Question

3. The market demand for labour is given by w = 18 – 0.05L, where w is the wage rate ($/hr) and L is the number of workers the firm want to employ. The market supply of labour is given by w = 10 + 0.15L, where w is the wage rate ($/hr) and L is the number of workers who want to work. The government introduces the payroll tax $1 per hr per worker.

a. What is the portion (economic incidence) of the tax that the workers pay (in cents per dollar of the tax)? What is the portion (economic incidence) of the tax that the employers pay (in cents per dollar of the tax)?

b. What is the deadweight loss resulting from this tax? Give the number.

Answer 1

3. Market demand for labour is given by w = 18 – 0.05L where L = (18 - w) / 0.05

Market supply of labour is given by w = 10 + 0.15L where L = (w - 10) / 0.15

To find the equilibrium wage rate and number of workers we equate

Market demand for labour = Market supply of labour

18 – 0.05L = 10 + 0.15L

18 - 10 = 0.15L + 0.05L

0.20L = 8

L = 8 / 0.20

L = 40

Putting the value of L in w = 18 – 0.05L

w = 10 + 0.05(40) = 10 + 6 = 16

So, the equilibrium wage rate is w = 16 and the number of workers, L= 40

A payroll tax of $1 is imposed by the government per hr per worker. Then, ws = wb - T where ws = wage paid by buyers,wb = wage received by sellers or workers, T = Tax rate

Let, Market demand for labour L = (18 - wb) / 0.05

Market supply of labour L = (ws - 10) / 0.15

The equilibrium condition is: Market demand for labour = Market supply of labour

(18 - ws) / 0.05 = (w_b - 10) / 0.15

Putting ws = wb - T in (18 - ws) / 0.05

[18 - (wb - T)] / 0.05 = (wb - 10) / 0.15

[18 - (wb - T)] * 0.15 = [(wb - 10)] * 0.05

2.7 - 0.15wb + 0.15T = 0.05wb - 0.5

Putting the value of payroll tax (T) = $1

2.7 + 0.5 + 0.15 (1) = 0.05wb + 0.15wb

3.2 + 0.15 = 0.20wb

0.20wb = 3.35

wb = 3.35 / 0.20

wb = 16.75

Now, ws = wb - T

ws = 16.75 - 1

ws  = 15.75

So, after the tax, wage paid by buyers = 16.75, wage received by sellers or workers = 15.75.

(a) The portion (economic incidence) of the tax that the workers pay (in cents per dollar of the tax) = Equilibrium wage rate before the tax - Wage received by them after the tax is imposed

= 16 - 15.75 = $ 0.25

The portion (economic incidence) of the tax that the employers pay (in cents per dollar of the tax) = Wage payed by them after the tax is imposed - Equilibrium wage rate before the tax

= 16.75 - 16

= $ 0.75

(b) The deadweight loss resulting from this tax = 1/2 * (P2 - P1) * (Q2 - Q1)

where P2 = Price after tax, P1 = Price before tax, Q2 = Quantity after tax, Q1 = Quantity before tax

where Q2 = Quantity after tax is calculated by substituting w in: L = (18 - w) / 0.05 = (18 - 16.75) / 0.05 = 25

So, Deadweight Loss =1/2 * (16.75 - 15.75) * (40 - 25)

Deadweight Loss = 1/2 * 1 * 15

Deadweight Loss = 7.5