

M = MD = kPY

Marshall and Pigou also expected k and Y to be fixed exogenously, thus generating another model that shows that changes in the money supply generate identical changes in the price level. Indeed, if k = 1/V, the Fisher and Cambridge equations are identical.

Therefore, both versions generate the same results, but the Cambridge approach generates a more economics-oriented argument by deriving the quantity theory as a money demand theory, not just a mathematical identity.

II. The Classical Aggregate Demand Curve

The quantity theory is an implicit theory of aggregate demand, and can be used to build the aggregate demand (AD) curve. Using the equation of exchange:

MV = PY (or M = kPY)

the AD curve is derived by plotting different combinations of P and Y for a fixed money supply (M). For example, if V is a constant 2.0 and M = 600, we know that PY = 1200. Supposing P=2.0 and Y = 600 gives us one point on the AD curve. Now suppose P = 3.0 and Y = 400. We have another point on the AD curve. Continuing with different combinations of P and Y that generate a product of 1200, we find a downward sloping AD curve: the aggregate quantity demanded increases as the price level decreases for a given quantity of money. This should make sense: if you have 50 pounds in your pocket, you will demand more goods the cheaper the goods are!

We note that an increase in the money supply (holding V constant) will generate an equal change on the other side of the equation. Therefore, we can plot a new AD curve with different combinations of P and Y for the new quantity of money. An increase (decrease) in the money supply shifts the AD curve to the right (left). Any point on the AD curve is a point of equilibrium in the money market—where money supply equals money demand. That is,

M = MD = kPY

Furthermore, any point on the AD curve is a point where P and Y are at levels where their product PY corresponds to the quantity of money M. If MV does not equal PY, we are at a point off the AD curve for money supply M. In summary, for any point on the AD curve for quantity of money M, it must be that M = MD and MV = PY.

Aggregate Demand and Supply in the Classical System

Combining the classical AD and AS curves gives equilibrium in the output (or product) market. The vertical AS curve shows that output is independent of the price level. Changes in the money supply generate shifts in the AD curve, which in turn generate changes in the price level. Therefore, only the real factors from the last topic determine the equilbrium level of output; changes in these variables shift AS and affect prices and output. The quantity of money determines the AD curve, which in turn determines the price level. Note that a change in the money supply leads to a change in prices but not output via the quantity theory.

III. The Classical Theory of the Interest Rate—The Loanable Funds Theory

In the classical model, the interest rate played a critical role in maintaining the stability of aggregate commodity demand. The classical model argued that any change in any component of aggregate demand—consumption, investment, and government spending—would be matched by a counterbalancing change in one of the other components, and the interest rate was the mechanism that ensured this result.

The equilibrium interest rate is determined by the amounts of borrowing and saving (saving = lending). All transactions were assumed to be in the form of bonds. If a firm wished to borrow money, it would issue a bond. The saver would then buy the bond, giving the firm money in exchange for it. The bond would bear an interest rate (r), as determined by the interaction of demand for bonds (lending) and supply of bonds (borrowing).

The demand for bonds is called supply of loanable funds in classical terminology. Likewise, the supply of bonds by borrowers is termed demand for loanable funds. The supply of loanable funds is expected to be a positive function of the interest rates. Recall that individuals can either consume or save their income. At higher interest rates, the opportunity cost of consumption increases and people are more willing to forego current consumption to take advantage of higher interest rates. Therefore, the supply of loanable funds curve is upward sloping.

The demand for loanable funds is the level of investment by businesses plus the amount of government borrowing, i.e. the government budget deficit (g-t). The amount of investment undertaken is expected to increase as the interest rate decreases. This is because firms invest up to the point where the interest rate equals the expected return of the project (i.e. MC=MR), and as interest rates decline, more projects become profitable and investment increases. Therefore, the demand for loanable funds for investment is a downward sloping function of the interest rate. The level of the government deficit (g-t) is assumed to be independent of the interest rate, so the total demand for loanable funds curve is shifted to the right by the amount of g-t.

Equilibrium is where the supply and demand of loanable funds curves intersect. At that intersection, the equilibrium interest rate is set, and demand and supply of loanable funds intersect, i.e. s = i + (g-t). (Recall that this is the same identity as the relationship derived in Topic I: I + G = S + T).

Why does the interest rate ensure that desired commodities demand (C+I+G) remains at a constant level? Assume that G is constant. Suppose that there is an increase in autonomous investment. The firms need money for the new investment, so the demand for loanable funds curve shifts right. At the new equilibrium, the interest rate has increased and the quantity of funds loaned out has increased. Therefore, more investment has taken place and people save a greater quantity of money to take advantage of the higher interest rates. We see that the increase in investment is exactly equal to the increase in savings. But recalling that people either consume or save their income, the increase in savings must yield an equal decrease in consumption. Therefore, investment and consumption have changed by equal and opposite amounts, and the net change in C + I + G is zero! Therefore, the interest rate in the classical model works to smooth out and eliminate any changes in desired demand.

IV. Government Policy in the Classical Model

Note that monetary and fiscal policy are known as demand management. The goal of these policies is to alter aggregate demand. We know that output in the classical model is determined by aggregate supply, not aggregate demand, so even if these policies succeed in shifting AD, output will be unchanged. However, it will also be shown that fiscal policy is generally ineffective even in adjusting AD, since only changes in the money supply shift AD.

Monetary Policy

We have seen that money is neutral in the classical model. Only real factors determine the level of aggregate supply and output. A change in the money supply only changes aggregate demand and the price level. Therefore, monetary policy does not cause real changes; it only affects inflation and prices. The quantity theorists argued that any short run non-neutrality of money that caused a recession and potential use of a monetary expansion was so short-term that it was not worth the long run cost of higher inflation.

It should be noted that money can be considered insignificant in the sense that it does not determine long-run output. However, money is significant in its use as a medium of exchange, and stable money is a requirement for stable prices. As John Stuart Mill wrote,

There cannot be intrinsically a more insignificant thing, in the economy of a society, than money; except in the character of a contrivance for sparing time and labour. It is a machine for doing quickly and commodiously, what would be done, though less quickly and commodiously, without it; and like many other kinds of machinery, it only exerts a distinct and independent influence of its own when it gets out of order.

Fiscal Policy

There are two types of fiscal policy—changes in government spending and changes in taxes. Assuming that taxes remain unchanged, the effects of a change in G can be analysed. An increase in government spending (fiscal expansion) will alter the government budget deficit g-t. Therefore, the government will have to finance this increase in the deficit by borrowing, thus shifting the demand for loanable funds curve to the right. What happens is similar to the case of an increase in investment. At the original level of interest, there is excess demand for loanable funds, so the interest rate increases. As the interest rate increases, some investment projects cease to be profitable, so investment declines. The increase in the interest rate causes savings to increase and consumption to decrease. Therefore, the increase in government spending is completely offset by the decreases in consumption and investment, and the sum of C + I + G is unchanged. The government spending crowds out private expenditures, and the fiscal policy is ineffective. Recalling that we constructed the AD and AS curves without mention of government, it is evident that a bond-financed increase in government expenditures will have no impact on prices or output. If, alternatively, the government finances the increased spending through the printing of more money, it is obvious that the increase in the money supply will only increase the price level.

