ECON 214: Intermediate Macro (2024/25, T2)
Assignment 3
due on March 6th
The Solow Model
In the Solow Model, the evolution of the (per effective labour) capital stock is determined by the equation
(1.1)
where is the current capital stock, is the capital stock next period, d, n, and g are, respectively, the depreciation rate, the rate of population growth, and the rate of technological progress. The constant s stands for the saving rate, and f() is the production function (in per-capita terms).
Assume that the production technology is Cobb-Douglas with , and that d=0.05, n=0.01, g=0.015, and s=0.3.
a) Find the steady-state level of capital, i.e. the amount of capital for which = in the equation (1.1) above. Also, compute (per effective labour) output , investment , and consumption in this steady state.
b) Now assume that the economy starts out in year 1 with a capital stock =6 below the steady-state level you found in part a). Use equation (1.1) to find the evolution of the capital stock for the following 10 years, i.e. years 2 to 11 (for the following 50 years if you are using a program like Excel to do the work for you). Does the capital stock approach its steady-state value? How long does it take to close 30% of the initial gap between the capital stock and its steady-state value?
c) Is the steady state you found in part a) the golden rule equilibrium, dynamically efficient, or dynamically inefficient? Explain how you got your result.