Question

A market for baby bottles has the following supply and demand functions qS = −6 + 3p qD = 14 − 2p

a) Calculate the Consumer Surplus, Producer Surplus, and Total Welfare levels. b) Now, suppose a per unit tax of 5 were charged to the buyer. What are the equilibrium quantity, price paid by the buyer, and price received by the seller? c) Mathematically, does it make a difference if the tax is applied to the buyer or the seller? Explain why or why not. d) How much tax revenue is raised? How much of that tax burden is borne by the buyer? e) Calculate the Consumer Surplus, Producer Surplus, Total Welfare Level, and Deadweight Loss associated with the tax.

Answer 1

(a)

In equilibrium, qD = qS.

14 - 2p = -6 + 3p

5p = 20

p = 4

q = 14 - (2 x 4) = 14 - 8 = 6

From demand function, when qD = 0, p = 14/2 = 7 (Vertical intercept).

Consumer surplus (CS) = Area between demand curve & price = (1/2) x (7 - 4) x 6 = 3 x 3 = 9

From supply function, when qS = 0, p = 6/3 = 2 (Vertical intercept).

Producer surplus (PS) = Area between supply curve & price = (1/2) x (4 - 2) x 6 = 3 x 2 = 6.

Total welfare (TW) = CS + PS = 9 + 6 = 15

(b)

The tax will increase the price paid by buyers, lowering demand by 5 units at every output. New demand function is:

qD = 14 - 2(p + 5) = 14 - 2p - 10 = 4 - 2p

Equating with qS,

4 - 2p = -6 + 3p

5p = 10

p = 2 (Price received by sellers)

Price paid by buyers = 2 + 5 = 7

q = 4 - (2 x 2) = 4 - 4 = 0

(c)

Whether the tax is legally imposed on buyers or on sellers, the decrease in quantity after tax, price paid by buyers after tax and price received by sellers after tax all remain the same. Therefore after-tax values do not depend on legal tax incidence.

(d)

Tax revenue = Unit tax x After-tax quantity = 5 x 0 = 0

NOTE: As per Answering Policy, 1st 4 parts are answered.