Question

In 1983, the Reagan administration introduced a new agricultural program called the Payment-in-Kind Program. To see how the program worked, let’s consider the wheat market:

1. Suppose the demand function is QD = 28 - 2P and the supply function is QS = 4 + 4P, where P is the price of wheat in dollars per bushel, and Q is the quantity in billions of bushels. Find the free-market equilibrium price and quantity.

2. Now suppose the government wants to lower the supply of wheat by 25 percent from the free-market equilibrium by paying farmers to withdraw land from production. However, the payment is made in wheat rather than in dollars— hence the name of the program. The wheat comes from vast government reserves accumulated from previous price support programs. The amount of wheat paid is equal to the amount that could have been harvested on the land withdrawn from production. Farmers are free to sell this wheat on the market. How much is now produced by farmers?How much is indirectly supplied to the market by the government? What is the new market price? How much do farmers gain? Do consumers gain or lose?

3. Had the government not given the wheat back to the farmers, it would have stored or destroyed it. Do taxpayers gain from the program? What potential problems does the program create?

Short answer

1. The free-market equilibrium price is $4 per bushel, and quantity is 20 billion bushels.

2. Farmers will produce 18 billion bushels. The government will supply 2 billion bushels in the market. The new market price is $5 per bushel. The farmers will gain $10 billion. The consumers lose.

3. The taxpayers will gain from the program indirectly. The program will create a surplus of wheat in the market.

Step-by-step solution

Step 1. Calculating the free market equilibrium price and quantity.

In a free market situation, the supply should be equal to demand. Hence, the free market equilibrium price and quantity are determined by the demand and supply equations.

$$\begin{gathered} Demand=Supply \\ 28-2P=4+4P \\ 6P=24 \\ P=4 \end{gathered}$$

The equilibrium price is $4 per bushel. By putting the value of P in the supply equation, the equilibrium quantity produced is calculated below:

$$\begin{gathered} Supply=4+4P \\ =4+\left(4\times 4\right) \\ =20 \end{gathered}$$

The equilibrium quantity of wheat produced is 20 billion bushels.

Step 2. Effect of the program on quantity produced by farmers, market price, consumer gain, and quantity supplied by the government.

The program will reduce the supply of wheat in the market by 25 percent. The new supply curve equation would be:

$$\begin{gathered} NewSupply=4+4P-25\%\left(4+4P\right) \\ =4+4P-1-P \\ =3+3P \end{gathered}$$

The reduction of 25 percent in supply will shift the supply curve leftward, causing a new equilibrium point on the demand curve. The quantity produced by farmers and the new price of wheat in the market can be determined by equating the demand equation with the new supply equation.

$$\begin{gathered} Demand=NewSupply \\ 28-2P=3+3P \\ 5P=25 \\ P=5 \end{gathered}$$

The new market price is $5 per bushel. By putting the value of P in the new supply equation, the equilibrium quantity produced is calculated below:

$$\begin{gathered} NewSupply=3+3P \\ =3+\left(3\times 5\right) \\ =18 \end{gathered}$$

Thus, after implementing the program, the farmers will produce 18 billion bushels of wheat for $5 per bushel.

Quantity supplied by the government: It is equal to the difference between the free market supplied quantity (Qf) and the quantity supplied by farmers after implementing the program (Qk). The quantity supplied by the government is:

$$\begin{gathered} Quantitysuppliedbygovernment=Q_f-Q_k \\ =20-18 \\ =2 \end{gathered}$$

Thus, the government supplied 2 billion bushels of wheat.

Gain to farmers:The difference between the return earned by farmers after the implementation of the program and before implementation of it is the gain to farmers.

The return gained by the farmers after the implementation of the program will be the product of supplied quantity (Qk) and the new price of the market (Pk). Similarly, the farmers’ return before implementation of the program will be the product of supplied quantity (Qf) and equilibrium price (Pf). It is calculated below:

$$\begin{gathered} Gaintofarmers=Q_k\left(P_k\right)-Q_f\left(P_f\right) \\ =5\times 18-4\times 20 \\ =90-80 \end{gathered}$$

Impact on consumers: The consumers had to pay a higher price of $1 on purchasing per bushel of wheat. The higher price will reduce the demand for wheat by consumers in the market. Hence, consumers lose from the program.

Step 3. Effect of this program on taxpayers and the potential problem it can cause in the market.

Impact on taxpayers:If the government had not given wheat back to farmers, the government would be compensating the farmers by paying some amount in money to lower the supply of wheat by 25 percent. A payment made by a government comes from the revenue generated through taxation. Hence, if the government chooses to make payments to the farmer in money, the burden will be on taxpayers.

But the government chose to pay the farmers in wheat instead of money. Thus, the taxpayers were relieved from the burden of payments made to farmers. Therefore, they gained from this policy.

A potential problem caused by the program:The reduction in the supply after the program’s implementation has caused the price of wheat to rice. The price increase would reduce the demand for wheat in the market. But quantity supplied by the government to the farmers will also be supplied in the market. The overall impact of the program will create a surplus of wheat in the market.

Either the market forces will bring down the price of wheat back to free equilibrium price because of surplus, or the government would be compelled to buy the surplus wheat. In both cases, the program will be affected negatively.