Country A and country B both have the production function:
Y = F(K, L) = K1/2 L 1/2.
Assume that in both countries capital depreciates at a rate of 10% each year. (Assume no population growth and no technological progress in either country.) Assume further that country A saves a constant 20 percent of its income each year and that country B saves 30 percent.
a) Compute the per-worker form of the production function above.
b) Using this and the steady-state condition, compute the steady-state level of capital per worker for each country.
c) Now compute the steady state level of consumption per worker in each country. Since the golden rule is defined as the level of capital that allows the greatest level of consumption in steady state, which of these two countries has a steady state closer to the golden rule steady state? Why does a smaller marginal propensity to consume here result in a higher steady state level of consumption?
d) Check your conclusion above by computing the golden rule level of capital stock, and the saving rate necessary to achieve it.