Question

1. A market has supply and demand curves that follow the following set of equations: Supply P = 30s + 6 Demand P = -20p + 146. For both of these problems pictures are not required but the problems may be much easier if you draw some. a) Find the equilibrium price and quantity in this market and the consumer and producer surplus from the equilibrium price and quantity. (1 point) b) If there is a ceiling price in this market of 78, find the new consumer surplus as well as the new producer surplus. Use these numbers to find the size of the deadweight loss. (1 point) c) Explain why, based on the numbers calculated above, someone could argue that, as a group, consumers are better off with the ceiling price even though some individual consumers are worse off with the ceiling price. (1 point)

Answer 1

a) At equilibrium,

Demand equals supply

3Q + 6 = -2Q + 146

Q = 28

P = 90

Equilibrium occurs at point D

Consumer surplus is area of triangle ABD whose area is (1/2) * (28 - 0) * (146 - 90) = 784

Producer surplus is area of triangle BCD whose area is (1/2) * (28 - 0) * (90 - 6) = 1,176

trie 2146 625 2813

b) With price ceiling at $78,

Consumer surplus is area of triangle AGF + area of rectangle FGHE whose area is (1/2) * (24 - 0) * (146 - 98) + (98 - 78) * (24 - 0) = 1,056

Producer surplus is area of triangle EHC whose area is (!/2) * (24 - 0) * (78 - 6) = 864

Deadweight loss is area of triangle GHD whose area is (1/2) * (28 - 24) * (98 - 78) = 40

A-146 fos ge- В 9 - Price Ceiling €278 13 24 28

c) Due to price ceiling, there is less supply of goods than the desired quantity in the market which creates a shortage of goods in the market. Consumers who are willing to higher quantity than this would be hurt off.