Question

# A firm’s demand for labor can be written as 〖VMP〗_E=40-0.01E_D. Labor is supplied to the firm...

A firm’s demand for labor can be written as 〖VMP〗_E=40-0.01E_D. Labor is supplied to the firm according to w=7+0.02E_S.

1, What is the firm’s marginal cost of hiring workers?

2. How much labor does the firm hire and at what wage when there is no minimum wage?

3. How much labor does the firm hire and at what wage when it must pay a minimum wage of \$20?

4. How much labor does the firm hire and at what wage when it must pay a minimum wage of \$30?

1) Marginal cost is the cost of hiring one additional labor. Now we have wage rate W = 7 + 0.02ES and wage bill at W*E = 7E + 0.02E^2. This gives marginal cost MC = derivative of wage bill = 7 + 0.04E.

2) Use VMPL = wage rate

40 - 0.01E = 7 + 0.02E

33 = 0.03E

Employment = 1100 and wage rate = 7 + 0.02*1100 = \$29.

3. A minimum wage of \$20 is not binding because the market wage is already higher than minimum wage.

4. Wage rate is 30. Hence, labor supplied is ES = (30 - 7)/0.02 = 1150 and labor demanded ED = (40 - 30)/0.01 = 1000. Firm hires a labor or 1000 units at a wage rate of 30.

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