Question

3) Consider the Solow model with population growth and labor-augmenting technological progress. Suppose that the aggregate production function is Cobb- Douglas, i.e. Y = AK"(E · L)1-a, where A is a constant, while E denotes technological progress and grows at rate g. Labor grows at an exogenous rate n, and capital depreciates at rate d. As usual, people consume a fraction (1 – s) of their income. a. Use a graph similar to what we have seen in class to illustrate the position of the steady state in this model (be as specific as you can on the lines/curves that you are drawing). b. Compute the steady state level of capital, output, consumption and investment per effective worker, i.e. k*, y*, c* and i*. C. Compute the steady state growth rate of (i) income per effective worker, (ii) income per worker, (iii) aggregate income, (iv) the MPL, and (v) the MPK. d. Compute the Golden Rule steady state level of capital, output, consumption and investment per effective worker, i.e. kĞR, YGR, CGR and IGR e. What is the best possible saving rate that should be targeted by a benevolent government?

Answer 1

The respective figure number is the answer to the question number respectively.

S, Fi(1) S2 Falr, 1) Fig. 3

-sf(r.1) 0 11 12 13 CAPITAL LABOUR RATIO Fig. 2

str.1) CAPITAL LABOUR RATIO Fig. 1

Steady state output (y) and depreciation (dk) Increase in Reduction in stcady Steady state steady state state capital capital per worker (kº) capital Fig. 4.7 Steady State Consumption

Sulur mineral F) டா nithima