Answer to Question #89117 in Macroeconomics for Linda

Question

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.

Answer 1

A. The own-wage (w) elasticity of labor demand is:

Ed = (105 - 100)/(95 - 100)×(95 + 100)/(105 + 100) = - 0.95.

B. The cross-elasticity of labor demand with respect to the price of capital (r) is:

Ed = (103 - 105)/(105 - 100)×(105 + 100)/(103 + 105) = -2/5×205/208 = -0.39.

So, capital and labor are gross complements.

C. The elasticity of substitution of labor and capital is:

E = (99 - 100)/(105 - 100)×(105 + 100)/(99 + 100) = -205/995 = - 0.21.