Tax Policy

Suppose the government chooses to expand the economy by a tax cut. On the demand side, a tax-cut could stimulate consumer demand. However, if the government sells bonds to finance the tax cut, the interest rate will adjust to ensure that the level of AD remains unchanged. The increased demand for loanable funds (g-t becomes larger) will increase the interest rate and cause saving to increase, thus partially eroding the initial increase in consumption stimulated by the tax cut. The higher interest rates would also cause investment to decline. The same crowding out effect as before would occur, with C + I + G unchanged. Likewise, paying for the cut by printing new money will just increase the price level. Therefore, tax policy is ineffective in changing AD.

However, if the tax cut is not lump sum, but a decrease in marginal tax rates, the change can have important impacts on supply decisions. A decrease in marginal income tax rates, for example, will make people more willing to work for a given real wage, since the worker gets to keep a larger percentage of his earnings. The labour supply curve will increase, generating an increase in the equilibrium quantity of labour and thus aggregate supply. Therefore, changes in marginal tax rates can have real effects on the economy. However, this affect is typically considered detrimental, as it simply distorts the market—note that employment (and thus output) are the highest when there is no income tax, and changes in the policy cause fluctuations, rather than cure them. Classical economists therefore viewed taxes as having either no effect or a detrimental effect, based on the case. Taxes were simply ways to pay for necessary government expenditure rather than a tool to manage the economy. In any case, there was no need for tax policy to stimulate the economy in the Keynesian sense due to self-correction. In the classical era there typically was no such thing as an income tax, or where it existed the rate was very low. Therefore, classical economists usually did not pay much attention to this type of situation—it is with hindsight that we can apply their theory to income taxes. Modern supply-side economics theories centre around this classical concept.

� The first known mention of the quantity theory is actually in the writings of Copernicus in the 1520s, although the development of the theory happened much later as a response to New World gold entering Europe.

� Fisher’s version actually looked at total transactions T such that MV=PT, not just transactions related to current production Y. If the proportion of transactions related to current production is stable, then replacing T with Y works—if not, it is a problematic assumption. Interestingly he also distinguished financial transactions, an idea which has been largely lost. See Fisher (1911)

1

ECON 1110 Intermediate Macroeconomics

Spring

2

020

Instructions for Essay

Due: Beginning of your scheduled lecture on Thursday 2nd April. A hard copy must be submitted to me—no emailed attachments.

Please read all of these instructions carefully as your grade depends on it.

The purpose of the essay is to use the techniques and concepts learned in class to analyse a particular issue. The ideal essay should be about 2500 words. (Please worry more about making it complete than whether or not it is exactly 2500 words!) You must include a reference list at the end AND appropriate in-text documentation (footnotes, endnotes, or parenthetical documentation). Failure to include references constitutes plagiarism and will not be accepted. It must be typed with 12 point font and 1.5 line spacing. Please include page numbers. You are of course permitted to include charts or graphs (which may be drawn by hand). Outside reading and research on the chosen topic are essential. Possible sources of information are the Internet and Pitt libraries. Another valuable resource for economists is the Journal of Economic Literature, which is available in the library. This quarterly publication compiles a list of all economics books and journal articles and organises them by subject. So if you are looking for recent journal articles about monetary economics, you simply have to look at the newest JEL under the topic “monetary economics” and you will find a list of all recent publications. Obviously, if you look at older copies of JEL you will find past publications. Only certain editions list book publications. Perhaps more handy is to use is EconLit, which is an online search engine for economics publications, which should be available to you from a Pitt computer at search.ebscohost.com (click on the EconLit link). You can access many full articles directly from the search engine, depending on whether Pitt has access to that particular publication. You should also note that you can access JSTOR from a Pitt computer (www.jstor.org). JSTOR is a collection of online files of hundreds of different journals from many subjects and is a valuable resource for finding full articles. Due to copyrights articles from the past few years are not yet available on JSTOR, but you can find most common journals at Pitt’s libraries anyway if you require a recent edition.

Essay Topic:

Choose ONE of the following topics for your essay (if you previously wrote an essay for me or for another class, you may not turn in the same or a very similar essay for this class). Note that I give you some suggested questions that you can address in each essay. You should not feel restricted to answering just these questions—just make sure that it flows coherently and is complete. Most of these essays leave you plenty of room to discuss the ideas that you find most interesting. I am mostly looking at your ability to conduct research, write coherently, and analyse issues and policies using proper economic techniques. It is much more advisable to pick a relatively narrow topic and do a more thorough discussion than to do a superficial treatment of a broad topic.

1. The US federal government has run deficits for the majority of recent history. There have been proposals in the past for requiring government’s to balance their budget, such as proposals for a balanced budget amendment or similar policy rules. What are the benefits of a balanced government budget? What are the potential problems? How do different schools of macroeconomic thought view this situation? You could also look at state-level analysis, as most US states do have some sort of balanced budget rule. A similar topic is the European Union’s Stability and Growth Pact (SGP) for eurozone nations, which requires them to maintain a budget deficit of less than 3% of GDP, except during times of economic turmoil (which has been ignored by some members and also be aware the SGP has been changed over time; the current version is different than the original). You could explain the purpose and goals of this act, the benefits and costs of fulfilling these requirements, and the problems that have occurred in under the SGP.

2. The Bretton Woods system provided a system of fixed exchange rates from the end of WWII until the early 1970s. Write an essay discussing some aspect of the international experience of under Bretton Woods. What are the benefits/costs of fixed exchange rates? How did the system operate? What difficulties were encountered that led to its eventual abandonment?

3. After the breakdown of Bretton Woods, some European nations decided to form their own system of fixed exchange rates called the Exchange Rate Mechanism (ERM) (which was a part of the European Monetary System, EMS). What were the motivations for its creation? How did it operate? Which nations had the most influence? What difficulties were encountered? There are many interesting essays that you can write on this situation, such as the exit of Britain from the ERM in 1992 or the role of West Germany in this system.

4. During the 1970s and early 1980s, many industrialized nations had massive inflation problems. There are many possible explanations: monetary policy, the breakdown of the Bretton Woods system, the oil embargoes launched by OPEC nations, or fiscal policy actions (excessive government deficits). These factors could affect aggregate demand or aggregate supply and thus create inflation. Possible essays in this area could focus on the supply shocks created by the oil embargoes, the breakdown of Bretton Woods and the resulting exchange rate volatility/monetary policy volatility in these nations, government budget problems. An effective essay could be an analysis of various attempts by governments to reduce inflation during the 1980s, or explaining why West Germany had such superior inflation performance relative to most other economies.

5. The Great Depression of the 1930s was a time of monumental change in many nations. Key industries such as manufacturing and agriculture were in massive slumps. Unemployment reached record heights. There are two approaches that you can take to this essay. You can analyse some of the causes of the Great Depression (it would be best to pick a few related ones since if you attempt to cover them all then you will not have a very in-depth discussion of any). Alternately, you can look at some of the economic policies used by governments to deal with the Depression. You can do this for any particular (more or less) capitalist nation, such as the US. Be cautious with this topic—there are many low-level history-type sources out there, most of which are dubiously accurate (e.g. falsely claiming Hoover was laissez-faire, etc.) and lack proper economic analysis. You could also analyse the policies taken by nations that explicitly abandoned capitalism for fascism or communism, although you should be warned that such an essay will require you to do some outside reading about non-capitalist economic theory. One particular topic along those lines would be to study Mussolini’s corporatist policies and how they influenced US policy and economic thought in the 1930s.

6. In the 1950s and 60s unemployment rates in Western Europe were substantially lower than unemployment rates in the US. By the 1980s the situation had reversed in many of these nations. Economists have done considerable research to explain this phenomenon. What factors caused high European unemployment? What is the effect of this unemployment on these nations? What policies have been tried/could be tried to reduce unemployment? (Hint: Charles Bean has a very good survey article on European Unemployment, which you can search for on JSTOR).

