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