Question

The change of inputs and production function determine the level of output in the long run. Suppose an economy described by the Solow model utilize capital and labour in production process which technology parameter ofa=1/2. Assuming that population has zero growth rate and technology is constant (A=1): a. Write down production function for this country, determine output per worker as function of capital per worker and explain the steady state of capital condition (6 POINTS) b. If 8 and s are depreciation rate and saving rate respectively, draw a graph indicating depreciation function, investment function and show steady state condition (4 POINTS) c. If 30 percent of output is saved, 10 percent of capital stock depreciates every year, determine unit of capital stock at the steady state (4 POINTS) Page 2 of 3 d. Letsupposenowthe level oftechnology is constant at 2, using information from point C, write down the production function and determine the level of capital that maximizes consumption (i.e. Golden Rule level of capital) (6 POINTS)

Answer 1

A) Production function;,

f(L,K)=A*K^a*L^(1-a)

f(L,K)=Y=K^1/2*L^1/2

Y/L=(K/L)^1/2

y=k^1/2{ y is output per worker and k ia capital per worker}

In steady state capital per worker remain same.

B)

(ا از te (Datey depnciation T Page No. Sarche Frases than steady state yal

C) capital per worker remain same so,

s*y=k*depreciation

0.3*k^1/2=0.1*k

1/(k^1/2)=1/3

k^1/2=3

k=9{ steady state capital per worker}

D)New production function:,

f(L,K)=Y=2*K^1/2*L^1/2

y=2*k^1/2

Golden rule level of capital is that MAXIMIZE consumption per worker.

Consumption is MAXIMIZES where,

MPK= depreciation

∆y/∆k=0.1

2/(k^1/2)=0.1

k^1/2=20

k=400