Question

The market for semiskilled labor can be represented by the following supply and demand curves: LD = 32000 - 4000W

LS = 8000 + 6000W,
where L = millions of person hours per year and W = the wage in dollars per hour.

a. Calculate the equilibrium price and quantity that would exist under a free market. What impact does a minimum wage of $3.35 per hour have on the market?
b. The government is contemplating an increase in the minimum wage to $5.00 per hour. Calculate the impact of the new minimum wage on the quantity of labor supplied and demanded.

c. Calculate producer surplus (laborers' surplus) before and after the proposed change. Comment on the net effect of the proposed change upon workers as a whole and on individual workers.

Answer 1

(a)

Setting LD = LS,

32000 - 4000W = 8000 + 6000W

10000W = 24000

W = 2.4

L = 8000 + 6000 x 2.4 = 8000 + 14400 = 22400

When W = 3.35,

LD = 32000 - 4000 x 3.35 = 32000 - 13400 = 18600

LS = 8000 + 6000 x 3.35 = 8000 + 20100 = 28100

Since LS > LD, market quantity of labor is 18600 and unemployment is (28100 - 18600) = 9500.

(b)

When W = 5,

LD = 32000 - 4000 x 5 = 32000 - 20000 = 12000 [LD decreases by (18600 - 12000) = 6600]

LS = 8000 + 6000 x 5 = 8000 + 30000 = 38000 [LS increases by (38000 - 28100) = 9900]

Since LS > LD, market quantity of labor is 12000 and unemployment is (38000 - 12000) = 26000 [Unemployment increases by (26000 - 9500) = 16500]

(c)

(I) When W = 3.35 and L = 18600,

From labor supply function, W = (L - 8000) / 6000 = (18600 - 8000) / 6000 = 10600 / 6000 = 1.77

PS = (1/2) x (3.35 + 1.77) x 18600 = 9300 x 5.12 = 47616

(II) When W = 5 and LD = 12000,

From labor supply function, W = (L - 8000) / 6000 = (12000 - 8000) / 6000 = 4000 / 6000 = 0.67

PS = (1/2) x (5 + 0.67) x 12000 = 6000 x 5.67 = 34020

(III) Therefore, PS has decreased by (47616 - 34020) = 13596, making workers worse off.