1. you need to use  Wolfram Mathematica to finish the economic problem in the file. make sure you use Wolfram Mathematica and I need the file. I have some ex that you can check.

HomeworkSet Mankiw Romer Weil 1992 (MRW) model
Advanced Macroeconomic Theory

Professor Mathieu-Bolh

Complete the three problems below.
To receive full credit, use Print[“”] to present your results in the order of the questions, writing
the question number and clearly labeling your results. Also use Print[‘’] to write answers to
questions that require explanations (so that they appear in the output of the program).

On the graphs, make sure to label axis, loci, and equilibrium.

Problem 1 –Your program name will be: “Yourname_2.1”
Labels as described above: 1 pt
Program runs: 1 pt
Use the predator-prey model described in the theory portion of the homework.
Suppose A=6; B=2; C=8; D=4

1- 2 pts Calculate the steady state values for the population of prey and predators.
2- 3 pts Draw a graph combining the loci, the stream plot, and the parametric plot for one

trajectory of the Lotka-Volterra Predator-Prey system in Mathematica.

Problem 2 –Your program name will be: “Yourname_2.2”
Labels as described above: 1 pt
Program runs: 1 pt
You are an economist working for the World Bank and are asked to answer the following
questions using the MRW model.

Your job is to compare the economic outlook of various countries. Initially, those countries are
similar in their structural parameters: Suppose sh=0.06, sk=0.2, n=0.015, g=0.015, delta=0.03,
alphak=1/3, alphah=1/3, A=2.

a. 3 pts In Gondor, there is a civil war and population growth is likely to fall to 1%. In
Groland, there is peace and the government is considering a policy that will increase the
saving rate sk to 23.8%. Write a Mathematica program that calculates and presents the
steady state output per effective worker and the steady state output per worker in
Gondor and Groland, as well as their respective percentage change between steady
states.

b. 2 pts Comparative statics: Compare initial and final steady state in each country.
Compare the effect of the two events in Groland and Gondor. Explain and comment on
those results.

c. 1.5 pts Suppose the economy of Gondor starts from la level of physical capital per
effective worker equal to 15 and a level of human capital equal to 3.5. Draw a graph
that shows the trajectory (of h relative to k) from this point to the steady state with a
population growth of 1%, as well as the stream plot.

d. 1.5 pts Suppose the economy of Groland starts from la level of physical capital per
effective worker equal to 15 and a level of human capital equal to 3.5. Draw a graph
that shows the trajectory (of h relative to k) from this point to the steady state with
sk=23.8% as well as the stream plot.

e. 2 pts Comparative dynamics Based on c) and d), explain why output per effective worker
(or per worker) evolves the way it does between the two steady states in each country
and why it is different in Groland and Gondor.

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