Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 4

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: a. Suppose the demand function is \(Q^{D}=28-2 P\) and the supply function is \(Q^{s}=4+4 P\), 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. b. 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 The amount of wheat paid is equal to the amount that could have been harvested on the land withdrawn from production.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? c. 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

Expert verified
The free-market equilibrium price and quantity for the wheat market are $4 and 20 billion bushels respectively. After the government's intervention, farmers now produce 15 billion bushels and the government supplies 5 billion bushels, maintaining the price at $4. Farmers gain $20 billion. Consumers neither gain nor lose. The program could potentially lead to reliance on government aid and decrease in farmers' productivity, and wastage if excesses are always dealt with the same way.

Step by step solution

01

Determine the free-market equilibrium

To find the equilibrium price and quantity, we must set the demand function equal to the supply function: \(Q^{D}=Q^{S}\) or \(28 - 2P = 4 + 4P\). Solving this equation for \(P\) we get the equilibrium price, \(P=\$4\). Putting this value back into equilibrium equation, we get the equilibrium quantity, \(Q=20\) billion bushels.
02

Calculate the new quantity produced

Next we deduct 25 percent from the original quantity: \(0.75 * 20 = 15\) billion bushels. This is now the amount of wheat produced by farmers.
03

Determine the amount supplied by the government

The amount of wheat supplied by the government equals the amount of the reduction, which is \(20-15=5\) billion bushels.
04

Find the new market price

We find the new price by substituting the total quantity after the government intervention (which is 15 billion bushels by farmers and 5 billion bushels by government, \(Q=20\) in total) into the demand function and solving it for \(P\). So, \(P=\(1/2)*(28-Q)=\$4\), the price remains the same.
05

Evaluate the gains for farmers and consumers

The farmers' gain equals the amount of wheat allocated by the government times the market price, which is \(5*\$4 = \$20\) billion. Given that the price doesn't change, consumers neither gain nor lose.
06

Assess the program's effect on taxpayers and potential problems

From taxpayer's point of view, this programs seems to be beneficial, as instead of storing or destroying excess wheat, it is used to compensate farmers. However, this might result in farmers becoming too reliant on government aid and dis-incentivizing them to increase their productivity. Moreover, this might lead to waste if the government always intervenes whenever there is a surplus.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The United States currently imports all of its coffee. The annual demand for coffee by U.S. consumers is given by the demand curve \(Q=250-10 P,\) where \(Q\) is quantity (in millions of pounds) and \(P\) is the market price per pound of coffee. World producers can harvest and ship coffee to U.S. distributors at a constant marginal \((=\text { average })\) cost of \(\$ 8\) per pound. U.S. distributors can in turn distribute coffee for a constant \(\$ 2\) per pound. The U.S. coffee market is competitive. Congress is considering a tariff on coffee imports of \(\$ 2\) per pound. a. If there is no tariff, how much do consumers pay for a pound of coffee? What is the quantity demanded? b. If the tariff is imposed, how much will consumers pay for a pound of coffee? What is the quantity demanded? c. Calculate the lost consumer surplus. d. Calculate the tax revenue collected by the government. e. Does the tariff result in a net gain or a net loss to society as a whole?

The domestic supply and demand curves for hula beans are as follows: \\[ \begin{aligned} \text {Supply:} & P=50+Q \\ \text {Demand:} & P=200-2 Q \end{aligned} \\] where \(P\) is the price in cents per pound and \(Q\) is the quantity in millions of pounds. The U.S. is a small producer in the world hula bean market, where the current price (which will not be affected by anything we do) is 60 cents per pound. Congress is considering a tariff of 40 cents per pound. Find the domestic price of hula beans that will result if the tariff is imposed. Also compute the dollar gain or loss to domestic consumers, domestic producers, and government revenue from the tariff

Suppose the market for widgets can be described by the following equations: \\[ \begin{array}{cl} \text {Demand:} & P=10-Q \\ \text {Supply:} & P=Q-4 \end{array} \\] where \(P\) is the price in dollars per unit and \(Q\) is the quantity in thousands of units. Then: a. What is the equilibrium price and quantity? b. Suppose the government imposes a tax of \(\$ 1\) per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? What amount per unit will the seller receive? c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. The tax is removed and a subsidy of \(\$ 1\) per unit granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government?

From time to time, Congress has raised the minimum wage. Some people suggested that a government subsidy could help employers finance the higher wage. This exercise examines the economics of a minimum wage and wage subsidies. Suppose the supply of lowskilled labor is given by \\[ L^{s}=10 w \\] where \(L^{\mathrm{s}}\) is the quantity of low-skilled labor (in millions of persons employed each year), and \(w\) is the wage rate (in dollars per hour). The demand for labor is given by \\[ L^{D}=80-10 w \\] a. What will be the free-market wage rate and employment level? Suppose the government sets a minimum wage of \(\$ 5\) per hour. How many people would then be employed? b. Suppose that instead of a minimum wage, the government pays a subsidy of \(\$ 1\) per hour for each employee. What will the total level of employment be now? What will the equilibrium wage rate be?

Among the tax proposals regularly considered by Congress is an additional tax on distilled liquors. The tax would not apply to beer. The price elasticity of supply of liquor is \(4.0,\) and the price elasticity of demand is \(-0.2 .\) The cross-elasticity of demand for beer with respect to the price of liquor is 0.1 a. If the new tax is imposed, who will bear the greater burden-liquor suppliers or liquor consumers? Why? b. Assuming that beer supply is infinitely elastic, how will the new tax affect the beer market?
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free