1. Consider a labor market under the assumption of perfect competition. Let the
ID: 1110218 • Letter: 1
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. (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
Ld = - 100w + 900
Ls = 100
(a) In equilibrium, Ld = Ls
- 100w + 900 = 100w
200w = 900
w = 4.5
L = 100 x 4.5 = 450
(b)
From labor demand function, when Ld = 0, w = 900 / 100 = 9 [Maximum 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]
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
(c) The payroll tax will increase the effective wage paid by firms by $2.75, so labor demand curve will shift leftward, and new labor demand function will be
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 = 3.125 + 2.75 = 5.875
L = (- 100 x 3.125) + 625 = - 312.5 + 625 = 312.5
(d) Share of tax borne by workers = (Initial wage rate - New wage rate received by workers) / Unit payroll tax
= (4.5 - 3.125) / 2.75 = 1.375 / 2.75
= 0.50
= 50%
NOTE: As per Chegg answering guideline, first 4 parts are answered.
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