Homework Set Ramsey (1928) Cass (1965) Koopmans (1965) (RCK) model
Advanced Macroeconomic Theory Professor Mathieu-Bolh
Problem 1 (Programming) Your program name will be: “Yourname_3.1”
The purpose of this exercise is to compare the results of the Solow growth model with those of the RCK model in the steady state.
1) For each set of parameters below:
– Calculate the steady state level of consumption per effective worker, capital per effective
worker and output per effective worker in the Solow model and the RCK model with
Mathematica.
– Compare and explain the results obtained in a) b) and c).
– Present your results as 1a), 1b) and 1c) and provide the comparison/explanation in 1d) Parameters:
a) s=0.2, n=0.015, g=0.015, delta=0.03, alpha=1/3, 𝜃 = 0.5, 𝜌 = 0.02.
b) s=0.2, n=0.01, g=0.01, delta=0.03, alpha=1/3, 𝜃 = 0.5, 𝜌 = 0.01.
c) s=0.2, n=0.015, g=0.015, delta=0.03, alpha=1/4, 𝜃 = 1, 𝜌 = 0.02.
2) a) Use the initial parameters in 1a), except for the saving rate. Calculate the level of steady state consumption per effective worker in the Solow model for values of s going from 0.1 to 1. (Use a loop and Solve[]).
b) Explain the obtained relation between the steady state level of consumption per effective worker and the saving rate in the Solow model and provide a conclusion
regarding the golden rule.
Problem 2 (Programming) Your program name will be: “Yourname_3.2”
1) Economists observe that a higher population usually tends to results in a higher number of scientists and engineers, and a higher number of scientists and engineers usually results in more technological progress. In the US population growth has been slowing down due to lower fertility rates and increase in life expectancy. Other things equal, this is likely to result in a slowdown in technological progress. We can model the effect of the slowdown in population growth and technological progress on the economy using the RCK model: Suppose the growth rate of the population falls to 0.01 and the growth rate of technological progress falls to 0.01. The purpose of this exercise is to understand how these changes influence the economy.
a) Draw the initial and final loci. Chose a different color and style for the new loci (Initial loci: black and dashed; new loci: green and default)
b) Show the new trajectory of the economy. Combine the loci and the new trajectory (The trajectory should be red).
c) Do economists rightfully or wrongfully worry about the slowdown in the growth rate of the population? Think carefully and justify your answer.