Final

Exam, Introductory Macroeconomics (Econ 2)

Winter 2019

18 March 2019

Version A

DO NOT OPEN THIS TEST UNTIL YOU ARE INSTRUCTED TO DO SO.

This exam has 24 questions (some with multiple parts). There are 6 sheets of paper (including

this cover sheet). The last sheet is scrap paper. You may tear off the scrap paper but must leave

the rest of the exam stapled.

You should write your answers in the space provided for each question. No credit will be given

for answers written anywhere else. On every question you must show your work and circle

your final answer.

Before exam time starts, you must fill in the information below in the space provided:

1) Your name, AS RECORDED WITH THE REGISTRAR (do not write your nickname)
2) your numerical student ID
3) Circle your officially registered section time

Failure to do any of the above will result in a one-point deduction from your exam score

You will NOT be given extra time to do this after exam time is over. Do it now.

Please write:

Name (as given to Registrar): __________________________________________

Numerical ID: __________________________________________

Circle your Section Time:

Naresh Kumar Wed 2:40-3:45 Fri 10:40-11:4

5

Anirban Sanyal Wed 10:40-11:45 Wed 12:00-1:05

Ted Liu Mon 12:00-1:05 Mon 1:20-2:25

Harrison Shieh Mon 8:00-9:05 Mon 9:20-10:25

Guanghong “Michael” Xu Fri 12:00-1:05 Fri 1:20-2:25

YOU MUST USE A PEN

A. Gains from Trade War
The US has 200 million workers (that’s 200,000,000). It can use these workers to produce either

Aluminum (A) or Engines (E). It takes 10 workers to produce 1 ton of aluminum and 40 workers to

produce 1 engine.

1. [2 p] Write down the PPF for the US.

10? + 40? = 200,000,000

2. [3 p] What is the cost of an engine? What is the opportunity cost? You must show your work and

specify the units of each cost for full credit.

Cost: 40 workers

Opportunity cost: ? = 20,000,000 − 4? => 4 tons of aluminum

Suppose the US starts trading with several countries at a mutually acceptable trade price of 10 tons of

aluminum for 1 engine.

3. [2 p] Will the US import engines or aluminum? Explain in 1 or 2 sentences.

Since the trade price of an engine exceeds its opportunity cost, the U.S. will want to export engines. That

means it must be importing aluminum.

4. [4 p] Write down the PPF of the US after trade.

Before trade: ? = 5,000,000 −
1

4
?

After trade: ? = 5,000,000 −
1

10
?

5. [2 p] Suppose the price of an engine is $8000.

a. What is the price of aluminum in the U.S. before trade?

??

??
= [???. ????] = 4 => ?? =

??

4
= $2000

b. What is the price after trade?

??

??
= [????? ?????] = 10 => ?? =

??

10
= $800

6. [6 p] Calculate nominal GDP and the nominal wage after trade. (Hint: Is the U.S. specializing in

producing one of the goods after trade?)

After trade the U.S. specializes in engines and imports aluminum. It will produce 5,000,000 engines (see

PPF for E above).

[???. ???] = $8000 × 5,000,000 + $2000 × 0 = $40,000,000,000

[???. ????] =
[???. ???]

[# ?? ???????]
=

$40,000,000,000

200,000,000
= $

200

The government puts a tariff on aluminum imports, causing the relative trade price of aluminum to rise

to 1/5 engines for 1 ton of aluminum. The (dollar) price of engines remains $8000.

7. [1 p] What is the (dollar) price of aluminum after the tariff?

??

??
= [??? ????? ?????] = 5 => ?? =

??

5
= $1600

8. [2 p] What is the nominal wage after the tariff?

The nominal wage is unchanged from #6 because the U.S. will still specialize in producing engines, and

the dollar price of engines is unchanged.

9. [7 p] What is the real wage after the tariff? Assume the basket of goods for a typical consumer is

1 engine and 3 ton of aluminum. Take the period after trade as the base for the consumer price

index (meaning you should use the prices that you solved for in Question 5b as the base year

prices).

[???? ?? ??????, ?????? ??????] = $8000 × 1 + $800 × 3 = $10,400

[???? ?? ??????, ????? ??????] = $8000 × 1 + $1600 × 3 = $12,800

?????? =
[???? ?????]

[???? ??????]
× 100 = 123.08

[???? ????] =
[???. ????]

