Suppose that the economy's production function is given by

1/3 2/3 Y K N =

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

b. Are there decreasing returns to capital? explain

c. Are there decreasing returns to labour? explain

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?

refer to book Olivier Blanchard, David R. Johnson - Macroeconomics-Pearson (2012)