Pindyck, Robert S. and Daniel L. Rubinfeld. Microeconomics. 3d ed. Prentice Hall: Englewood Cliffs, NJ, 1995, pp.300-305.

9.5 Import Quotas and Tariffs

Many countries use import quotas and tariffs to keep the domestic price of a product above world levels and thereby enable the domestic industry to enjoy higher profits than it would under free trade. As we will see, the cost to society from this protection can be high, with the loss to consumers exceeding the gain to domestic producers.

Without a quota or tariff, a country will import a good when its world price is below the market price that would prevail if there were no imports. Figure 9.15 illustrates this. S and D are the domestic supply and demand curves. If there were no imports, the domestic price and quantity would be Po and Qo, which equate supply and demand. But the world price Pw, is below Po, so domestic consumers have an incentive to purchase from abroad, which they will do if imports are not restricted. How much will be imported? The domestic price will fall to the world price Po, and at this lower price domestic production will fall to Qs, and domestic consumption will rise to Qd. Imports are then the difference between domestic consumption and domestic production, Qd - Qs.
Now suppose the government, bowing to pressure from the domestic industry, eliminates imports by imposing a quota of zero (i.e., forbidding any importation of the good). What are the gains and losses from such a policy?

With no imports allowed, the domestic price will rise to Po. Consumers who still purchase the good (in quantity Q0) will pay more and will lose an amount of surplus given by trapezoid A and triangle B. Also, given this higher price, some consumers will no longer buy the good, so there is an additional loss of consumer surplus, given by triangle C. The total change in consumer surplus is therefore

chCS = -A - B - C

What about producers? Output is now higher (Qo instead of Qd) and is sold at a higher price (Po instead of Pw). Producer surplus therefore increases by the amount of trapezoid A:

chPS = A

The change in total surplus, chCS + chPS, is therefore -B - C. Again, there is a deadweight loss consumers lose more than producers gain.

Imports could also be reduced to zero by imposing a large enough tariff. The tariff would have to be equal to or greater than the difference between Po and Pw. With a tariff of this size, there will be no imports and therefore no government revenue from tariff collections, so the effect on consumers and producers would be the same as with a quota.

More often, government policy is designed to reduce, but not eliminate, imports. Again, this can be done with either a tariff or a quota, as Figure 9.16 shows. With free trade the domestic price will equal the world price Pw,, and imports will be Qd - Qs. Now suppose a tariff of T dollars per unit is imposed on imports. Then the domestic price will rise to P* (the world price plus the tarif0; domestic production will rise; and domestic consumption will fall.

In Figure 9.16 this tariff leads to a change of consumer surplus given by

chCS = -A - B - C - D

The change in producer surplus is again

chPS = A

Finally, the government will collect revenue in the amount of the tariff times the quantity of imports, which is rectangle D. The total change in welfare, chCS plus chPS plus the revenue to the government, is therefore -A - B - C - D + A + D = -B - C. Triangles B and C again represent the deadweight loss from restricting imports. (B represents the loss from domestic overproduction, and C the loss from too little consumption.)

Suppose the government uses a quota instead of a tariff to restrict imports: Foreign producers can only ship a specific quantity (Qd' - Qs' in Figure 9.16) to the United States. Foreign producers can then charge the higher price P* for their U.S. sales. The changes in U.S. consumer and producer surplus will be the same as with the tariff, but instead of the U.S. government collecting the revenue given by rectangle D, this money will go to the foreign producers as higher profits. Compared with the tariff, the United States as a whole will be even worse off, losing D as well as the deadweight loss B and C?14

This is exactly what happened with automobile imports from Japan in the 1980s. The Reagan administration, under pressure from domestic automobile producers, negotiated "voluntary" import restraints, under which the Japanese agreed to restrict their shipments of cars to the United States. The Japanese could therefore sell those cars that were shipped at a price higher than the world level and capture a higher profit margin on each one. The United States would have been better off by simply imposing a tariff on these imports.

The Sugar Quota

In recent years the world price of sugar has been as low as 4 cents per pound, while the United States price has been above 25 cents per pound. Why? By restricting imports the U.S. government protects the $3 billion domestic sugar industry, which would virtually be put out of business if it had to compete with low-cost foreign producers. This has been good news for U.S. sugar producers. It has even been good news for some foreign sugar producers---those whose successful lobbying efforts have given them big shares of the quota. But like most policies of this sort, it has been bad news for consumers.

To see just how bad, let's look at the sugar market in 1989. Here are the relevant data for that year:

At these prices and quantities, the price elasticity of U.S. supply is 1.54, and the price elasticity of U.S. demand is -0.3?15

We will fit linear supply and demand curves to these data, and then use them to calculate the effects of the quotas. You can verify that the following U.S. supply curve is consistent with a production level of 13.7 billion pounds, a price of 23 cents per pound, and a supply elasticity of 1.5416:

U.S. Supply: Qs = -7.46 + 0.92P

where quantity is measured in billions of pounds and price in cents per pound. Similarly, the -0.3 demand elasticity together with the data for U.S. consumption and U.S. price give the following linear demand curve:

U.S. Demand: Qd = 22.8 - 0.23P

These supply and demand curves are plotted in Figure 9.17. At the 12.5 cent world price, U.S. production would have been only 4 billion pounds, and U.S. consumption would have been about 20 billion pounds, most of this imports. But fortunately for U.S. producers, imports were limited to only 3.8 billion pounds, which pushed the price up to 23 cents.

What did this cost U.S. consumers? The lost consumer surplus is given by the sum of trapezoid A, triangles B and C, and rectangle D. You should go through the calculations to verify that trapezoid A is equal to $929 million, triangle B to $509 million, triangle C to $126 million, and rectangle D to $399 million, so that the total cost to consumers in 1989 was about $2 billion.

How much did producers gain from this policy? Their increase in surplus is given by trapezoid A (i.e., $929 million). The $399 million of rectangle D was a gain for those foreign producers who succeeded in obtaining large allotments of the quota because they received a higher price for their sugar. Triangles B and C represent a deadweight loss of $635 million.

    14. Alternatively, an import quota can be maintained by rationing imports to U.S. importing firms or trading companies. These middlemen would have the rights to import a fixed amount of the good each year. These rights are valuable because the middleman can buy the product on the world market at price Pw and then sell it at price P*. The aggregate value of these rights is therefore given by rectangle D. If the government sells the rights for this amount of money, it can capture the same revenue it would receive with a tariff. But if these rights are given away, as sometimes happens, the money will go instead as a windfall to middlemen.

    15. These data and elasticity estimates are based on Morris E. Morkre and David G. Tart, Effects of Restrictions on United States Imports: Five Case Studies and Theory, U.S. Federal Trade Commission Staff Report, June 1981, and F. M. Scherer, 'The United States Sugar Program,' Kennedy School of Government Case Study, Harvard University, 1992. For a general discussion of sugar quotas and other aspects of U.S. agricultural policy, see D. Gale Johnson, Agricultural Policy and Trade (New York: New York University Press, 1985); and Gail L. Cramer and Clarence W. Jensen, Agricultural Economics and Agribusiness (New York: Wiley, 1985).

    16. Turn to Section 2.5 of Chapter 2 to review how to fit linear supply and demand functions to data of this kind.