Question

The United States Department of Agriculture is interested in analyzing the domestic market for corn. The USDA’s staff economists estimate the following equations for the demand and supply curves:

Qd= 1600-125P

Qs= 440+165P

Quantities are measured in millions of bushels; prices are measured in dollars per bushel.

A. Calculate the equilibrium price and quantity that will prevail under a completely free market.

B. Calculate the price elasticities of supply and demand at the equilibrium values.

C. The government currently has a $4.50 bushel support price in place. What impact will this support price have on the market? Will the government be forced to purchase corn under a program that requires them to buy up any surpluses? If so, how much?

Answer 1

(A) In equilibrium, Qd = Qs

1600 - 125P = 440 + 165P

290P = 1160

P = $4

Q = 1600 - (125 x 4) = 1600 - 500 = 1100

(B) When Q =Qd = Qs = 1100 & P = $4,

Elasticity of demand = (dQd/dP) x (P/Qd) = - 125 x (4/1100) = - 0.45

Elasticity of supply = (dQs/dP) x (P/Qs) = 165 x (4/1100) = 0.60

(C) When P = $4.5,

Qd = 1600 - (125 x 4.5) = 1600 - 562.5

Qs = 440 + (165 x 4.5) = 440 + 742.5 = 1182.5

Since Qs > Qd, there is a surplus equal to (1182.5 - 562.5) = 620 units.

Therefore government will be forced to buy this surplus at $4.5 per unit, for a total of ($4.5 x 620) = $2790.