Homework Set 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.