Question

Consider a market for beer with a demand curve which is: Qd = 25 - 2p and a supply curve which is: Qs = 3P

a) Find the equilibrium price and quantity. Suppose that the government decided they wished to levy a $2 tax on suppliers.

b) Find the new price paid by the consumer and the price received by the seller.

c) Based on the tax sharing burden by both the consumer and the seller, comment on the relative elasticity of the demand and supply curve.

d) Calculate the tax revenue for the government.

Answer 1

(a)

Setting Qd = Qs,

25 - 2p = 3p

5p = 25

p = 5

Q = 3 x 5 = 15

(b)

The tax shifts supply curve leftward by $2 and new supply function is

Qs1 = 3(p - 2) = 3p - 6

Setting Qd = Qs1,

25 - 2p = 3p - 6

5p = 31

p = 6.2 (Price paid by buyers)

Price received by sellers = 6.2 - 2 = 4.2

(c)

Tax burden of buyers = 6.2 - 5 = 1.2

Tax burden of sellers = 5 - 4.2 = 0.8 (= 2 - 1.2)

Since tax burden of buyers is higher, it means demand is more inelastic and supply is more elastic.

(d)

When p = 6.2,

Q = 3 x 6.2 - 6 = 18.6 - 6 = 12.6

Tax revenue = Unit tax x After-tax quantity = 2 x 12.6 = $25.2