Answer to Question #307390 in Macroeconomics for Thom

Question

Consider an economy descried by the production function: 𝑌 = 𝐹(𝐾, 𝐿) = 𝐾^0.3 L^0.7

a) Derive the per-worker production function

b) Assuming no population growth or technological progress, find the steady state capita stock per worker, output per worker and consumption per worker as a

function of the saving rate and depreciation rate.

c) Define the Golden rule level of capital.

d) Under the Solow growth model, explain the effects of population growth on the steady-state level of capital and on output per worker (Show on a sketch).

Answer 1

Y= K^{0.3}L^{0.7}

Y/L= (K^{0.3}L^{0.7})/L

Y= K^{0.3}

b. Sy=kβ

sK^{0.3} =βk

K= (s/β)^{1.77}

Y=K^{0.3}

=[(s/β)^{1.77}]^{0.3}

Steady state level is (s/β)^{0.53}

Steady level of consumption per worker

C=y-s

=(s/β)^{0.53}-s

c. golden rule level of capital show the point that maximize the usage in a firm state.

d. population growth marks how the growth rate of the economy. When population rises the steady-state labor ratio reduces thus the level of capital falls and the output per worker decreases.