Question

1. Consider a tax on the producers in a market. By using supply and demand curves, show the consumer surplus, producer surplus, the equilibrium price and quantity traded before tax. Now show the consumer surplus, producer surplus, equilibrium price and quantity traded after tax.
2. Finally make sure to show the revenue of the tax and the deadweight loss associated with the tax. Now do the same exercise in part-c by assuming a tax on consumers.
3. What happens to consumer surplus, producer surplus, equilibrium price and quantity traded after tax?

Answer 1

(a)

In following graph, D0 and S0 are initial demand and supply curves intersecting at point E with equilibrium price P0 and quantity Q0.

Initial consumer surplus (CS) = area AEP0

Initial producer surplus (PS) = area BEP0

After tax, supply decreases, shifting S0 leftward to S1. New equilibrium is at point F where D0 intersects S1 with price paid by buyers (= market price) being P1, price received by sellers being P2 and quantity being lower at Q1.

Unit tax = P1 - P2

New CS = area AFP1

New PS = area BGP2

Tax revenue = area P1FGP2

Deadweight loss = area EFG

(b)

In following graph, D0 and S0 are initial demand and supply curves intersecting at point A with equilibrium price P0 and quantity Q0.

Initial consumer surplus (CS) = area DAP0

Initial producer surplus (PS) = area EAP0

After tax, demand decreases, shifting D0 leftward to D1. New equilibrium is at point B where D1 intersects S0 with price paid by buyers being P1, price received by sellers (= market price) being P2 and quantity being lower at Q1.

Unit tax = P1 - P2

New CS = area DCP1

New PS = area EBP2

Tax revenue = area P1CBP2

Deadweight loss = area ABC

(c)

In both cases, CS decreases, PS decreases, market price increases and quantity decreases.