Question

Suppose the demand and supply of mining workers are (D): w=200-4E and (S): w= 50+E, where w is wage and E is employment.

a. What are the equilibrium wage and employment? Draw demand and supply curves.

b. Suppose the government imposes $10 of payroll tax on employer, what are the new equilibrium wage and employment? Draw demand and supply curves.

c. Suppose the government imposes $10 of payroll tax on employee, what are the new equilibrium wage and employment? Draw demand and supply curves.

d. What are the tax burdens for employers and employees?

Answer 1

*Demand: w= 200-4E or wf= 200-4E (wf= wage paid by firm)

•X intercept (keeping w=0)= 50

•Y intercept (keeping E=0) = 200

*Supply: w= 50+E or ww= 50+E (ww=wage recieved by worker)

•X intercept (keeping w=0) = -50

•Y intercept (keeping E=0) = 50

Answer a) At equilibrium Demand= Supply

200-4E= 50+E

150= 5E

E*= 30

W*= 50+E* or 200-4E*

W*= 80

Answer b) with a payroll tax of $ 10 on employer

wf= ww+10

So, new Demand: ww+10= 200-4E

•X intercept ( keeping ww=0)= 47.5

• Y intercept (keeping E=0) = 190

Supply : ww= 50+E

At equilibrium New demand= Supply

190-4E= 50+E

140= 5E

•E'= 28

ww'= 50+E'

•ww'= 78

wf'= ww'+10

•wf'= 88

Answer c) Woth $10 tax on employee

ww=wf-10

Demand: wf= 200-4E

New supply: wf-10 = 50+E

• X intercept (keeping wf=0)= -60

•Y intercept ( Keeping E=0) = 60

At equilibrium Demand= New Supply

200-4E= 60+E

140= 5E

•E"= 28

•wf"= 200-4E"

wf"= 88

•ww"= wf"-10

ww"= 78

Answer d) Without tax Wages= 80

•With tax ww= 78

So, worker pays 2 dollars of the 10 dollar tax

Worker share of tax burden= 2/10= 1/5

•With tax wf= 88

So, firm pays 8 dollars of the 10 dollar tax

Firm's share of tax burden= 8/10 = 4/5

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