when are a tariff and a quota equivalent?

When Are a Tariff and a Quota Equivalent?Author(s): Rachel McCullochSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 6, No. 4(Nov., 1973), pp. 503-511Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/134087 .

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WHEN ARE A TARIFF AND A QUOTA EQUIVALENT?

RACHEL McCULLOCH Graduate School of Business, University of Chicago

When Are A Tariff and A Quota Equivalent? This paper extends the work of Bhagwati and others on the "nonequivalence" of tariffs and quotas by taking the motive for protection into account. Specifically, the welfare cost associated with tariff or quota protection of a monopolized domestic industry is shown to depend on the objective underlying protection. Where the objective of protection is to raise domestic price, an import quota results in a lower welfare cost than a tariff which achieves the same objective. A quota may also! provide a less costly means of fixing domestic monopoly profits at a predetermined level than a comparable tariff.

Quand un droit de douane et un contingentement sont-ils equivalents ? Cet article prolonge les travaux de Bhagwati et d'autres sur l'absence d'equivalence entre les droits et les contingentements, en tenant compte des raisons de la protection douaniere. Meme s'il n'y a pas d'equivalence - naturelle - entre les droits et les contingentements quand la production domestique est monopolisee, on peut redefinir l'equivalence en terme de l'objectif particulier qui sous-tend la protection. L'etape suivante consiste 'a comparer les couts en bien-etre de la poursuite de cet objectif par differents moyens.

Quand la protection a pour objectif d'augmenter le prix domestique, un contingentement a l'importation conduit a un cout en bien-etre plus faible qu'un droit de douane qui permettrait d'atteindre le meme resultat. Un contingentement represente probablement aussi un moyen momins cofuteux de fixation des profits de monopoles domestiques a des niveaux predetermines, par comparaison avec un droit comparable. Ces resultats presentent un intetre certain dans la mesure oiu l'on suppose souvent que les contingentements sont particulierement contre-indiques quand la production domestique est monopolisee. Par contraste, lorsque l'objectif vise est l'accroissement de la production domestique ou la reduction des importations, un droit permet d'atteindre les r'sultats vises a un coAt en bien-etre inferieur.

This paper extends the results of Bhagwati (1965) on the "nonequivalence" of tariffs and quotas by adding an essential element to the analysis - the motive for protection.' Specifically, the welfare cost associated with tariff or quota protection of a monopolized domestic industry is shown to depend on the objective underlying protection. Thus, contrary to notions held by many international economists, some goals may be achieved at lower welfare cost with a quota than with a tariff.

The material here contains no major theoretical innovation. Instead, it provides a new way of looking at what is already known about the corn-

1Several notable contributions to the theory of international trade have assessed the use of tariffs as a means of achieving "noneconomic" objectives. See, especially, Johnson (1960) and Bhagwati and Srinivasan (1969). This paper extends earlier results by comparing tariffs and quotas as alternative means of achieving policy objectives. These may be the relevant alternatives where political considerations rule out the use of direct subsidies, or where a weak fiscal authority makes additional domestic taxation impractical.

In place of the term "noneconomic" which Johnson, Bhagwati and Srinivasan, and others use, it seems preferable to distinguish objectives which are "outside the model" - usually because they are difficult to formulate precisely. Most of the objectives are indeed economic. (An alternative approach suggested by Bhagwati and Srinivasan is to treat the level of the objective as an argument of the social welfare function. In this way, the level of the objective is itself the outcome of an explicit maximizing process.)

Canadian Journal of Economics/Revue canadienne d'Economique, VI, no. 4 November/novembre 1973. Printed in Canada/Imprime au Canada.



504 RACHEL MCCULLOCH

parative effects of tariffs and quotas. Studies which overlook the motive for protection may yield an irrelevant measure of its cost.

Nonequivalence under domestic monopoly

Tariffs and quotas are alternate methods of reducing imports below the free trade level. Where all relevant markets are competitive, for any tariff there is a quota which is equivalent in the following sense: if the level of imports under the tariff regime is alternatively set as an import quota, the resulting domestic price will be exactly the foreign price plus the original tariff. Hence the import quota is equivalent to the tariff in every way except, perhaps, the tax revenue generated.2

As Bhagwati shows, this kind of equivalence breaks down if any of the markets is monopolized. For the case of monopoly in domestic production, Bhagwati derives the following result: suppose that all other markets are competitive. If, as above, the tariff is replaced by a quota equal to the level of imports under the tariff regime, the monopolist will now maximize profits with a lower level of domestic production and a higher domestic price than under the tariff, so that domestic price now exceeds foreign price by more than the previous tariff. Since the elasticity of foreign supply is effectively zero (when the quota is fully used), the monopolist now faces a less elastic demand curve, and hence lower marginal revenue at the original output. Thus the tariff and the quota which produce the same level of imports can no longer be considered equivalent. The quota results in a higher domestic price, lower domestic output, and higher profits for the domestic producer than does the tariff.3

