Question

The demand curve for a good is Q =60 - p and the supply curve is Q = p. The government imposes a specific tax of t = 2 per unit of output. (a) find the market equilibrium output (Q) and the price (p) before tax? (b) Find the new market equilibrium output (Q) and the price (p) after tax. (c) Explain the effect the tax has on consumer surplus and producer surplus.

Answer 1

a)

$Qd=60-P$

$Qs=P$

At equilibrium $Qd=Qs$

Hence

$60-P=P$

$60=2P$

$P=30$

Equilibrium price is 30

$Q=60-P$

$=60-30$

$=30$

Equilibrium output is 30

b)

after-tax of 2

$Qd=60-P$

$Qs=P+2$

$Qd=Qs$

$60-P=P+2$

$58=2P$

$P=29$

The equilibrium price after tax is 29

$Q=60-P$

$=60-29$

$=31$

The equilibrium quantity after tax is 31

c)

Consumer surplus falls because the price to the buyer rises, and producer surplus (profit) falls because the price to the seller falls.