Tariffs in a partial equilibrium framework

Begin by considering the effects of a tariff imposed on a single commodity. Assume that the industry involved is a very small part of the total economy. It is so small, in fact, that changes in this industry have negligible effects on the rest of the economy, and these effects can be ignored. We call this framework partial equilibrium analysis. Also, we consider the case of a competitive market, where an industry supply curve represents the aggregate response of many individual firms to the market price. No single firm is big enough to affect the market price by its own decision to increase or decrease output. The fortunes of one farmer lucky enough to produce 90 bushels of oats per acre under perfect weather conditions or unlucky enough to have a hail storm reduce the farm's output to 10 bushels per acre will be too small to affect the market price of oats. In Chapter 6 we consider situations where there are fewer firms in an industry and each one has some power to influence the market price.

The small-country case

In the left panel of Figure 5.1, we show Country A's domestic demand (D) and supply (S) curves for a particular commodity, say, oats. If trade is free, oats will be imported into Country A at the prevailing world price, Pw. At that price, Country A's total consumption will be 100, its production will be 60, and imports will make up the difference, 40. Total supply (60 of domestic output plus 40 of imports) equals total demand (100) at that price. Alternatively, we can show this same situation in the right panel of Figure 5.1, where we use the residual import demand curve first presented in Chapter 2. Note that there is no demand for imports at a price of oats greater than the autarky price, PA. At a price lower than PR where the domestic supply curve cuts the vertical axis and the quantity supplied equals zero, then the import demand curve is the same as the market demand curve. At prices between PA and PR the quantity of imports demanded is simply the difference between the quantity demanded and the quantity supplied domestically. At the world price PW the import quantity is 40.

Now suppose that Country A imposes a tariff, equal to T or $.50 per bushel, on imports of oats. The immediate result of the tariff is that the price of oats in Country A will rise by the amount of the tariff to PT. In this section of the chapter we assume that the world price of oats remains unchanged when Country A imposes its tariff. That is, we assume that Country A is a small country whose actions will not affect the world market. The increase in price has a number of effects that can conveniently be examined in Figure 5.1. The first effect is that the consumption of oats is reduced from 100 to 95. The second effect is that domestic output rises from 60 to 70. Domestic producers do not pay the import tariff, of course, and the higher domestic price gives them an incentive to increase their output, as indicated by a movement along the supply curve. The third effect is that imports fall from 40 to 25. Both the fall in consumption and the rise in production cut into the previous level

Quantity of oats Imports of oats

Figure 5.1 The effects of a tariff: partial equilibrium, small-country case. The imposition of a $50 per ton tariff shifts the world supply price from PW at $100 to PT at $150, reducing the volume of imports from 40 tons to 25. The lost consumers' surplus, a + b + c + d, is divided between the government, which takes in tariff revenues of area c, and the domestic industry, which receives additional producers' surplus of area a. Triangles b and d are deadweight losses.

Quantity of oats Imports of oats

Figure 5.1 The effects of a tariff: partial equilibrium, small-country case. The imposition of a $50 per ton tariff shifts the world supply price from PW at $100 to PT at $150, reducing the volume of imports from 40 tons to 25. The lost consumers' surplus, a + b + c + d, is divided between the government, which takes in tariff revenues of area c, and the domestic industry, which receives additional producers' surplus of area a. Triangles b and d are deadweight losses.

of imports of oats. Note that if the tariff were large enough to raise the price to PA imports would fall to zero. Domestic producers would supply the entire demand. This would be a prohibitive tariff.

We can also use Figure 5.1 to show the welfare gains and losses that result from the tariff. To show these gains and losses, we use the concepts of consumers' surplus and producers' surplus. First, we recognize that the area under the demand curve shows what consumers are willing to pay for a product. Consumers are willing to pay a lot for the first bushel of oats fed to a champion race horse, but because consumers value each succeeding bushel less they offer a progressively lower price shown as we move downward along the demand curve. Another way of interpreting this downward slope is that many consumers are likely to require a reduction in price to convince them to switch from a breakfast of bacon and eggs or bagels and cream cheese to oatmeal. When consumers pay the market price for all of the bushels purchased, they receive a benefit given by the difference between the price they are willing to pay and the price they actually have to pay for each of the bushels bought. At the world price PW this measure of consumers' surplus is the triangle PKNPW, which is the total area under the demand curve, PgNj^O, less the amount spent on oats, P^Nj^O. Imposition of the tariff reduces the consumers' surplus to PKMPT, a reduction equal to the area of the trapezoid PWPTMN. That trapezoid includes the separate areas a, b, c, and d. For those who like to confirm such calculations numerically, the area is $4,875 for the values show in the diagram.

