Question

1. Assume that labor demand for low-skilled workers in the United States is: w = 22 – 0.1E where E is the number of workers (in millions) and w is the hourly wage. Assume there are currently 120 million domestic U.S. low-skilled workers who supply labor inelastically. If the U.S. opened its borders to immigration, 20 million low-skilled workers would enter the U.S. and supply labor inelastically.

a. What is the market-clearing wage if immigration is not allowed?

b. What is the market-clearing wage with open borders?

c. How much is the immigration surplus when the U.S. opens its borders?

Answer 1

Labor demand: w = 22 - 0.1E

0.1E = 22 - w

E = 220 - 10w

Market is cleared when labor demand equals labor supply. Inelastic labor supply means that supply of labor is fixed.

(a) When immigration is not allowed, labor supplied = 120 million

220 - 10w = 120

10w = 100

w = $10

E = 120

(b) When immigration is allowed, labor supplied = (120 + 20) million = 140 million

220 - 10w = 140

10w = 80

w = $8

E = 140

(c) Immigration surplus = (1/2) x Change in wage rate x Change in employment

= (1/2) x $(10 - 8) x (140 - 120) Million

= (1/2) x $2 x 20 Million

= $20 Million