Question

1. The market for rice in a country has the following demand and supply functions: Demand function:                      P = 6 – 0.5QD

Supply function:         P = 2 + 0.5QS

Where QD is the quantity demanded, QS is the quantity supplied and P is the unit price of rice.

1. Determine the equilibrium price, quantity, consumer surplus and producer surplus in the rice market. Illustrate your answers with a suitable rice market diagram.

(8 marks)

2. To help the rice farmers, the government has decided to impose a price floor on rice at $5.50 per unit. At this price, calculate the consumer surplus, the producer surplus and the deadweight loss in the rice market. Are the farmers better off under this policy? Explain.

(12 marks)

Answer 1

free Price 3.3 Desmond 7 12 puentity - 1 4

Demand: P = 6 - 0.5Q

Supply: P = 2 + 0.5Q

a) At equilibrium, demand equals supply

6 - 0.5Q = 2 + 0.5Q

Q = 4

At this quantity, P = 4

Consumer surplus in this market is area of portion A + B + C whose sum is (1/2) * (4 - 0) * (6 - 4) = 4

Producer surplus in this market is area of portion D + E + F whose sum is (1/2) * (4 - 0) * (4 - 2) = 4

b) Under price floor of $5.5

Consumer surplus in this market is area of portion A whose sum is (1/2) * (1 - 0) * (6 - 5.5) = 0.25

Producer surplus in this market is area of portion D + B + F whose sum is (1/2) * (1 - 0) * (2.5 - 2) + (5.5 - 2.5) * (1 - 0) = 3.25

Deadweight loss under price floor is sum of portion C + E whose sum is (1/2) * (4 - 1) * (5.5 - 2.5) = 4.5

Farmers as a producer are not better off as producer surplus falls from 4 to 3.25.