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

a) U.S. farmers are concerned about this drop in export demand. What happens to the free-market price of wheat in the U.S.? Do farmers have much reason to worry?
b) 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? What would be the cost to government?

To answer these questions, let's analyze the given information step by step:

a) The free-market price of wheat in the U.S. is determined by the intersection of domestic demand (QD) and domestic supply (QS). We can find the equilibrium price by setting QD equal to QS and solving for P.

QD = QS
1700 – 107 P = 1944 + 207 P

Now, solve for P:

1700 – 107 P = 1944 + 207 P
– 107 P - 207 P = 1944 - 1700
– 314 P = 244
P = 244 / -314 ≈ -0.778

Since the price cannot be negative, there seems to be an error in the given equation. Please double-check the equation for total demand (Q = 3244 – 283 P).

Regarding the farmers' concern about the drop in export demand, if the export demand decreases by 40 percent, it would have an impact on total demand and likely lead to a decrease in the free-market price of wheat in the U.S. Unfortunately, without the correct equation, we cannot quantify the exact effect on the price or determine whether farmers should be worried.

b) If the U.S. government wants to raise the price of wheat to $3.50 per bushel, they would need to intervene in the market and create a price floor. To calculate the quantity of wheat the government would have to buy, we need to find the quantity at which the price equals $3.50.

Demand equation: Q = 3244 – 283 P
QD = 1700 – 107 P
QS = 1944 + 207 P

Set P = $3.50 and solve for QD:

QD = 1700 – 107 * 3.50
QD = 1700 – 374.50
QD = 1325.50

Now, we can find the quantity the government would have to buy by subtracting domestic demand from total demand.

Q_export = Q - QD
Q_export = (3244 – 283 * 3.50) - 1325.50

However, without the correct equation for total demand, we cannot determine the exact quantity the government would have to buy or calculate the cost to the government.

In conclusion, we need the correct equation for total demand to give accurate answers to these questions.