Question

# The United States Department of Agriculture is interested in analyzing the domestic market for corn. The...

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?

(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.