7. Central Banking and Monetary Policy: You can write an essay analysing the policies taken by the Fed or another central bank in a specific situation, such as during the Great Depression, the stock market crash of 1987, the East Asian financial crisis, etc. There is much debate about what central banks should be doing to deal with the current financial market instability—you could write a very good essay comparing the events of today with the actions taken by central banks in response to previous financial market problems. You should investigate the actual policies that were taken, their effects, and any problems that were encountered.

8. The Austrian model developed by Mises, Hayek and others has proven to have some value in predicting the recent economic situation. Write an essay on some aspect of Austrian theory. One example would be to investigate the Austrian explanation of the 1930s depression and discuss its application to today. Another example would be to compare the ideas of Hayek and Keynes (who had a spirited correspondence with each other) on the macroeconomy. The best source on Austrian theory is mises.org, which has many full-text books and articles available for free.

9. There have been numerous instances of hyperinflation through modern history, such as what is presently occurring in Zimbabwe. Perhaps the most famous example of hyperinflation is what occurred in 1920s Germany, although other nations as diverse as Turkey and much of South America have also experienced massive inflation problems. What factors caused these hyperinflationary episodes? What economic theories can be used to explain hyperinflation? What were the consequences of these inflationary periods on the economies of these nations?

10. An analysis of economic growth could provide an effective essay topic. You could analyse the causes of economic growth and then apply them to a particular nation (e.g. explaining the causes of US growth in the post-Civil War period, the growth in Japan after WWII or China since the 1980s, for example), or you could compare the economic performance of different countries today, e.g. explaining different productivity levels internationally. Many of these topics cross over into aspects of development economics, which is fine as long as you concentrate on macroeconomic issues.

11. Alternatively, you can select your own topic in macroeconomics, subject to the following:

a) You must pick something suitable for an upper-level undergraduate student. Very basic topics or topics not related to the course are not acceptable. Pick something feasible about which you can find information. Do not pick something that is too complicated—an essay on a complex subject that you do not understand very well is not conducive to a higher grade, contrary to popular belief. Also, try to be specific in your topic—writing on “the Fed’s monetary policy” is very vague and will not allow you to show much in-depth research, whereas writing on, for example, how the Fed responded to the oil price shocks will allow a much more detailed discussion.

b) You may select a topic that we do not explicitly cover in class provided that it is sufficiently related to macroeconomics

c) If you choose your own topic, you must have it approved by me BEFORE you start. Please email (maloy@pitt.edu) me with your proposed topic so that I can check it and provide any advice/warning about your topic. If you wait until two days before the essay is due to ask me to approve a topic you should expect to get a sarcastic email in reply.

A few notes on writing techniques:

You should put considerable effort into the structure and coherency of your essay. You should include an introduction and conclusion. Your introduction should introduce your paper and should
clearly indicate the purpose of your paper. Be particularly careful to ensure that your conclusion is a summary of your key points and does not bring in a bunch of new information. When writing the main body, pay attention to the organisation of your discussion. Make effective transitions between paragraphs; in other words, make sure that your discussion flows coherently from section to section.

This essay must be written in the third person. The word ‘I’ should NOT be in this essay. I especially do not want to see the phrases “I think” or “I believe” anywhere; in my experience such phrases are typically followed by some pre-conceived opinion that has nothing to do with the evidence you have presented. Any conclusions you draw should be the result of the evidence and theories you have discussed and your economic analysis of the strengths and weaknesses of issues, not on random personal opinions about how you think butterflies are pretty with no factual foundation. You should give the impression that your views and conclusions are the direct result of what you have learned. Any opinions should be supported by evidence.

Please ensure that you are writing an economics essay, not a history or a politics essay. Although such issues are important and can be brought into your essay where appropriate, you are expected to concentrate on economic issues and use economic analysis in your essay.

Try to include economic theory and relate it to the issue at hand, rather than just writing a summary of events. For example, if you were writing about monetarism in the US during the 1980s then you should include monetarist theory to supplement your summary of the policies taken by the Fed. In other words, you should be using theory to explain the evidence.

Please consult outside sources and research your topic thoroughly. Just reading the textbooks and some random articles from the National Enquirer does not constitute research. Make sure that your sources are at an appropriate level for this class. This is particularly important for internet sources: just because something is on the internet does not make it true! For example, something found on the European Central Bank’s website should be fine, but something from some random blog may be, but is not necessarily, accurate. However, keep in mind that good sources may be factually correct but biased towards a particular point of view, e.g. you probably will not find much effective criticism of Fed policy on the Fed’s own website.

At the university level you should not be using an encyclopaedia as a primary reference for the bulk of your essay. However, if you do consult one do make sure that it is a properly-edited one, not something where anyone with internet access and an IQ of 60 can post random things. Wikipedia is not an acceptable reference for a university-level student. YOU MAY NOT USE WIKIPEDIA OR ANY SIMILAR TYPE OF NON-REFERENCE. The use of inappropriate sources will result in a significantly lower grade.

Also, you MUST include appropriate documentation, including both references in the text (parenthetical or footnotes/endnotes) AND a full, alphabetized reference list at the end. Failure to use appropriate documentation constitutes plagiarism and will not be accepted. Use an appropriate format for references. You should purchase a guidebook that shows you an appropriate style, such as MLA. Most such books show methods of both parenthetical documentation and footnote documentation. Usually, parenthetical documentation is used in economics but I will accept footnotes/endnotes as well. Any style is acceptable as long as you are consistent (i.e. don’t switch from footnotes to parenthetical halfway through the essay), with the exception that using numbered parenthetical references such as [3], with the [3] referring to “source 3” in a numbered bibliography at the end is complete rubbish; no proper academic papers use such a style.

As for WHEN to use documentation:

The basic rule is that you must give the source of anything that is not common knowledge. What is common knowledge? Basically, anything that should be known by a student at your level is common knowledge. For example, you do not have to give credit to Adam Smith if you start talking about supply and demand. However, any figures or advanced theories must be referenced. If you say that some country had inflation of 4.5654 percent in 1984 or discuss Friedman’s theory of the velocity of money, you MUST provide documentation crediting your sources. Any fact, figure, or theory you mention must be referenced in the text by using a parenthetical reference/footnote. As a general rule, in an essay of this type where most of what you write will be other people’s ideas, probably almost every paragraph should have at least one reference in it. Exceptions are introductions/conclusions or transition paragraphs between sections. Also, any charts/graphs that use data must have the data source referenced. If you are in doubt about how/when to use documentation, please ask! Improper documentation constitutes plagiarism. My general advice if you are unsure if you should document something is to go ahead and put in the citation—simple cost/benefit analysis indicates that excessive documentation is less costly than inadequate documentation (aka plagiarism).

