Suppose that the economy's production function is given by

Y = K N^{1 -} and assume that = 1/3.

a. Is this production function characterized by constantreturns to scale? Explain.

b. Are there decreasing returns to capital?

c. Are there decreasing returns to labor?

d. Transform the production function into a relation betweenoutput per worker and capital per worker.

e. For a given saving rate, s, and depreciation rate, , give anexpression for capital per worker in the steady state.

f. Give an expression for output per worker in the steadystate.

g. Solve for the steady-state level of output per worker whens = 0.32 and = 0.08.

h. Suppose that the depreciation rate remains constant at = 0.08, while the saving rate is reduced by half, tos = 0.16. What is the new steady-state output per worker?