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Question on lowering the supply

The Reagan Administration introduced new agricultural program named as the Payment-in-Kind Program, in the year of 1983. In order to distinguish how the program worked, let's assume the wheat market. Now assume the government desire to lower the supply of wheat by 25 percent from the free-market equilibrium by paying farmers to withdraw land from production. Though, the payment is made in wheat instead of in dollars--hence the name of the program. The wheat comes from the government's vast reserves that resulted from previous price-support programs. The amount of wheat paid is equivalent to the amount which could have been harvested on the land withdrawn from production. Farmers are free to sell this wheat on the market. How much is produced by farmers now? How much is supplied indirectly to the market by the government? What is the new market price? How much do the farmers gain? Do consumers gain or lose?
Since the free market supply by farmers is 20 billion bushels, the 25 percent reduction needed by the new Payment-In-Kind (PIK) Program would imply that the farmers now generate 15 billion bushels. To encourage farmers to withdraw their land from cultivation, the government have to give them 5 billion bushels, which they sell on the market.
Since the total supply to the market is still 20 billion bushels, the market price does not change; this remains at $4 per bushel. The farmers gain $20 billion, equal to ($4)(5 billion bushels), from the PIK Program, since they incur no costs in supplying the wheat (which they received from the government) to the market. The PIK program does not influence consumers in the wheat market, since they purchase the similar amount at the same price as they did in the free market case.

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