Finally, do not cheat or plagiarise on your essay in any way, shape or form. Do not turn in an essay identical to one that you have done for another class. Any formal complaints I receive or evidence I find of a student cheating, plagiarizing or attempting to free-ride off the work of another student will be treated as an academic integrity offense. This assignment is subject to the University’s policies on academic integrity, as specified here:

http://www.cfo.pitt.edu/policies/policy/02/02-03-02.html

2

E

C

ON 1110 Lecture Notes 5

ECON 1110 Intermedi

a

te Macroeconomics

James R. Maloy

Spring 2020

Lecture Notes for Topic 5: Keynesian Macroeconomics (I)

Readings: Froyen Ch. 5 (8th Ed. Ch. 6)

I. The Foundations of the Keynesian Revolution

The Great

D

epression of the 1930s and the enormous long-term persistency of high unemployment and low output could not

b

e explained by the classical model. In the classical framework, recessions were possible but were expected to be of relatively short duration and would correct themselves. A depression that lasted for years with no sign of recovery was unfathomable. According to the classical model, output was entirely determined by supply factors, and no change in aggregate demand, and no government policy, could be effectively used to alleviate the problems. Indeed, many of the policies undertaken at the time, such as tax and tariff increases, were exactly opposite of those we typically expect to see from government policy in a recession. For example, governments at the time faced falling tax revenues due to the high level of unemployment. To close the resulting budget deficit, governments raised taxes. Under the classical analysis, such tax increases should not affect the economy, but in reality caused great harm. Indeed, it is generally agreed that governmental mistakes greatly lengthened the Depression. However, we shall see in this course that there is considerable disagreement on precisely what was wrong about these policies and what (if anything) should have been done instead.

The fundamental problem was that the assumptions of the classical model were not realistic in describing the state of the US economy in that period. Two main approaches emerged. One, espoused by some such as Mises, centered on interferences with market mechanisms that prevented efficient, market-clearing outcomes. These arguments varied but typically centered on market imperfections and interventionist policies in the 1920s that created an economic bubble, which collapsed in the 1930s, which were in turn made worse by more interventionist policies. These ideas argued that markets work properly but the conditions for them to do so were impeded during this entire time period, such as by rampant expansionary monetary policy in the 1920s or Hoover’s policies on preventing wage cuts in the misguided belief that high wages cause prosperity.

An alternative approach centered on free markets being fundamentally inefficient. Some were fundamental criticisms of the system, such as Marxism or economic fascism (corporatism), the latter of which was proposed by Mussolini as a “third way” between the extremes of capitalism and communism, and was a major influence on Hoover and FDR’s market intervention policies.
Many of these types of communist and corporatist policies involve micro-level intervention, e.g. controlling production, wages, etc. (often via government-managed cartels) in individual firms or industries.

Keynes too looked at markets and viewed them as fundamentally inefficient, but developed a radical new way of looking at the problem. Rather than focusing on micro-management of individual industries, he proposed macro-management that focused on macro aggregates without consideration for what was actually being done at the micro level. This is simultaneously a strong point and weak point of his model. He correctly noted a fundamental flaw of micro-intervention that has led to extreme inefficiency and eventual collapse of all such attempts: lack of information. Central planning of micro-level production decisions requires an amount of information and co-ordination that simply does not exist. For example, if you order your automobile industry to produce a certain amount of cars, you must ensure that all industries that produce components such as steel or tires also produce the correct amount. One of the key strengths of private markets is that efficiency does not require much information: all that you need to know are your own costs and revenues. If there is a shortage of tires, the price will rise and supply will follow!

Heavily influenced by mercantilism
, he argued that aggregate demand, not aggregate supply, was the factor that determined output. He asserted that the Depression was the result of aggregate demand being too low; the economy had become stuck in a sub-optimal equilibrium with low demand causing low production, which in turn causes low levels of employment, which of course leads to low demand. At a micro level this behavior was optimal: if you own a firm and no one is buying your product, the optimal strategy is to lay off workers and cut back production. However, at a macro level this leads to poor economic outcomes, contradicting the classical view that micro optimality leads to macro optimality. He argued for a positive role for government to intervene in markets: to ensure that aggregate demand was sufficient to achieve full employment levels of production. Essentially, this is macro-planning: the job of the government is to ensure that total demand is at a sufficient level, but let the private sector decide which products are actually produced. This reduces the inefficiencies of micro-planning; Keynes recognised that the private sector, not the government policymaker, was best placed to make individual production decisions. However, this strength is also a weakness: his model therefore does not distinguish between $1tn on infrastructure such as roads and rail and $1tn on worthless gadgets at Walmart. Indeed, Keynes wrote that in the extreme, a government could create the necessary aggregate demand by burying a big pile of money and then letting the private sector decide how to dig it back out again. In reality, the long-run effects are very much dependent on what is bought-and how it is paid for, e.g. borrowing the money and then burying it, which leaves future generations with a bill for the $1tn that was buried. Keynes ignored these long-run effects; his model was a short-run model and only was concerned about the jobs created today by burying money, not the long-run effects of such a blatant misallocation of scarce resources. This is a key problem: Keynesians argue that these policies are socially optimal but do not properly account for long-run costs and benefits in their analysis.

Keynes’ model was fundamentally a disequilibrium model designed to explain how the economy
operates when it is not in the full-employment classical equilibrium. He did not really argue that the classical model was “wrong”–he argued that it was a special case of the economy operating the way we’d like it to behave, i.e. the ideal state, akin to the physics assumption of being in a vacuum. However, he argued that this special case was not realistic as the real world was not characterized by perfect information and fully flexible wages and prices. This is expressed in the title of his General Theory: how the economy operates in general, such as during the disequilibrium that classical economists largely ignored as a transitory, self-correcting event, or times when the economy is in an equilibrium, but it is a sub-optimal one. He and his followers produced a model that made aggregate demand the major determinant of output, and argued that aggregate demand was not stable and required government intervention to stabilise it.

It is interesting to note Keynes’ rationale for his new model. As one observer of economic thought put it: “The liberal capitalism of the modern age, which Smith had heralded, whose victory Ricardo had proclaimed, and which Marx sought to destroy, was transformed by Keynes and given a new life.”
During the apparent collapse of capitalism during the 1930’s and greater adherence to communist and fascist ideology (although there is some debate about what Keynes actually thought of fascist economics), Keynes decided that his task was to save capitalism–although some opponents of Keynes argue that his system actually destroys it
. Keynes was most closely associated with the old UK liberal party, which was mostly centrist, and was not a proponent of socialism/communism/fascism.

The model considered here is VER

Y

incomplete and is not remotely realistic. In the next topic, we will add the effects of money and interest rates. In later topics, we will also look at the role of aggregate supply. For now, we assume that there is no money or interest, prices are constant and the quantity of output demanded will be supplied at that price (e.g. a horizontal AS curve at that price level). In the Keynesian model demand determines output, not supply.

II. Conditions for Equilibrium in the Simple Keynesian Model

The simple Keynesian model hypothesised that equilibrium required aggregate supply (output, Y) to be equal to aggregate demand (E).

Y

=

E

Assuming that the economy is closed with no imports or exports, aggregate demand (E) consists of three components: consumption (C), investment (I), and government purchases (G). So in equilibrium we have:

Y = C

+

I + G

Recalling some of the simplification to national income accounts discussed in the first week of lectures, we know that we can define Y as both national income and national product. Defining Y as national product implies that:

Y ≡ C + Ir + G

where Ir is realised, or actual, investment. The difference between realised and planned investment (I) lies in the inventory component of investment. A firm will plan to have a certain quantity of goods in inventory at the end of the year, but unexpectedly high or low sales may leave them with more or less inventory than the management had planned.

So in equilibrium, it must be that:

C + I + G = Y ≡ C + Ir + G

Or that there are no unplanned changes in inventories:

I = Ir

Now defining Y as national income implies that:

Y ≡ C + S + T

since national income is divided among consumption, savings, and taxes.

