Question

Q3. Suppose the market for clothes in the U.S. is perfectly competitive and is characterized by the following demand and supply equations (Q=quantity and P=Price): (34 pts in total) Demand for clothes: Qd 40 – 0.2P Supply of clothes: Qs 0.4P - 20 A. Find the market clearing equilibrium price P* and quantity Q* and draw a carefully labeled graph illustrating the market equilibrium. Also calculate the consumer surplus and producer surplus. (8pts) B. Suppose that the U.S. opens up to the world market and the price for clothes is in the world market is 70. What is the quantity demanded by consumer (Qd)? What is the quantity supplied by U.S. suppliers (Qs)? What is the new equilibrium price P′ in the U.S.? Does the U.S. import or export clothes? What is the new CS for U.S. consumers and PS for the U.S. suppliers? Illustrate the new CS and PS on another graph(12 pts) Q* =20 P* =100 CS =1000 PS =500

Answer 1

(A) In equilibrium, Qd = Qs

40 - 0.2P = 0.4P - 20

0.6P = 60

P* = 100

Q* = 40 - (0.2 x 100) = 40 - 20 = 20

From demand function, When Qd = 0, P = 40/0.2 = 200 (Vertical intercept)

From supply function, When Qs = 0, P = 20/0.4 = 50 (Vertical intercept)

In following graph, AB & CD are demand & supply curves with above intercepts, intersecting at point E with price P* (= 100) and quantity Q* (= 20).

Consumer surplus (CS) = Area between demand curve & market price = Area AEP*

= (1/2) x (200 - 100) x 20 = 10 x 100 = 1,000

Producer surplus (PS) = Area between supply curve & market price = Area CEP*

= (1/2) x (100 - 50) x 20 = 10 x 50 = 500

(B) When world price is 70,

Qd = 40 - (0.2 x 70) = 40 - 14 = 26

Qs = (0.4 x 70) - 20 = 28 - 20 = 8

New price = World price = 70

Since World price < Free-market equilibrium price, US is an importer.

New CS = Area AFP' = (1/2) x (200 - 70) x 26 = 13 x 130 = 1,690

New PS = Area CGP' = (1/2) x 8 x (70 - 50) = 4 x 20 = 80