Answer to Question #88195 in Microeconomics for Sabreen Rehana Nisha

Question

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.
P 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:

E = (105 - 100)/(95 - 100)×(95 + 100)/(105 + 100) = 5/(-5)×195/205 = - 0.95, so the labor is inelastic.

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

E = (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 = (105 - 100)/(99 - 100)×(99 + 100)/(105 + 100) = 5/(-1)×199/205 = - 4.85.