Question

Suppose the market demand for labor and market supply of labor are given as QD = 700−4W and QS = 5W − 200, respectively.

Find the equilibrium quantity of workers and the wage under:

(a) Perfect Competition

(b) Monopoly

(c) Monopsony

Answer 1

A) perfect Competition

Qd = Qs

700-4w = 5w-200

900 = 9w

w* = 100

L* = 500-200

= 300

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b) MONOPOLY

at eqm, MR = MC ( supply curve )

Inverse demand curve

W = 175 - .25Q

MR Curve : W= 175-.5Q

So, 175-.5Q = .2Q + 40

135 = .7Q

Qm = 192.86

wages = 175-.25*192.86

= 126.78

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c) Monopsony:

in eqm, MRPL = Marginal factor cost MFC

Demand curve is MRPL Curve

MFC is labor supply curve, with Slope twice of that of Labor supply curve

As inverse supply curve

5w = Q+200

W = Q/5 + 40

MFC curve : W = 40+2Q/5

Inverse demand Curve

W = (700-Q)/4

At eqm,

MFC = MRPL

40+.4Q = 175 - .25Q

.65Q = 135

eqm Q of labor = 207.692

then Wages found from supply curve

W* = Q*/5 + 40

= 81.538