The supply and demand curves for corn are as follows:
Q_D = 3,750 - 725P
Q_S = 920 + 690P,
where Q = millions of bushels and P = price per bushel.
a. Calculate the equilibrium price and quantity that would prevail in the free market.
b. The government has imposed a $2.50 per bushel support price. How much corn will the government be forced to purchase?
c. Calculate the loss in consumer surplus that would occur under the support program.

a.set Q_D = Q_S
3,750 - 725P = 920 + 690P
2,830 = 1,415P
P = 2.00
Q_D = 3,750 - 725(2) = 2,300
b.To solve for government quantity, Q_G, we realize that:
Q_G = Q_S - Q_D
920 + 690P = 3750 - 725P + Q_G
Q_G = 1415P - 2830
Quantity supplied at the support price of $2.50 is:
Q_S = 920 + 650(2.50)
Q_S = 2645
Quantity demanded at the support price of $2.50 is:
Q_D = 3750 - 725(2.50)
Q_D = 1937.50
Government quantity purchased is then 707.5 bushels.
c.Solve supply and demand for P in terms of Q:
Q_D = 3750 - 725P
P = 5.17 - 0.0014Q
Q_S = 920 + 690P
P = -1.33 + 0.00145Q Q_D at P = 2.50
Q_D = 3750 - 725(2.50)
Q_D = 1937.50
C.S. under free market: = 0.5(5.17 - 2.00) × 2300
C.S. under free market = 3645.5
C.S. under support price: = 0.5(5.17 - 2.50) × 1937.50
C.S. under price support = 2586.56
Price support results in a loss of $1058.94 in consumer surplus.