Handout 1-
You are given the following production function:
Y = F(K, L) = AK1/3L2/3
1) Draw a sketch of the production function with output, Y, on the vertical axis and the quantity of labor, L, on the horizontal axis. Assume that capital, K, is held constant when drawing this graph.
2) Suppose you triple K and L simultaneously, what happens to output, Y?
3) What is the MPL?
a. Sketch a graph of the relationship between the MPL and output, placing output on the vertical axis and the quantity of labor on the horizontal axis.
b. Holding everything else constant, what happens to the MPL if the amount of K available to this economy increases?
c. Holding everything else constant, what happens to the MPL if the amount of L available to this economy increases?
4) What is the MPK?
a. Holding everything else constant, what happens to the MPK if the amount of K available to this economy increases?
b. Holding everything else constant, what happens to the MPK if the amount of L available to this economy increases?
5) Rewrite the MPL as a function of output per worker.
6) Rewrite the MPK as a function of output per unit of capital.
7) Write an expression for the total wage bill.
8) Write an expression for the total return to capital.
9) What is the ratio of labor income to capital income for this production function?