Question

Taxes

qd= 12-3p

qs= -2+2p

Using the supply and demand functions from problem 1, suppose a per unit tax of 1 were charged to the buyer.

a) How much does the buyer pay?

b) How much does the seller receive?

c) What is the equilibrium quantity?

d) How much tax revenue is generated?

e) How much tax burden do the buyer and seller each bear?

f) Calculate the consumer surplus, producer surplus, welfare level, and dead weight loss with this tax.

g) Suppose the per unit tax were charged to the seller. How would our results change?

Answer 1

We have the following information

Demand: qd= 12-3p

Supply: qs= -2+2p

Now suppose a per unit tax of $1 were charged to the buyer.

This implies new demand is qd = 12 - 3(p + 1) or qd = 9 - 3p. New equilibrium has

9 - 3p = - 2 + 2p

11 = 5p

pseller = 2.2

pbuyer = 2.2 + 1 = 3.2

q = -2 + 2*2.2 = 2.4

a) Price buyer pay = $3.2 per unit

b) Price seller receive = $2.2 per unit

c) Equilibrium quantity after tax = 2.4 units

d) Tax revenue generated = tax * quantity = 1 x 2.4 = $2.4

e) Buyer's burden = 3.2 - 2.8 = $0.4 or 40% of tax. Seller's burden = 2.8 - 2.2 = $0.6 or 60 percent.

f) Consumer surplus = 0.5*(4 - 3.2)*2.4 = $0.96

Producer surplus = 0.5*(2.2 - 1)*2.4 = $1.44

Total welfare = PS + CS + revenue = $4.8

Dead weight loss with this tax = 0.5*1*(3.6 - 2.4) = $0.6

g) There would have been no change since the burden of tax and its result are irrespective of on whom it is imposed