Question

Suppose that the demand for cars in Australia is given by

Q= 400 – 0.4P, and the supply is given by Q= 0.4P.

A. Illustrate the market equilibrium on a graph. (Calculate and clearly label the equilibrium price and quantity.) (Draw your graph on a piece of paper, take a picture with your phone and then attach the image to your answer here.)

B. Calculate the consumer surplus, producer surplus and total economic surplus of the market when it is in equilibrium.

C. The Australian Government, wanting to protect consumers, imposes a price ceiling of $125. Using your graph, show and explain how this this intervention will affect the quantity supplied and demanded in this market.

D. Illustrate on your graph the consumer surplus and the deadweight loss in this market with the price ceiling. Overall, has the policy made consumers better or worse off? Are all consumers better off? Explain your answer.

Answer 1

(A)

In equilibrium, QD = QS.

400 - 0.4P = 0.4P

0.8P = 400

P = 500

Q = 0.4 x 500 = 200

From demand function: When QD = 0, P = 1000 (vertical intercept) & when P = 0, QD = 400 (horizontal intercept).

From supply function: When QS = 0, P = 0 (vertical intercept)

In following graph, D0 and S0 are demand and supply functions intersecting at point E with price P0 and quantity Q0.

(B)

CS = area AEP0 = (1/2) x (1000 - 500) x 200 = 100 x 500 = 50,000

PS = area BEP0 = (1/2) x 9500 - 0) x 200 = 100 x 500 = 50,000

TS = CS + PS = area AEB = 50,000 + 50,000 = 100,000

(C)

When P = 125,

QD = 400 - 0.4 x 125 = 400 - 50 = 350

QS = 0.4 x 125 = 50

Since QD > QS, there is a shortage of (QD - QS) = 350 - 50 = 300 units.

In graph, at ceiling price Pc (= 125), quantity demanded rises to Qd and quantity supplied falls to Qs.

(D)

With P = 125, market quantity = Qs = 50

When Q = 50, from demand function: 50 = 400 - 0.4P, or P = (400 - 50) / 0.4 = 350 / 0.4 = 875

New CS = area ACFB = (1/2) x [(1000 - 125) + (875 - 125)] x 50 = 25 x (875 + 750) = 25 x 1625 = 40,625

DWL = area CEF = (1/2) x (875 - 125) x (200 - 50) = (1/2) x 750 x 150 = 56,250

Overall CS has decreased. However, those consumers who were able to buy the good at lower ceiling price will be better off.