Question

20. (7 marks) Use the diagram below to answer the following questions 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Q a. If there is a price floor at P = 6 calculate the consumer surplus b. If there is a price floor at P=6 calculate the producer surplus. c. If there is a price floor at P=6 calculate the deadweight loss. d. If there is a price ceiling at P=2 calculate the shortage. e. If there is a price ceiling at P=2 calculate the producer surplus. f. If there is quota at Q=2 calculate the consumer surplus. g. If there is quota at Q=2 calculate the producer surplus.

Answer 1

Solution: The equilibrium price is at $4 and equilibrium quantity is at 8 units.

a) If there is a price floor at P=6, the consumer surplus is:

area of triangle ABE' = 1/2*base*height

area of triangle ABE' = 1/2*(6-0)*(12-6)

area of triangle ABE' = 1/2*6*6 = 18

The consumer surplus is $18

b) If there is price floor at P=6, the producer surplus is:

area of BODE' = area of rectangle BCDE' + area of triangle OCD

area of BODE' = (length*breadth) + 1/2*(base)*(height)

area of BODE' = (6-3)*(6-0) + 1/2*(3-0)*(6-0)

area of BODE' = 18 + 9 = 27

The producer surplus is $27

c) If there is price floor at P=6, the Deadweight loss is:

area of triangle DEE' = area of EFE' + area of FDE

area of triangle DEE' = 1/2*(6-4)*(8-6) + 1/2*(8-6)*(4-3)

area of triangle DEE' = 2 + 1 = 3

Deadweight loss is $3

d)

The shortage is given by : Quantity demanded - Quantity supplied

Here at Price ceiling at $2 the quantity demanded is 10 and the quantity supplied is 4 hence

Shortage = 10 - 4 = 6

e) The producer surplus at price ceiling $2 is

area of COE' = 1/2*base*height

area of COE' = 1/2*4*2 = $4