Question

Calculate the Golden Rule capital-labor ratio. Do this for the model
economy considered in problem 3 above. To answer this question it is helpful
to know that the marginal product of capital is Fk(k, 1) = .3k to the power of −.7

This is problem 3

3. Suppose that three countries have the same technology and follow the
logic of the Solow growth model. If country 1 always saves 10 percent of output
(i.e s = .1), country 2 always saves 20 percent of output (i.e s = .2) and country
3 always saves 30 percent of output (i.e s = .3) then what is GDP per capita in
each country in steady state? What is the marginal product of capital in steady
state in each country?
Additional Assumptions:
Yt = F(Kt, Lt) = (Kt) to the power of .3 x (Lt) to the power of .7
Kt+1 = Kt(1 − δ) + It , It = sF(Kt, Lt), Lt+1 = Lt(1 + n)
δ = .06, n = 0 and s = .1, s = .2, s = .3
Hint: Find the capital-labor ratio k that makes investment i = sF(k, 1) equal
to depreciation δk. It is easy to see that y = F(k, 1) = k to the power of .3
for the production function above.

Answer 1