??????
× 100 = $162.50

B. Political Business Cycle
The nation of Dystopia has a long-run aggregate supply curve of �⃑� ? = 2. The velocity of money has

growth rate ? = 0.

Initially the country has a rate of money growth equal to �⃑⃑� = 3.

1. [2 p] Write down the aggregate demand curve.

�⃑� + �⃑� ? = �⃑⃑� + ? => �⃑� ? = 3 − �⃑�

2. [4 p] Solve for long-run equilibrium.

�⃑� ? = �⃑� ?

3 − �⃑� = 2

1 = �⃑� ∗

�⃑� ∗ = �⃑� ? = 2

3. [2 p] Write down the short-run aggregate supply curve.

�⃑� ? = ( �⃑� − ?[ �⃑� ]) + �⃑� ? = ( �⃑� − 1) + 2

The president of Dystopia is up for re-election this year. The president’s political consultants believe that

he will win 45 + �⃑� percent of the vote, where �⃑� is the growth rate of GDP. He needs to win at least

50% to be re-elected.

4. [6 p] The president pressures the central bank to permanently raise the rate of money growth to

�⃑⃑� = 10. Assuming the election happens immediately after the change (before expectations

adjust), would the president be re-elected? Justify your answer by solving for the president’s

vote share (you must show all steps for full credit).

New AD curve: �⃑� 2
? = 10 − �⃑�

New Short-run Equilibrium:

10 − �⃑� = ( �⃑� − 1) + 2

9 = 2�⃑�

4.5 = �⃑� ∗

�⃑� ∗ = 10 − �⃑� ∗ = 5.5

[?????????′? ???? ?ℎ???] = 45 + �⃑� ∗ = 50.5

Yes, he will win re-election.

5. [6 p] After the election firms adjust their expectations. What is the rate of inflation in the ne

w

long-run equilibrium? What is the new short-run aggregate supply curve?

�⃑� 2
? = �⃑� ?

10 − �⃑� = 2

8 = �⃑� ∗

�⃑� ∗ = �⃑� ? = 2

�⃑� 2
? = ( �⃑� − ?[ �⃑� ]) + �⃑� ? = ( �⃑� − 8) + 2

6. [5 p] Most advanced democracies (e.g. the US, Canada, Britain, the European Union, Japan) have

made their central banks almost completely independent of the political branches of

government. Given your answers to Questions 4 and 5, why might these countries consider

central bank independence a good policy? Explain your answer in 1 or 2 sentences.

Since the central bank can engineer booms and recessions, politicians will want the central bank to

create good economic conditions just before elections to sway the vote. The only way to prevent this is

to make the central bank independent of elected politicians.

C. Solow Below Trend

In the figure above, each dot shows the GDP growth versus initial GDP for a single country. The trend

line shows the average relationship among the black dots.

1. [4 p] According to the Solow Model, what is likely to be true about the countries represented as

black dots? Why might we expect the trend line to be negative? Explain your answer in 2 or 3

sentences. [Hint: think about the parameters of these economies and what that implies about

their GDP in the long run.]

The black dots are likely to be countries that are converging to the same steady state. In that case we

would expect the trend to be negative because the countries with the lowest 1950 GDP would have to

grow at a higher rate to catch up to the countries with higher 1950 GDP.

2. [4 p] Country A (see figure) does not fit the trend line. How would the Solow Model explain why

Country A falls below the trend? Explain in 1 or 2 sentences.

Country A likely has a less favorable set of parameters (a lower investment rate, a lower productivity, a

higher depreciation rate) and is thus converging to a lower steady state than the other countries.

G
D

P
G

ro
w

th
,

1
9

5
0

t
o

2
0

1
8

GDP in 1950

A
Trend Line

D. What does it all mean!?

1. [3 p] Each of the 3 letters shown in the diagram above represents a quantity from those named

in the table below. Write the name for the quantity represented by each letter (several will not

be used).

a. Number of employed

b. Number of unemployed

c. Labor force

Number of unemployed
Number of non-
institutionalized adults

Number of employed Labor force

Number of underemployed

2. [2 p] Write down a formula for the unemployment rate using the letters from the figure above

(for example, a + b – c).

Either

?

?
× 100% or

?

?+?
× 100% would give the unemployment rate in percentage points. Since we

didn’t specify it had to be in percentage points (as opposed to a proportion), you could leave off the

100% and still get full credit.

3. [2 p] Explain in 1 or 2 sentences why the demand curve for labor has a negative slope.

