Question

Consider a perfectly competitive market with

Market demand function: ?? = 1000 − 2?

Market supply function: ?? = 2?

a. Suppose there is no sales tax. What is the equilibrium price and equilibrium quantity? What is the consumer surplus and producer surplus?

b. Now suppose the government imposes a sales tax of $50 per unit on consumers. What is the new equilibrium price and equilibrium quantity? What is the new consumer surplus and producer surplus? What is the tax revenue?

c. Show your answer in a) and b) in a well labelled diagram (Place the total quantity on the horizontal axis and the market price on the vertical axis). Discuss the effect of the sales tax on the market efficiency.

Answer 1

a) No tax equilibrium

Qd = Qs

1000 - 2P = 2P

P = 1000/4 = $250

Q = 500 units

CS = 0.5*(max price - price paid)*qty purchased = 0.5*(500 - 250)*500 = $62500

PS = 0.5*(Price received - reservation price)*qty sold =  0.5*(250 - 0)*500 = $62500

b) After tax equilibrium

Qd = Qs

1000 - 2(P + 50) = 2P

1000 - 2P - 100 = 2P

P = 900/4 = $225 (received by sellers)

P = $275 (paid by buyers) (equilibrium price)

Q = 450 units (equilibrium quantity)

CS = 0.5*(max price - price paid)*qty purchased = 0.5*(500 - 275)*450 = $50625

PS = 0.5*(Price received - reservation price)*qty sold =  0.5*(225 - 0)*450 = $50625

Tax revenue = 50*450 = $22500

c) Market efficiency is reduced as there is a deadweight loss worth 0.5*50*50 = $1250