Question

1. Let the production function for an economy by given by Y=AK^1/2L^1/2 where Y is output, K is capital, L is labor and A is “ideas.”

a. If L=25, A=10, the savings rate is ¼ and the depreciation rate is ½, what will the steady-state values of output, capital and consumption be?

b. On a graph, show what will happen to steady-state output and capital of there is a decrease in the depreciation rate.

2. As capital increases, the marginal product of capital _________________________.

3. Country X and Country Y have identical population, institutions and technology but country X has more physical capital. Which country will have a higher level of output and which will have a higher rate of growth?

4. Two countries, country A and country B are identical in every meaningful way. Then there is a massive earthquake in country B that destroys much of the capital.

a. What will be the immediate effect on the level of output in country B according to our model?

b. What will be the effect on the growth rate of country B shortly after the earthquake according to our model?

c. What will happen to the levels of output and rates of growth of these two countries over time? (This question can be answered in one word. A couple sentences is fine but don’t write a novel!)

Answer 1