Question

Tax Incidence: How do the effects of a tax differ in the short run between markets with different elasticities of supply? Consider two hypothetical markets. In both cases, the demand function is QD = 1000 - P The two supply functions are QS1 = P - 200 and QS2 = 4P - 2000 a. Solve for equilibrium price and quantity for both cases and show that the equilibrium values are the same in these two cases (for QS1 and QD and for QS2 and QD). b. Plot the demand and supply curves (with P on the vertical axis and Q on the horizontal axis) for the two markets on the same graph. c. Now suppose a tax is imposed in both markets, equal to $60 per unit purchased. Model this as a shift in the demand curve (so that QD now depends on P, the net price paid to the firm, plus the tax). Illustrate the new demand curve on your graph (label everything clearly). Derive the new equilibrium price (the net price received by the firm) and quantity for each of the two cases. In which case is the producer’s share of the tax burden greater?

Answer 1

QD = 1000 - P.

QS1 = P - 200

QS2 = 4P - 2000

a. Qd=Qs1

1000-P=P-200

1200=2P

P1=600

Q1=1000-600=400

Qd=Qs2

1000 -P= 4P-2000

3000= 5P

P2= 600

Q2= 1000-600=400

B.

C. Market 1:

Tax on Consumer

Qd new= 1000-(P+60)= 940-P

Qs1= P-200

Qd new= Qs1

940-P=P-200

1140=2P

New Equilibrium price received by sellers P*=$570

New Equilibrium Price Paid by consumers= 570+60= $630

Quantity=570-200=370

Qd new= Qs2

940-P=4P-2000

2940=5P

New Equilibrium price received by sellers P*=$588

New Equilibrium Price Paid by consumers= 588+60= $648

Quantity=940-588=352

Market 1

Producer share= 600-570=$30

Market 2

Producer share= 600-588= $12

In market A producer share is more.