Therefore, in equilibrium:

C + I + G = Y ≡ C + S + T

Simplifying gives another way to state equilibrium for the model:

I + G = S + T

So the three ways of stating equilibrium are:

Y = E = C + I + G (aggregate demand equals aggregate supply)

I + G = S + T (government spending and investment must be paid for by savings and taxes)

I = Ir (no unexpected changes in inventory)

Note that in this model it is aggregate demand (C + I + G) driving aggregate supply—the reverse of the Classical model and Say’s Law. Unlike the classical theory, aggregate demand in Keynes’ model is neither neutral nor stable. Keynes therefore had to throw out the entire classical model—the vertical AS curve which leads to AD shocks affecting only prices, as well as classical demand theory—the loanable funds framework and the quantity theory of money. Keynes’ attack centered on the role of interest rates in creating the self-balancing and stable classical aggregate demand curve as well as the stability of velocity in the quantity theory. Much of this will be covered in later topics—right now, we will start by analyzing the factors that drive consumption, investment and government spending as a starting place to understanding Keynesian AD theory.

III. The Components of Aggregate Demand

Again, assume a closed economy with no imports or exports.

Consumption:

Unlike classical loanable funds theory which argued that interest rates drove savings and consumption, Keynes argued that consumer expenditures was a stable function of disposable income, where disposable income (YD) is the difference between national income and taxes (Y – T).
Keynes proposed the following consumption function:

C = a + b YD a > 0, 0 < b < 1

Or:

C = a + b(Y – T)

The intercept a is autonomous consumption (the amount people would consume if they had no income), and b is the slope of the consumption function, or the marginal propensity to consume (MPC). It gives the percentage of a change in disposable income that will go toward consumption. The MPC can be defined as the derivative of the consumption function with respect to disposable income (dC/dYD).

The Saving Function

Recall that disposable income can be divided into consumption or savings:

YD = Y – T = C + S

Or

S = YD – C

Substituting for C yields:

S = YD – (a + b YD)

S = -a + (1 – b)YD

Why is the intercept of the savings function (-a)? Because remember that if disposable income is zero, consumption is a. So people are therefore dissaving a, and saving is negative at zero income. As disposable income increases, we eventually reach a point where people earn enough to stop borrowing and start saving.

The Keynesian consumption function was a direct result of Keynes’ view of the psychology of the consumer from the General Theory:

The fundamental psychological law, upon which we are entitled to depend with great confidence both a priori from our knowledge of human nature and from the detailed facts of experience, is that men are disposed, as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.

The Keynesian consumption function therefore does not show a proportional relationship between consumption and income because of the autonomous consumption (a) term. The ratio of consumption to income is given by the average propensity to consume (

APC

):

b
Y
a
Y
C
APC
D
D
+
=
=

APC is therefore greater than the MPC and decreases as disposable income increases, just as Keynes’ statement above implies. This Keynesian consumption function is also known as the absolute income hypothesis. Consumption reacts to actual current income. Any change in current disposable income will yield a change in consumption.

Empirical tests of the Keynesian function have yielded mixed results. An example of one estimated for the period 1929-41 for the United States is:

D
Y
75
0
5
26
C
.
.
+
=

Thus for short-run periods, the Keynesian theory appears to be a plausible description of reality.

The idea that APC declines (and corresponding APS, the average propensity to save, rises) as income increases worried early Keynesian economists, who feared that the economy might stagnate as national income grew. As it turns out, studies have shown that, even as national income has grown over the past century, the estimated values of APC for any given decade do not change by very much. It is obvious from these studies that in the long run the relationship between consumption and income is proportional, indicating that the original Keynesian theory is not a good explanation of this long run phenomenon. New models had to be devised to explain why APC is proportional to income in the long run, but not proportional in the short run..

Another empirical failing of the Keynesian model is that quarterly changes in consumption were not explained by changes in income; the idea of Keynes’ absolute income hypothesis that consumption changes when current income changes is not well supported by data. Two newer models were developed to correct these failings of the Keynesian theory, the life cycle hypothesis and the permanent income hypothesis (see appendix to these notes).

Investment

Keynes believed that changes in investment were a major source of the instability of aggregate demand and national income. Indeed, evidence has shown that investment is by far the most variable component of aggregate demand. Consumption generally changes only as a result of changes in income (hence Keynes argument that it was a stable function of income), but investment seems to change wildly over time. This observation becomes the key to the Keynesian explanation of business cycles.
Keynes listed two sources of changes in investment. The first, as in the classical model, is the interest rate (MC of investment). Keynes also expected a negative relationship between investment and the interest rate, although he argued that this relationship was weaker than in classical theory.
The simple Keynesian model of this topic does not include interest rates, so we’ll ignore this until a later topic when interest rates are introduced. The other source was business expectations (MR of investment). Keynes was heavily influenced here by his work in financial markets, which he viewed as fundamentally inefficient and prone to volatility induced by herd mentality. Buying shares of stocks and building a factory have the same decision-making environment: uncertainty regarding the future. Long term investments have to be decided on with very little knowledge of future events. An individual will not possibly be able to predict the future (psychics aside), so the decision-maker will make decisions based on past experiences or simply see what everyone else was doing and follow their lead. The latter was the primary factor in the instability of investment. Investment decisions would follow a herd mentality, and changes in information or changes in the behaviour of others would have drastic effects on investment decisions. Note that this is a fundamentally different view of human behavior than the classical theory. Rather than rational, optimal individuals, people are part of a collective herd which is prone to irrational, inefficient behavior. Keynes’ model therefore used early versions of social psychology. If the crowd believes that the future is awesome, expected returns on both financial and real assets will be inflated; both financial markets and business investment will thus increase drastically in a bubble. In a panic, the opposite occurs.
We have now established that factors other than current income (Y) influence investment—it is driven by expectations of future income. Therefore, we can take investment as exogenous for now in our calculation of national income. The investment function for now will just be I, and it is independent of the current level of income. However, it is fundamentally volatile and can suddenly change. We will expand our study of investment in the next topic.

Government Spending and Taxes

Like investment, government spending is not considered to be directly influenced by the level of income, but rather by the decision-making of politicians, who may or may not take economic factors in their budget decisions. For now, we will leave government spending as G. To simplify things, we will assume that the government just sets taxes as a fixed lump-sum amount (T), and taxes do not vary with income. Therefore, the only component of national income which is itself dependent on national income (Y) in the simple Keynesian model is consumption.
IV. Determining Equilibrium Income (or Output)
Recall that equilibrium is where aggregate demand and aggregate supply are equal:

Y = C + I + G

Y is the endogenous variable we are trying to calculate. I and G, as well as T, are determined exogenously, as well as the autonomous part of consumption, a. The other component of consumption is income-induced expenditure which is dependent on the level of income. Recalling that we defined consumption as:

C = a + b(Y – T)
substituting yields:

Y = a + bY – bT + I + G

Solving for equilibrium Y:

Y – bY = a – bT + I + G

Y(1 – b) = a – bT + I + G

Y = [1/(1 – b)] [(a – bT + I + G)]
We therefore have solved for equilibrium output in this economy. The first term, 1/(1-b), is called the autonomous expenditures multiplier. Note that b is the MPC, and that 1-b is the marginal propensity to save (MPS). Multipliers will be discussed in more detail below. The second term is called autonomous expenditures; that is, the expenditures that do not depend on the level of income. We have already discussed a, I, and G. The other component, bT, shows the (negative) effect of taxes on income.