Either answer below is acceptable:

Minimum
Wage

w

L
a

b

c

Market for Labor

 Since there is a diminishing marginal product of labor, firms get less benefit from each

additional worker. Their willingness-to-pay for each additional worker is thus decreasing.

 Firms differ in their willingness-to-pay for hiring an additional worker. As the market wage

increases, fewer and fewer workers find it profitable to hire an additional worker, reducing the

demand for workers.

E. Gains from Trade Peace

The figure above shows the market for rice in India. India is about to allow trade in the market for rice at

the world price ?? shown above.

1. [4 p] Who loses from opening to trade in the market for rice? How much surplus do they lose?

(Show your work!)

Since ?? > ?∗, consumers lose from trade. We calculate their loss in surplus:

????????ℎ? =
1

2
× 200 × (80 − 30) = $5000

??????? =
1

2
× 150 × (80 − 50) = $2250

?? ???? = $2750

P

Q
D

S
80

5

30

200

?? = 50

150 300

Market for Rice in India

Alternative Answer: Some students may have calculated the loss in consumer surplus as the trapezoid

bounded by the axis, the world price, the equilibrium price, and the demand curve. In that case they’d

get ?? ???? =
1

2
(200 + 150) × 20 = $3500. We will also accept this answer for full credit as long as

the calculations make it clear this is how you got your answer.1

2. [4 p] Suppose the Indian government wants to compensate the losers by transferring surplus

(through a lump sum tax) from the winners to the losers. If the tax extracts just enough surplus

to leave the losers no worse off from trade, how much of the gains from trade would be left to

the winners?

Gains from trade before tax:

????????ℎ? =
1

2
× 200 × (30 − 5) = $2500

??????? =
1

2
× 300 × (50 − 5) = $6750

?? ?????? = $4250

The tax would transfer $2750 of surplus from producers to consumers. Producers would be left with

$1500 of the gains from trade.

Alternative Answers: If you used the trapezoid method above you’d have to use $3500 as the surplus

needing to be transferred. IF you calculated PS gained as $4250 as above, you’d get that producers are

left with $750 after the transfer. If you calculated PS gained again using trapezoids you’d get

?? ?????? =
1

2
(300 + 200) × 20 = $5000, in which case you’d get the same answer for how much of

the gains are left to producers ($1500). One final approach is to calculate the size of the deadweight loss

triangle bounded between the two curves and the world price, which represents the overall gains to

society from trade. That is
1

2
× (300 − 150) × (50 − 30) = $1500, again the same answer.

3. Bonus [2 p] Suppose the market for rice is the only market in India that is open to trade,

meaning it has no other imports or exports. Net transfers are zero. If India has a capital account

of ??? = −5000, what must be India’s net factor payments?

We know from the balance of payments that

[??? ???????] + [??? ?????? ????????] + [??? ?????????] = −[????????? ???????]

Net exports is just the value of India’s exports in rice (300 − 150) × $50 = $7500. Net transfers is 0.

Then

[??? ?????? ????????] = −(−5000) − 7500 = −2500

1 Thanks to Chenhan Xu for suggesting this alternative calculation.

F. Half-Baked
1. [3 p] The manager of the local bakery wants to motivate her 15 workers to bake more bread.

She is considering two schemes for paying bonuses. One would pay each baker an extra 50 cents

for each loaf he bakes. The other would pay all 15 bakers an extra 50 cents for every loaf baked

by any one of them. According to the model of individual incentives, which scheme would yield

more bread? Explain your answer in 1 or 2 sentences.

Since the wording of this question is a little unclear, we’ll accept two answers for full credit.

If it’s clear from your answer that you interpreted “pay all 15 bakers an extra 50 cents” to mean the 50

cents is split across all workers (which is how I’d intended it to be read), the correct response would be:

The scheme that pays each worker only for the bread he or she bakes would yield

more bread because the marginal benefit to individual effort is the full 50 cents,

whereas the other scheme splits the benefit across 15 workers.

If it’s clear from your answer that you interpreted “pay all 15 bakers an extra 50 cents” to mean each

worker would be paid 50 cents for each additional loaf of bread baked by anyone (meaning the manager

hands out a total of $7.50 every time someone bakes a loaf), the correct response would be:

Since under both schemes each worker receives an extra 50 cents for each loaf he or

she bakes, the two schemes would induce an equal amount of effort and thus yield an

equal amount of bread.