Macroeconomics 5th Edition by Olivier Blanchard

Exercise 2

The Cobb-Douglas production function and the steady state. This problem is based on the material in the chapter appendix. Suppose that the economy's production function is given by
and assume that a = 1/3.
a. Is this production function characterized by constant returns 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 between output per worker and capital per worker. e. For a given saving rate, s, and depreciation rate, , give an expression for capital per worker in the steady state.
f. Give an expression for output per worker in the steady state.
g. Solve for the steady-state level of output per worker when s = 0.32 and = 0.08.
h. Suppose that the depreciation rate remains constant at = 0.08, while the saving rate is reduced by half, to s = 0.16. What is the new steady-state output per worker