Question

Consider an economy with the following production function:

Y = AK^.5L^.5

The labor force is constant. The rate of depreciation is δ = .1, the savings rate is s = .3.

a. Has this production function constant returns to scale? Why?

b. Write the production function in per worker variables.

c. Does the per worker production function have diminishing marginal returns to capital? Why?

d. Write the fundamental Solow equation in per worker variables.

e. Depict the steady state of this economy.

f. What are the growth rates of per worker output and capital in steady state?

g. Calculate the steady state level of capital, output, consumption and savings.

h. Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth rates change?

i. Redraw the initial equilibrium and show what happens when there is a one time increase in population. Do the growth rates change?

j. Redraw the initial equilibrium and show what happens when there is a one time innovation that increases productivity. Do the growth rates change?

k. Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do the growth rates change?