Question

Consider a firm with the following production technology q = k0.5l0.5. The market price of the firm’s product is 10, and the rental rates of capital and wage rate for labor are given, respectively, by 2 and 3.

(e) If wage rate goes up to 4, what is the new level of profit maximizing labor?

(f) Find the profit maximizing level

Answer 1

(e) MPL = 0.5k^0.5 L^-0.5

At the profit maximizing level of labor , w = VMPL

Value of marginal product of labor ,VMPL = P(MPL)

Price = 10 (Given)

VMPL = 10(0.5k^0.5 L^-0.5)

K= 4 (Given)

VMPL = 10(0.5)(4)^0.5 L^-0.5

VMPL = 10 L^-0.5

w = 4 (given)

4 = 10L^-0.5

L = 6.25 units. (profit maximizing level of labor)

(f) Profit maximizing level = TR-TC

TR = P(q)

q = (4)^0.5 (6.25)^0.5 = 2(2.5)= 5

TR= P(q) = 10(5)= $50

TC = wL + rK

= 4(6.25) + (2)(4)

=25+ 8 = $ 33

So, the profit maximizing level = TR-TC

= $(50-33) = $ 17