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 percent.

1. 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?

2. 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?

The export demand is the difference between total demand and domestic demand. The export demand will be:

$$\begin{gathered} Qe=QD-Qd \\ =3244-283P-1700+107P \\ =1544-176P \end{gathered}$$

The price and quantity before the fall in export demand are calculated below:

$$\begin{gathered} Q_D=3244-283P \\ {Q}_S=1944+207P \\ D=S \\ 3244-283P=1944+207P \\ 283P+207P=3244-1944 \\ 490P=1300 \\ P=\$2.65 \\ Q=3244-283\left(2.65\right) \\ =2494.05 \end{gathered}$$

The price was $2.65, and the quantity was 2494.05 million bushels.

After a 40% fall in export demand, the export demand curve will be:

$$\begin{gathered} Q{\text{'}}_e=0.6Q_e \\ =0.6\left(1544-176P\right) \\ =926.4-105.6P \end{gathered}$$

Now, the change in total demand will be:

role="math" localid="1643449819603" $$\begin{gathered} Q{\text{'}}_D=Q_d+Q{\text{'}}_e \\ =1700-107P+926.4-105.6P \\ =2626.4-212.6P \end{gathered}$$

The new price and quantity are calculated below:

$$\begin{gathered} Q{\text{'}}_D=2626.4-212.6P \\ {Q}_S=1944+207P \\ D=S \\ 2626.4-212.6P=1944+207P \\ 212.6P+207P=2626.4-1944 \\ 419.6P=682.4 \\ P=\$1.63 \\ Q=2626.4-212.6\left(1.63\right) \\ =2626.4-346.54 \\ =2279.86 \end{gathered}$$

The price is $1.63, and the quantity is 2279.86 million bushels.

The total revenue when the price was $2.65 will be $6609.23 million (=2.65*2494.05), and the total revenue, when the price is $1.63, will be $3716.17 million (=1.63*2279.86). Thus, the farmer has a reason to worry as the total revenue has decreased after the change in export demand.

At $3.50, the quantity demand and quantity supply are calculated below:

$$\begin{gathered} Q{\text{'}}_D=2626.4-212.6\left(3.50\right)=1944+207P \\ =2626.4-744.1 \\ =1882.3 \\ {Q}_S=1944+207\left(3.50\right) \\ =1944+724.5 \\ =2668.5 \end{gathered}$$

The supply is more than the demand; thus, the excess amount will be 786.2 (=2668.5-1882.3) million bushels. The government buys the excess output; thus, the cost to the government will be $2751.7 million (=3.50*786.2).