Although consumers lose from the imposition of the tariff, domestic producers gain. They are now able to charge a higher price and sell a larger quantity, which causes their revenues to rise by areas a, b, and f. Not all of that additional revenue represents higher profits, though, because domestic costs of production rise too. In a competitive industry where the supply curve is based upon the marginal cost of output of the firms in the industry, the extra cost of producing QQ2 of output is areas b + f. Therefore, the change in producers' surplus is the change in revenue minus the change in cost, area a, which equals $3,250 for the numerical values shown. Alternatively, area a can be interpreted as a windfall gain to domestic producers. Previously, they were willing to sell Q1 of output at PW, and now they receive PT, a gain of $.50 per bushel. Also, as they expand output from Q1 to Q2, PT exceeds the extra cost of producing that output for all bushels except the very last one at Q2. The gain on existing output plus additional output motivated by the tariff is represented by area a. A final way to think of this change in producers' surplus is to calculate the value of producers' surplus before the tariff is imposed and then calculate it after the tariff is imposed. We define producers' surplus as the difference between the price that a supplier is willing to accept compared to the price actually received in the market. Because the price a firm is willing to accept is given by the supply curve, area e represents the initial value of producers' surplus. When price rises to PT, then the producers' surplus triangle becomes e + a, and the change in producers' surplus is represented by the trapezoid a.

Not only do domestic producers gain, but the government also gains tariff revenue equal to area c. The tariff revenue is equal to the tariff, T, times the imports on which the tariff is collected, Q2Q3, which equals $1,250 for the numerical values shown. It is a transfer from consumers to the government.

From a national point of view, therefore, areas a and c are not net losses; they are transfers from consumers to producers and to the government, respectively. But the situation is different for the remaining pieces of the decreased consumer surplus. Areas b and d are lost to consumers, but they are not gained by any other sector. These areas therefore represent the net welfare loss resulting from the tariff, sometimes called the deadweight loss. Area b can be thought of as a loss resulting from inefficiency in production, as resources are drawn into oats production and paid more than would be needed to buy imported oats through free trade. Similarly, area d is a loss from a less favorable consumption choice. Consumers are willing to pay areas d + g for Q3Q4 of oats, but when the tariff causes them to buy other products they only get satisfaction equivalent to g and lose area d. The numerical values of areas b and d are $250 and $125, respectively, giving a total deadweight loss of $375.

The net effects of a tariff that we have identified in the left panel of Figure 5.1 can also be derived in the right panel. The apparent loss in consumers' surplus that we infer from the import demand curve is given by areas c + b + d. Because this is a residual demand curve, however, it represents the loss to consumers net of the gain to producers. Thus, area a does not appear, and looking at the import market alone misses important distributional effects within the country that imposes the tariff. Nevertheless, we can observe the same gain in tariff revenue, given by T times the quantity of imports, or area c. The same deadweight loss, areas b + d, arises as the quantity of imports falls. We know the single deadweight loss triangle in the import market must equal the two deadweight loss triangles in the domestic market; the change in price is identical and the two quantities that serve as the bases of triangles b and d (the change in domestic production and the change in consumption) are exactly equal to the change in the quantity of imports that serves as the base of the triangle in the import market. For the numerical values shown in Figure 5.1, the deadweight loss triangle shown in the import market is $375, which is identical to what we reported earlier based on the left panel of the figure. The import market representation is particularly useful when we consider other policies and relax the small country assumption of a horizontal foreign supply curve, and therefore we introduce it here.

Calculations of deadweight losses from tariffs often turn out to be quite small when expressed as a share of GDP, which causes some critics to say there is no reason to worry about the loss in efficiency from current tariffs. Nevertheless, that may not be the most

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