Question

Suppose that the supply of quarterbacks is given by:

w = $5, 000, 000 + 1, 000, 000L

Further suppose that the marginal revenue product of professional basketball players is:

MRPL =$29,000,000?2,000,000L

Suppose that we are in a competitive market.

a) What is the optimal labor (LC ) and wage (wC )?

b) Find the buyer surplus.

c) Find the producer surplus.

Answer 1

(a) For a monopsonist, profit is maximized by equalizing MRPL and Marginal cost of labor (MC), where

MC = dw/dL = 1,000,000

By equalizing MRPL and MC,

29,000,000 - 2,000,000L = 1,000,000

2,000,000L = 28,000,000

L = LM = 28,000,000/2,000,000 = 14

w = wM = 5,000,000 + (14 x 1,000,000) = 5,000,000 + 14,000,000 = $19,000,000

(b) From MRPL function, we get: When L = 0, MRPL = $29,000,000 (Maximum possible wage rate)

Buyer surplus = Area between MRPL curve and market wage rate = (1/2) x $(29,000,000 - 19,000,000) x 14

= 7 x $10,000,000 = $70,000,000

(c) From labor supply function, we get: When L = 0, w = $5,000,000 (Minimum wage rate)

Producer surplus = Area between supply curve and market wage = (1/2) x $(19,000,000 - 5,000,000) x 14

= 7 x $14,000,000 = $98,000,000