Consider the Cobb-Douglas production function:
Y = AK1−αL
where K and L are the capital stock and labor uses respectively.
Consider that the economy is composed of a representative firm that maximizes profits by hiring L workers and
paying them some real wage w, for a total wage bill of
The firm also rents capital K at a rate r, paying
Labor and capital are its only costs.
a) Define the labor share and the capital share of income. What do they represent?
b) Write the firm’s profit function.
c) Calculate the firm’s choice of labor and capital inputs, taking prices as given.
d) Express the labor and capital shares of this economy in terms of a parameter.
e) Given the data plotted in class, what should be a reasonable approximation to the value of α?
Part 2) Consider the capital accumulation equation:
Kt+1 = It + (1 − δ) K