Question

The wheat market is perfectly competitive, and the market supply and demand curves are given by the following equations: 

QD = 20,000,000 - 4,000,000P 

QS = 7,000,000 + 2,500,000P, 

where QD and QS are quantity demanded and quantity supplied measured in bushels, and P = price per bushel.

 a. Determine consumer surplus at the equilibrium price and quantity.

 b. Assume that the government has imposed a price floor at $2.25 per bushel and agrees to buy any resulting excess supply. How many bushels of wheat will the government be forced to buy? Determine consumer surplus with the price floor.

Answer 1

a)

Given QD=20000000-4000000P

QS=7000000+2500000P

In equilibrium,QD=QS

20000000-4000000P=7000000+2500000P

13000000=6500000P

P=(13000000/6500000)=$2 per bushel

QD=20000000-4000000*2=12000000 bushels

QS=7000000+2500000*2=12000000 bushels

So,

Equilibrium Price=$2 per bushel

Equilibrium Quantity=12,000,000 bushels

For finding the CS, we need to find the price at which quantity demanded is zero i.e. QD=0

20000000-4000000P=0

P=20000000/4000000=$5

Consumer surplus is the area below demand curve but above existing price. So, CS at equilibrium price is given by

CS=1/2*(12000000)*(5-2)=$18,000,000

b)

If Price floor mandates a minimum price of $2.25 per bushel

QD=20000000-4000000P=20000000-4000000*2.25=11000000 bushels

QS=7000000+2500000P=7000000+2500000*2.25=12625000 bushels

Excess Supply=12625000-11000000=1625000 bushels

Government will be forced to buy 1,625,000 bushels

Consumer Surplus in the case of price floor is given by

CS=1/2*(11000000)*(5-2.25)=$15,125,000

Answer 2