1. Consider a labor market under the assumption of perfect competition. Let the

Question

1. Consider a labor market under the assumption of perfect competition. Let the labor demand and supply curves be given by Ld--100w + 900 and Ls = 100w, respectively, where w denotes workers' wage. Answer the following questions. (a) Compute the equilibrium wage and quantity of labor exchanged in the market. (b) Find firms' and workers' surpluses under the competitive equilibrium in part (a). (c) Suppose a payroll tax is imposed by a government in the amount of $2.75 per unit of labor. Find the equilibrium in the market with payroll tax. What is the net wage received by the workers, gross wage paid by firms, and quantity of labor exchanged in the market? (d) What is the share (in terms of proportion or percentage) of tax born by the workers? (e) Under the equilibrium with payroll tax in part (c), compute the change in firms' surplus, govern- ment's tax revenue, and deadweight loss

Explanation / Answer

In pre-tax equilibrium, Ld = Ls

- 100w + 900 = 100w

200w = 900

w = 4.5

L = 100 x 4.5 = 450

From labor demand function, when Ld = 0, w = 900 / 100 = 9 [Firm's reservation wage]

Firm surplus = Area between labor demand curve and market wage = (1/2) x (9 - 4.5) x 450 = 225 x 4.5 = 1,012.5

From labor supply function, when Ls = 0, w = 0 [Minimum wage acceptable by workers]

Worker surplus = Area between labor supply curve and market wage = (1/2) x (4.5 - 0) x 450 = 225 x 4.5 = 1,012.5

The payroll tax will increase the effective wage paid by firms by $2.75, shifting labor demand curve to left. New labor demand function:

Ld = - 100(w + 2.75) + 900 = - 100w - 275 + 900

Ld = - 100w + 625

Equating new Ld with Ls,

- 100w + 625 = 100w

200w = 625

w = 3.125 (Wage received by workers)

Wage paid by firms = Wage received by workers + Unit payroll tax = 3.125 + 2.75 = 5.875

L = 100 x 3.125 = 312.5

(Part e)

After tax, firm surplus = (1/2) x $(9 - 5.875.5) x 312.5 = (1/2) x $3.125 x 312.5 = $488.28

Change in firm's surplus = $(1.012.5 - 488.28) = $524.22

Government's tax revenue = $2.75 x 312.5 = $859.375

Deadweight loss = (1/2) x Unit tax x Difference in quantity = (1/2) x $2.75 x (450 - 312.5) = (1/2) x $2.75 x 137.5

= $189.0625

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