Question

Assume the market demand and market supply functions for pears in the United States are given by Q^D= 32-4p and Q^S= -8+4p, respectively. p represents the price of pears.

1) Find producer and consumer surplus when the market is in equilibrium.

2) Suppose the federal government introduces a consumer subsidy program that that pays consumers buying pears 30 cents (effectively reducing consumer price) if the market price is above $5.

a. Compute and graphically show the impact of the program on producer surplus.

b. Calculate and graphically show the impact of the program on consumer surplus.

c. How much money will the government need to finance this program?

d. What is the deadweight loss of this policy? (calculate and show graphically)

Answer 1

(1)

In equilibrium, QD = QS.

32 - 4p = - 8 + 4p

8p = 40

p = $5

Q = 32 - (4 x 5) = 32 - 20 = 12

From demand function, when QD = 0, p = 32/4 = $8 (Vertical intercept of demand curve).

Consumer surplus (CS) ($) = Area between demand curve and price = (1/2) x (8 - 5) x 12 = 6 x 3 = 18

From supply function, when QS = 0, p = 8/4 = $2 (Vertical intercept of supply curve).

Producer surplus (PS) ($) = Area between supply curve and price = (1/2) x (5 - 2) x 12 = 6 x 3 = 18

(2)

The subsidy will effectively reduce the price paid by consumers, so demand curve will shift rightward. New demand function:

QD = 32 - 4(p - 0.3) = 32 - 4p + 1.2 = 33.2 - 4p

Equating with QS,

33.2 - 4p = - 8 + 4p

8p = 41.2

p = $5.15 (Price received by producers)

Price paid by consumers = $5.15 - $0.3 = $4.85.

Q = - 8 + (4 x 5.15) = - 8 + 20.6 = 12.6

In following graph, D0 and S0 are initial demand and supply curves intersecting at point E with initial price P0 (= $5) and quantity Q0 (= 12). Initial CS is area AEP0 and PS is area BEP0. After subsidy, D0 shifts right to D1, intersecting S0 at point F. Price received by producers rises to P1 (= $5.15), price paid by consumers falls to P2 (= $4.85) and quantity rises to Q1 (= 12.6). New CS is area AGP2 and new PS is area BFP1. Government cost of subsidy is area P1FGP2 and deadweight loss is area EFG.

(a)

New PS ($) = Area BFP1 = (1/2) x (5.15 - 2) x 12.6 = 6.3 x 3.15 = 19.845

Increase in PS ($) = 19.845 - 18 = 1.845

(b)

New CS ($) = Area AGP2 = (1/2) x (8 - 4.85) x 12.6 = 6.3 x 3.15 = 19.845

Increase in CS ($) = 19.845 - 18 = 1.845

(c)

Government cost of subsidy ($) = Area P1FGP2 = 0.3 x (12.6 - 12) = 0.3 x 0.6 = 0.18

(d)

Deadweight loss ($) = Area EFG = (1/2) x 0.3 x  (12.6 - 12) = 0.15 x 0.6 = 0.09