Question

Suppose the corn market has the following equations: QD = 3000 - 400P QS = 900 + 300P Where QD and QS are quantity demanded and quantity supplied measured in bushels, and P = price per bushel.

Determine consumer surplus at the equilibrium price and quantity. 6 marks

Assume that the government has imposed a price floor at $3.50 per bushel and agrees to buy any resulting excess supply. How many bushels of corns will the government be forced to buy? Determine consumer surplus with the price floor. 6 marks

Answer 1

The equilibrium occurs at a point where Qd=Qs, Qd = 3000 - 400P, at Q=0, P = 7.5 and QS = 900 + 300P at Q=0, P = -3

3000 - 400P = 900 + 300P

700P = 2100

P = $3 (Price at equilibrium)

Q = 900+300*3 = 1800 (Quantity at equilibrium)

The Consumer Surplus = 0.3*(7.5-3)*1800 = 2430

if price floor of 3.5 is imposed, Qd = 3000-400*3.5 = 1600 and Qs = 900+300*3.5=1950

Excess unsold stock = 1950*1600 = 350 this is the quantity which the govt will be forced to buy

Consumer surplus = 0.5*(7.5-3.5)*1600 =3200 at price floor