Changes in Equilibrium Income: The Multiplier

A feature of the Keynesian system is that changes in autonomous components of national income generate even larger changes in equilibrium income. Note that this is very different from the classical model—rather than self-correction, demand is wildly volatile. This is known as the multiplier process. Basically, a change in one component of national income yields an initial increase in income. The person who receives this income saves a portion (MPS) and spends the rest (MPC). This portion that is spent becomes the income of another, and the process continues.
Multipliers in the Keynesian model are calculated by taking partial derivatives of the equation for equilibrium income:

Y = [1/(1 – b)] [(a – bT + I + G)]
For example, the investment multiplier is ∂Y/∂I = 1/(1 – b), which is 1/MPS. If MPC (b) is 0.8, then MPS is 0.2. Therefore, the value of the multiplier is 1/(0.2) = 5. A $1 increase in investment increases income by $5. Since Y = C + I + G, and Y has increased by $5, the right-hand side of the equation must also increase by $5 to maintain equilibrium. We already know that $1 of this $5 increase in income is because of the change in investment. How do we account for the other $4? The other $4 represents an increase in consumption—remember that if b, the MPC, is 0.8, it means that 80% of any change in income will go towards consumption. Therefore, when income increased by $5, consumption increased by $4. The other 20% of the increased income $1) was saved—and channelled to investment, hence the original $1 increase in investment! Now our equation is in balance and equilibrium is attained. This result must be true because of the one of the other conditions for equilibrium:

I + G = S + T

Since nothing has happened to G or T, the increase in investment must be matched by an increase in savings. Therefore, this $1 increase in investment has increased income by $5, consumption by $4, and savings by $1.
Similar multipliers can be found for other components of national income. The government spending multiplier, ∂Y/∂G, is also 1/(1 – b). The tax multiplier, ∂Y/∂T, is -b/(1 – b). Note that the simplicity of this model makes the multipliers very similar–this is not realistic. Also, this model greatly overstates the magnitude of the multiplier. The multipliers in the more complete IS/LM model in the next topic will be smaller.
Fiscal Stabilisation Policy

We have established that fiscal policy—changes in taxes and government spending—can indeed influence aggregate demand and output in the Keynesian economy. Keynes argued that the government not only could influence output, but that it would be necessary to use policy to smooth out the fluctuations in aggregate demand that are caused by volatile investment. If the output is too high or too low, the government can use policy to bring the economy back to where it should be.

Appendix: Life Cycle and Permanent Income Hypotheses of Consumption
I. The Life Cycle Hypothesis of Consumption

The idea behind that life cycle theory is that consumption does not just depend on current income as it did in the Keynesian theory, but rather on expected earnings over one’s entire lifetime. People do not want to live in a mansion one year and a cardboard box the next; rather the person does what is commonly known as consumption smoothing and tries to maintain a relatively constant consumption level throughout his lifetime. The person therefore saves during periods of high income and dis-saves or borrows during periods of low income. A simple graph can capture the essence of the life cycle hypothesis. Assume the person lives for T years. When the person is young, and still a student, income is very low. Although it may not feel like it at times, the average student lives above his means; rather than starving and having no clothes during their education, you buy your necessities and spend far in excess of your income. This is done by dis-saving. If you had some wealth given to you earlier in life, you spend it; or you take out a loan, or you resort to begging from your parents and other family members, but you are willing to do so to maintain an adequately high level of consumption. After graduation, you enter the workforce, eventually make enough to consume less than your income, and pay back your loans and save for retirement. After retirement, your income falls and you now dis-save again, by spending the wealth you accumulated while working. There is some disagreement on whether consumption will stay constant or gradually increase over the lifetime, but either way it is obvious that consumption is being smoothed.
The life cycle hypothesis can also be expressed more completely by using some simple mathematics. Assume again that the person lives for T years, and for simplicity assume that he wants to consume the same amount each period. Therefore, during each period t, he consumes 1/T of his expected lifetime resources. Further assume that the person wants to leave no bequest for his heirs; he wants to spend the total amount of his current wealth and future earnings. Also assume that there is no interest paid on assets; this greatly simplifies the equations.

Therefore, consumption in each period t,
[
]
(
)
T
1
t
,
Î
, is given by:

(
)
[
]
t
e
1
1
t
t
A
Y
1
N
Y
T
1
C
+
–
+
=

where
1
t
Y
is the individuals labour income in the current period, N is the remaining number of years before retirement (i.e. if the person plans to work for 10 more years then N = 10),
e
1
Y
is the average annual labour income expected over the future (N – 1) years of employment, and A is the value of presently held assets. Basically, the first term in brackets is how much he is currently earning, the second term is how much in total he plans to earn in the future, and the third term is the amount of assets saved, i.e. wealth, from previous periods.

Consumption depends not just on current income, as it did in the Keynesian model, but also on expected future income and current wealth. The life cycle hypothesis, however, argues that consumption is generally unresponsive to a change in current income that does not affect future income. For example, the effect of a temporary change in income can be calculated by taking the derivative of the consumption function above with respect to the change in current income:

T
1
Y
C
1
t
t
=
¶
¶

If the increase in current income is expected to be permanent, the total change in current consumption is significantly higher:

T
N
T
1
N
T
1
Y
C
Y
C
e
1
t
1
t
t
=
–
+
=
¶
¶
+
¶
¶

Therefore, unless the individual is extremely close to retirement (N is small), the effect of a permanent change in income on consumption today is much greater. Therefore, we can conclude that current consumption is not very responsive to temporary changes in income but is much more responsive to permanent changes in income. This should make sense. If you are 30 years old and wish to smooth consumption, you will not go out and blow a one-time $100,000 windfall all today; you will want to save it and divide it up over future periods. Current consumption will not change by very much. If you expect to get the same $100,000 bonus for the rest of your working life, then you will spend a much greater proportion of today’s $100,000 right away; after all, you will get another similar amount every year so there is no need to save it to smooth consumption. Empirical studies have given some support to these ideas, indicating that a person spends a much larger portion of a permanent change in income right away than of a one-time increase in wealth. The textbook discusses some of these studies.

Note that relaxing our initial assumptions will make the equation given above more difficult. Therefore, it is useful to express the general form of the above consumption function as:

t
3
e
1
2
1
t
1
t
A
b
Y
b
Y
b
C
+
+
=

Again, consumption depends not just on current income, but on future income as well as the level of wealth. The strongest change on current consumption comes from a change in expected future labour income.

It should now be evident that this model provides an explanation why empirical studies have found little relationship between quarterly changes in income and consumption. If the change in income is considered temporary, then it should not have much impact on consumption.
II. The Permanent Income Hypothesis of Consumption

The permanent income hypothesis is an alternative theory of consumption (although in many ways it is very similar to the life-cycle hypothesis) developed by Milton Friedman. Like the life-cycle hypothesis, Friedman proposes that consumption depends on the long-run average of income, but the permanent income hypothesis offers a different explanation. Friedman postulates that consumption is some proportion (κ) of permanent income (Yp):

C = κ Yp
Permanent income is defined as expected average long-run income from labour and asset holdings. However, income in any given period is not necessarily going to be at the long-run average; there is a random component called transitory income (Yt) that will be positive in a “good” year and negative in a “bad” year. Actual income is given by:

Y = Yp + Yt
Basically, transitory income is the deviation of current income from the expected long-run average. The key to the permanent income hypothesis is that consumption depends only on permanent income, not transitory income, as shown in the above consumption function.

