Question

Much of the demand for U.S. agricultural output has come from other countries. In 1998, the total demand for wheat was Q = 3244 − 283P. Of this, total domestic demand was QD = 1700 − 107P, and domestic supply was QS = 1944 + 207P. Suppose the export demand for wheat falls by 40%.

U.S. farmers are concerned about this drop in export demand. What happens to the free market price of wheat in the United States? Do farmers have much reason to worry?

Now suppose the U.S. government wants to buy enough wheat to raise the price to $3.50 per bushel. With the drop in export demand, how much wheat would the government have to buy? How much would this cost the government?

Answer 1

Domestic supply equation

$Q_s = 1944+207P$

Total demand equation

$Q_d=3244-283P$

Domestic demand equation

$Q_D = 1700-107P$

Export demand equation

$Q_E=Q_d-Q_D \\ Q_E = (3244-283P)-(1700-107P) \\ Q_E = 1544-176P$

Market price is determined at the point where demand equals supply.

$Q_d = Q_s \\ 3244-283P = 1944+207P \\ 1300=490P \\ P =\frac{1300}{490} = 2.65$

A 40 percent drop in export shifts the demand curve to the left by 40 percent. The quantity demand will be 60 percent of what it was. This change is shown by multiplying the export demand equation by 0.6.

The new export demand equation will be

$Q_E = 0.6(1544-176P) \\ Q_E = 926.4-105.6P$

The new total demand will be

$Q_D + Q_E = 1700-107P + 926.4-105.6P \\ = 2626.4-212.6P$

The new price is determined where the supply is equal to new total demand

$Q_s=Q_d \\ 1944+207P = 2626.4-212.6P \\ 419.6P = 682.4 \\ P = \frac{682.4}{419.6} = 1.63$

Due to the fall in the export demand of wheat the price of wheat has fallen from $2.65 to $1.63 which has lowered the earnings of the farmers and is a reason for worry for the farmers.

When price is raised to $3.50, the total demand will be

$2626.4-212.6 \times 3.50 = 1882.3$

Total supply will be

$Q_s = 1944 + 207P \\ = 1944 + 207 \times 3.50 = 2668.5$

The difference between the demand and supply will be the quantity of wheat that the government has to buy to clear the market at the raised price. Thus the government buys

$= 2668.5 – 1882.3 = 786.2$ million bushels

The amount that the government has to pay will be

$= 786.2 \times 3.50 = 2751.7$ million per year