While there is no longer a "natural" equivalence between tariffs and quotas when domestic production is monopolized, equivalence can be redefined in terms of the particular objective4 which underlies protection. In the above instance, the tariff and quota are alternative devices for reducing imports to a given level; a quota is seen to result in a higher domestic price and lower production and consumption than an "import-equivalent" tariff.5 Once equivalence has been redefined in terms of the protective objective, an obvious next step is to compare the cost of achieving the objective using alternative instru-

21f the import licences are auctioned in such a way as to prevent monopolization of the import privilege, the revenue thus generated will be the same (except for any difference in the cost of administering the two systems) as that raised by the equivalent tariff. 3Profits must be higher since the monopolist still has the option of selling the same amount at the same price as he did when the tariff was in effect; the new demand curve faced by the monopolist passes through his former profit-maximizing output and price combination. However, he will always produce less and set a higher price. 4Any policy results in a "package" of effects - changes in domestic prices, incomes and income distribution, government revenue, and so on. Policy makers weigh these results and choose the most favourable package. Here this process is simplified by assuming that a single objective underlies any given protective policy. 5Bhagwati (1965) thus poses the following question: under what market conditions does import-equivalence imply an identical discrepancy between foreign and domestic price? His answer is that competition in all markets is required for this result. Shibata (1968) extends this analysis by showing that import-equivalence implies (domestic) price-equivalence when foreign supply is monopolized.



Tariff and Quota 505

ments. The well-known "cost of protection" is transmuted into a more relevant measure - the cost of achieving the protective objective. In the following sections, four possible objectives of protection - profits, production, price, and imports6 - are analysed. In each case, the welfare cost7 of achieving the particular objective with a tariff is contrasted with the cost incurred when the equivalent (in achieving the objective) quota is used. The model assumes that the world price is unaffected by the volume of imports, domestic production is monopolized and subject to increasing marginal cost in the relevant region,8 and other markets are competitive.

Profit-equivalence

A tariff and a quota are "profit-equivalent" if they result in the same level of profits for the domestic producer. From the foregoing analysis it can be seen that a quota will allow more imports from abroad than the profit-equivalent tariff.

If the underlying objective of protection is to provide the domestic monopolist with a certain level of profits (for reasons which may range from the monopolist's lobbying power to a possibly misguided attempt to foster increased private investment), it is possible to compare the welfare cost associated with alternate methods of achieving the profits. In general, the relative welfare cost will depend on domestic social cost of production, foreign supply price, and elasticity of domestic demand.

A profit-equivalent tariff and quota are compared in Figure 1. D is the domestic (real income constant) demand curve for the protected good, PF is the world price, and MC/, is the marginal cost schedule of the domestic monopolist. With a tariff rate t, the monopolist faces a "price ceiling" of PT- PF (1 + t), since PF is given. His maximized profit, with domestic output of XT, is measured by PTGV (minus any fixed costs). Imports are restricted to GL.

Alternatively, the same profit level9 can be provided by a quota which allows imports of EL, facing the domestic monopolist with a "net" demand curve DN1O and corresponding marginal revenue curve MRN. The monopolist achieves a maximum profit of ABV (= PTGV) with domestic production of XQ and price PQ. In contrast to the tariff regime, a quota used to achieve the

6McCulloch and Johnson analyse the cost of achieving various policy objectives where all markets are competitive. Under these conditions tariffs and quotas are completely equivalent; they are compared with a "proportionally-distributed" quota as a means of achieving protective objectives. The proportionally-distributed quota features import licences allotted to producers or consumers in proportion to their individual production or consumption of the protected good. 7The measure of welfare cost used is the sum of the changes in consumer and producei surplus, or the "dead-weight loss" to the economy. For extensive discussions of this approach, see Johnson (1960) and Harberger (1971). 8With constant or declining marginal cost, a fixed world price allows only corner solutions: either the domestic monopolist produces nothing, or he satisfies the entire domestic demand. 9For any tariff rate there is a corresponding profit-equivalent quota; however, a non-zero quota may be profit-equivalent to a prohibitive tariff. '-This assumes that the import licences are not monopolized by the domestic producer or another importer. A total suipplv monopoly wouild permit higher profits.