Friedman theorised that people used backwards looking (or adaptive) expectations to determine permanent income, and that this expectation was revised after each period:

(
)
,
p
1
t
t
p
1
t
p
t
Y
Y
j
Y
Y
–
–
–
+
=

0 < j < 1 Basically, people expect some proportion j of the difference between actual income and last period's expectation of permanent income to represent a change in permanent income. For example, if this deviation in income this year (the deviation between actual income and expected permanent income) is $20,000 and j = 0.2, then the consumer believes that 20% of this change in income is a change in permanent income and will increase his expectation of permanent income by $4,000. The remaining 80% is considered transitory income. Since consumption only depends on permanent income, consumption will increase by ( ) ( ) 000 4 Y p , k k = D , not by κ(20,000). Consumption is therefore smoothed, as it was in the life-cycle hypothesis. Like the life-cycle hypothesis, the permanent income hypothesis shows that in the long-run, consumption is some proportion (κ) of actual income (since in the long run, expectations are correct and expected permanent income is equal to actual income). In the short run, consumption is not proportional to income, since during periods when transitory income is high, people will save more and thus APC will be lower during periods of high income. The opposite will happen during periods of low income. This result is consistent with the empirical studies that first shed doubt on the viability of the original Keynesian consumption function for long-run analysis. The model also explains why there is little connection between actual quarterly changes in income and consumption levels. Transitory changes in actual income will not affect consumption, in contrast to Keynes' theory. � Note that, despite the completely historically inaccurate and frankly baffling urban myth that Hoover was laissez-faire and believed in the classical model, Hoover was actually a staunch interventionist and many of his policies and FDR's policies were similar.) � Recall that mercantilism argued for government policy to direct a nation's consumption towards a desirable macro outcome. Keynes' monetary theory also re-introduced a link between money and wealth, which will be covered in Topic 6. � A key issue, which was (and still is) largely ignored as US economists quickly adopted Keynes' ideas, was that Keynes' model was developed to explain the UK economy of the 1920s-30s. The UK situation was in many respects very different from the US and other nations. Some have argued that using Keynes' ideas as a general theory of all economies at all time periods is fundamentally flawed. Note that this is a different argument than the more common one that Keynes' model is simply wrong altogether. � Spiegel, H. W. The Growth of Economic Thought, 3rd ed. (Durham: Duke University Press, 1999), 607. � This logical absurdity of saving something by destroying it is best expressed by the quote from a US officer regarding the destruction, with many civilian casualties, of the city of Ben Tre during the Vietnam war: "It became necessary to destroy the town to save it [from the communist Viet Cong]". � Note that this argument indicates that the counter-balancing we saw in the classical model that kept AD stable no longer occurs! � Again, this reduces or eliminates the counter-balancing we saw in the classical demand theory--AD is therefore not fundamentally stable in the Keynesian model! 1 _1577002679.unknown _1577002681.unknown _1577002683.unknown _1577002685.unknown _1577002686.unknown _1577002684.unknown _1577002682.unknown _1577002680.unknown _1577002677.unknown _1577002678.unknown _1577002676.unknown

ECON

1

1

10

: Intermediate Macroeconomics

Lecture Notes for Topic

4

: Economic Growth

James R. Maloy, Department of Economics, Spring

2

020

Readings: Froyen, Chapter 20 (

8

th Ed. Ch.

5

) has a basic form of

the Solow model. These lecture notes present a simplified version

of a very detailed presentation of the Solow model from David

Romer’s Advanced Macroeconomics postgraduate textbook.

1 Introduction

The purpose of this section is to understand the determinants of long-run

economic growth. Economic growth is the change in output (GDP) over

time. Long-run growth theory is concerned with what is typically called

trend or potential GDP, not short-run business cycles which are simply

fluctuations around this trend. Long-run growth is due to changes in supply

factors which affect the production abilities of societies (recall the vertical

long-run AS from the classical model–most growth theories are founded in

classical theory). The focus in long-run growth is usually per capita; it is

true that more population will allow more total GDP, but economic growth

theorists are typically more interested in the factors that affect output per

capita, which is known as labour productivity.

There are many important questions in growth theory, which typically

centre around two key ways of looking at growth: inter-temporally or cross-

sectionally. The first is to look at a particular society over a period of

time–why does a particular nation have more per capita output today than

in, say, 18

7

2? The second approach asks why GDP (and GDP growth rates)

1

differ amongst nations at the same time–why is the US relatively affluent

while India is relatively poor? And furthermore, will India be able to catch

up in the future? The basic way to start answering these types of questions is

determine the factors which affect economic growth. Many of the much older

theories of economic growth focused on variables such as savings and capital

formation as the driving factors. However, the Solow Model, developed

in the 1

9

50s and the original model behind much modern growth theory,

actually argues that such factors are not the most important things.

2 Assumptions and Variables in the Solow Model

Let us begin by identifying some variables:

Y = output

K = capital stock

N = labor

A = effectiveness of labour. This is basically a variable that encom-

passes all factors that determine how effective labor is, such as knowledge,

technology, etc. Often this is just simplified to technology only.

AN = effective unit of labor

y = Y
AN

: This is defined as output per unit of effective labor.

k =

K

AN

: This is a similar measure of capital per unit of effective labor.

Note the difference between Y and y, and K and k. They are distinct

items; do not get them confused. Now that we have some basic ideas, let us

define an aggregate production function:

Y = F(K,AN) (1)

Output is a function of the capital stock and the amount of effective

2

labour. More specifically, we can define a Cobb-Douglas production function

as:

Y = Kα(AN)1−α (2)

Note that this production function has constant returns to scale (the

exponents sum to 1). This greatly simplifies the model. However, the model

relies not on the aggregate production function Y , but on the intensive form

production function, y. Recalling our definition of y from above, dividing

the above production function by AN yields:

y =
Y

AN
=

Kα(AN)1−α

AN
=

Kα

ANα
= (

K

AN
)α = kα (

3

)

Therefore, the intensive form production function is:

y = kα (4)

This production function gives output per unit of effective labour. Graph-

ically, it looks like the familiar production function from topic 2, only note

that the axes are different; the vertical axis is y and the horizontal axis is k.

To make this a model of growth, we must introduce time into the model.

Specifically, all of our variables in the original production function (for total

output Y ) are functions of time (t):

Y = [K(t)]α[A(t)N(t)]1−α (5)

Therefore, output at time t depends on that period’s capital stock, labor

force, and the level of technology and other factors that determine labour

effectiveness. In order to finish building the model, Solow makes some as-

sumptions about the growth rates of these items. The growth rate is calcu-

lated by taking a time derivative, i.e. a derivative of each item with respect

3

to time. A time derivative is symbolised by placing a dot over the variable.

Much of this math involved in this requires some knowledge of differential

equations, which if you have not taken Calc II you will not know how to do,

so don’t get bogged down in worrying about where these equations come

from as it really isn’t necessary to understand the model.

1. Assumption 1: The labor force N grows at a constant, exogenously

given rate n.

2. Assumption 2: The level of effectiveness of labor A grows at a constant,

exogenously given rate g.

3. Assumption 3: Investment in each period is some fraction of output.

We can assume that investment is equal to the fraction of output that

is saved, e.g. all savings are channelled to investment (like in the

classical loanable funds theory with a balanced government budget).

This can be expressed as I(t) = sY (t). Therefore, the amount invested

each period is determined by the savings rate s, where 0 ≤ s ≤ 1. The

savings rate s is also assumed to be constant and given exogenously.

