Question

Consider s perfectly competitive market with

Market demand function Qd= 1000-2P

Market Supply function Qs= 2P

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

At eqm, Qs = Qd

2P =1000-2P

4P = 1000

P* = 250

Q* = 2P*

= 500

.

As inverse demand curve , P = 500-Q/2

CS = .5*(500-250)*500

= (250)² = 62,500

PS = .5*250*500

= 62,500

.

B) t = 50

New demand curve

Q= 1000-2(P+50)

Q = 1000 - 2P - 100

Q = 900-2P

At new eqm, 900-2P = 2P

P' (new price received by sellers)= 900/4 = 225

new Price paid = 225+50

= $ 275

New Q = 1000-2*275

= 1000-550

= 450

.

new CS = .5*(500-275)*450

= (225)² = 50,625

.

PS = .5*225*450

= 50,625

​​​​

.

c) graph

Market gets inefficient due to tax