Use the table that follows to answer the following questions. The table uses index numbers to describe the values of K, L, w, r, and Q for a business firm at three points in time. K and L are the amounts of capital and labor used in the production process. The price of labor and capital are given by w and r respectively. Q is the level of output produced. Use the midpoint method for all elasticity calculations.
Period K L w r Q
1
100
100
100
100
100
2
99
105
95
100
105
3
102
103
95
105
110
A. Using data from periods 1 and 2, compute the own-wage (w) elasticity of labor demand.
B. Using data from periods 2 and 3, compute the cross- elasticity of labor demand with respect to the price of capital (r). Are capital and labor gross substitutes or gross complements?
C. Using data from periods 1 and 2, compute the elasticity of substitution of labor and capital.