4. Assumption 4: Finally, we must indicate how the (total) capital stock

K changes over time, i.e. the value of K̇. It is assumed that the rate

of change of the capital stock is a function of the level of investment

(from assumption three) and the depreciation of the existing capital

stock. This can be given by K̇(t) = sY (t) − δK(t)

Therefore, the rate of change of the capital stock over time is the

level of investment minus the amount of depreciation, δ. Note that

0 ≤ δ ≤ 1. It is also taken exogenously.

4

3 The Solow Equation and the Solow Diagram

We are now ready to formulate the “Solow equation”. The key to the Solow

model lies with the time derivative of k (capital per unit of effective labor).

Specifically, this is given by

k̇(t) =
˙

(
K(t)

A(t)N(t)
) (

6

)

This is solved by differentiating and plugging in values for the variables.

The mechanics are given by Romer but rather than working it out, which

makes no one happy except for the one person in this course who actually

enjoys the chain rule, I will save us a headache and simply assert that this

will yield the key Solow equation. Using the Cobb-Douglas intensive form

production function from equation 4 above, this is given by:

k̇(t) = skα − (n + g + δ)k (7)

This equation has two components. The first component indicates that

savings increases the rate of change of capital per unit of effective labor over

time. Recalling assumption three above, this is because savings is channelled

into investment in new capital goods. The second component (which is

subtracted) indicates that the growth of labor n, labour effectiveness g, and

depreciation δ (see assumptions 1, 2 and 4 respectively) all decrease the rate

of change of capital per unit of effective labour. Showing each of these parts

of the equation separately on a graph (the Solow diagram) will help this to

make sense.

The Solow diagram shows capital per unit of effective labor k on the

horizontal axis and investment per unit of effective labor on the vertical

axis (which is a fraction of output per unit of effective labor y, as noted

5

above in assumption 3). Recalling our production function, we note that

the first term in the Solow equation is just a fraction s of the production

function. Therefore, it is sloped just like the production function. The

second component is a linear function, since we assumed that n, g and δ

are constant. Note that the two lines intersect. We shall call the value of k

where the curves intersect k∗.

It is now necessary to explain these curves in more detail. The curved

line, skα, is the actual level of investment. Since we assumed that all savings

are chanelled into investment, the fraction s of output that is saved must

be the level of investment by definition. The straight line, given by (n +

g + δ)k is what is called break-even investment. It is the level of investment

needed simply to maintain k at its current level. What does that mean?

Well, suppose initially that there are 5 units of capital K and 5 units of

effective labour AN. Therefore, k is equal to 1. Now suppose that you have

population growth n. Specifically, suppose that now AN = 6 due to this

increase in N. In order to maintain k = 1, you must invest in one more

unit of K to make K also equal to 6. This is why it is called break-even

investment. It is the amount of investment that is needed to maintain k at

its current level. Looking back at the Solow diagram, note that at values

of k below k∗, actual investment exceeds break even investment. Therefore,

the amount of capital per unit of effective labour is growing, e.g. k is getting

bigger. Looking back at the Solow equation, note that the first term is bigger

than the second term so the rate of change of k is positive. If k is greater

than k∗, then actual investment is below break even investment, and k is

getting smaller; from the Solow equation, the second term is larger then the

first term and the rate of change of k is negative. The model thus implies

that k converges to k∗, and k will be constant at that point. This is what

6

is known as the steady state or balanced growth path. The actual value of

k∗ can be calculated by setting the Solow equation equal to zero (since k

is constant at the steady state so its rate of change is zero) and solving for

k. Note that just because the economy reaches a steady state in which k

becomes constant does not mean the economy as a whole is not growing;

it just means that, in the steady state, all of the variables are growing at

a constant rate. The implication is that regardless of its initial starting

position, the economy will move to a long-run steady state, with constant

growth. We will now turn to a description of the steady state, and also

discuss how changes in the values of savings and other variables will cause

the economy to converge to a new steady

state.

7

It was mentioned above that all variables grow at a constant rate in the

steady state. Some simple calculations can show that these growth rates

are:

Variable Growth Rate

N n

A g

K n + g

AN n + g

Y n + g

K/N g

Y/N g

k 0

y 0

The most interesting conclusion is that output Y is growing at a constant

rate n + g. This indicates that in the steady state, the growth rate of

output depends on the growth rate of population and labour effectiveness.

Furthermore, the growth rate of output per worker Y/N depends only on

the growth rate of labour effectiveness A. This may come as a surprise; it

is often thought that the level of savings determines the growth rate of the

economy. The Solow model indicates that savings do not affect the growth

rate of output in the steady state. What we will see is that saving levels do

effect the level of output, but not the rate of growth of output in the steady

state.

Changes in savings will only affect growth rates in the short run transi-

tion period. If output was growing at 5% before the increase in savings rates,

it will be growing at 5% once the new steady state is reached. This does not

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mean that savings does not affect the economy—quite the contrary. During

the transition period, variables will be affected. This temporary change has

permanent effects on the level of variables. To think of an example, suppose

that every year you get a 10% raise on the previous year’s pay, which we say

is $100 in 2015. Now suppose that in 2016 you get a special bonus that dou-

bles your income to $200. The next year, you go back to getting 10% raises,

but this is now 10% of a much bigger value than it would be otherwise—it

is 10% of $200 instead of $

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0! Therefore, although after the transition

period the growth rate is back to 5%, you are at a higher level of income

thanks to the bonus. A similar type of thing is occurring with savings in the

Solow model. The Solow model indicates that, once the new steady state is

achieved, output will be growing at the same rate as before, say 5%, but the

change in savings will affect the level of output, and an increase in savings

means that we are now taking 5% of a larger level of output than we would

have had if savings had not increased. A few simple graphs can capture the

essence of a change in the savings rate. Suppose initially the economy is in

the steady state, and at time t0 there is a permanent increase in the savings

rate. This can be shown as:

We know from the Solow diagram that capital per unit of effective labour,

k, increases to the new steady state. Once the new k∗ is attained, the rate

of change of k is again zero.

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The effects of the increase in savings on the natural logarithm of Y/N

can now be seen. Output per unit of labour climbs until the new steady

state is reached, when it becomes parallel to the original growth path, once

again growing at a rate of g.

4 Conclusions of the Solow Model

We have spent considerable time deriving and working with the Solow model,

but have yet to draw any fundamental conclusions. By going a bit deeper

than we have here, it can be shown that the Solow model indicates two

main sources of differences in output per worker Y/N over time (or across

nations). Differences in capital per worker K/N and differences in the ef-

fectiveness of labour A will affect the value of output per worker Y/N.

Furthermore, the model indicates that only growth in the effectiveness of

labour can cause a permanent change in growth rates. Before Solow, many

theorists had suggested that differences in capital stocks per worker were the

reason why some nations are rich and others poor; the Solow model indicates

that different capital stocks alone can not account for differences between

nations, or for that matter differences in a particular nation over time. The

key seems to rest with differences in the effectiveness of labour. However,

the Solow model assumes that the value of A and the growth rate of A are

exogenous and constant; therefore, it takes as given the very thing which

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causes economic growth! Furthermore, Solow just treats A as a catch-all

phrase that incorporates everything except capital. A can include knowl-

edge, technology, human capital, property rights, attitudes towards work, or

anything that can determine labour effectiveness; often it is just simplified

to technology (Froyen does this) although Solow was not that specific. This

is a key weakness in the model; the model indicates that growth depends

on A but does not give any indication of what A is or how it is determined,

which has led to later theories that expand on this concept.

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