P, MR MC

A

Q 0\M PF(l+t)=PT L

P R I\RN I N\D F - / IS Jl H I NI MI

/ ~~~I I ! I I\ V D

0 XQ XT CQ CT X, C

FIGURE 1 The figure is drawn so that PQRUPT = UGB. Hence the monopolist's profit under an import quota of RK = EL is the same as with a tariff which raises the price of imported goods to PT and results in imports of GL

same level of domestic profits results in a higher domestic price, lower domestic production and consumption, and more imports."1 The revenue generated by the auction of import licences exceeds the revenue from the profit-equivalent tariff; the difference is measured by EGHJ + RKTU, reflect- ing the larger volume of imports and the greater difference between domestic and foreign prices, respectively.

Corresponding to these differences in the resulting equilibria are differences in the cost of achieving the objective of protection, in this case a given level of profits. On one hand, the tariff alternative allows higher consumption and hence increased consumer surplus. On the other hand, the quota alternative results in increased productive efficiency through substitution of imports for higher-cost domestic production. Consumer utility provided by the protected

llThese results do not depend on linearity of demand or marginal cost. Since a quota per- mitting a level of imports equal to that under the tariff will give higher maximized profits, the profit-eqtuivalent quota must permit greater imports. Because MC(XT) --PT, with MC an increasing function of X, and P a decreasing function of both X and imports, the profit- maximizing XQ must be less than XT. Similarly, PQ must be greater than PT for monopoly profits under the quota to equal those attained with the tariff.




good is higher under the tariff by KLCTCQ. Total resource cost of the protected good is higher under the tariff by BGHS + NMCTCQ, the net effect of higher domestic production and fewer imports than under the quota. The net welfare gain (or loss) through use of a quota in place of a profit-equivalent tariff is thus FGHJ -- REFB, which is positive for the case depicted in Figure 1. More generally, the advantage of a quota over a profit-equivalent tariff is greater, the lower is foreign price relative to domestic costs, the more elastic is domestic marginal cost, and the less elastic is domestic demand for the protected good. Lower foreign cost and more elastic domestic marginal cost both increase the cost incurred through import substitution under the tariff. Less elastic domestic demand reduces the gain in consumer surplus induced by higher domestic consumption under the tariff.12

The possibility that a quota may achieve the desired protective effect at a lower welfare cost to the community than would be incurred with a comparable tariff may seem surprising to those who view quotas as a superfluous and even pernicious component of national commercial policies. This view follows directly from considering the instruments as ends in themselves, rather than as means of achieving particular policy objectives. Where the use of quotas is proscribed, as under the GATT rules, without any change in the objectives which underlie protection, the result may be lower welfare for the protecting country, since it can no longer use the instrument which minimizes the social cost of achieving the objective.

Output-equivalence

Another possible motive underlying protection in a world of adjustment costs and incomplete price flexibility is to maintain a given level of output in a particular industry. If factor proportions are relatively rigid in the short run, this is closely related to the maintenance of a given level of employment in the industry. A quota and a tariff are "output-equivalent" if they result in the same level of domestic output. From the analysis of the domestic monopolist's profit-maximizing equilibrium, it can be seen that a tariff will result in more imports than an output-equivalent quota. In Figure 2, a tariff is output- equivalent to a quota which allows only two-thirds as much to be imported (HB instead of EB). The use of a quota in place of a tariff thus results in an additional welfare cost of ABFG, the consumer surplus lost through the higher price under the quota regime. In general, the superiority of a tariff in this case is greater, the lower the foreign supply price relative to domestic costs.13

12The net welfare gain (or loss) from use of a quota in place of a profit-equivalent tariff is given by

fXT [MC(X) - PF]dX - fCT [P(C) - PF]dC.

Since consumption is equal to domestic production X plus imports I, this becomes

X MC(X)dX- P(C)dC - (IQ - IT)PF-

13Not taken into account here is the possibility that the monopolist may also be a monop- sonist in factor markets. In this case, an even smaller quota would be output-equivalent to the tariff.




P, MR MC

PQ

PF(i+t)-PT

P / | WN i\D N F

0 XQ-XT CQ CT X, C

FIGURE3E 2 The quota HB is chosen so that the monopolist's profit-maximizing output will be the same as that resulting from the tariff which restricts imports to EB

Price-equivalence

A third possible motive for protection is to maintain the domestic price at an agreed level. The quotas restricting imports of agricultural products into the US are part of such a program. (Much of the domestic output is produced under government-fostered cartel arrangements, with market shares determined by acreage allotments and similar output-restricting devices, so that the monopoly model for domestic production may be reasonably appropriate.) A tariff and a quota are "price-equivalent" if they result in the same level of domestic price. (Since this in turn implies that domestic consumption is the same, the label "consumption-equivalent" would be equally appropriate.) From the analysis of the domestic monopolist's profit-maximum, it can be seen that a quota will allow more imports from abroad than a price-equivalent tariff. Since total domestic consumption is determined by the price common to both alternatives, the difference in welfare cost depends only on the proportion of imports in the composition of that total. Thus, the quota, which results in more low-cost imports and less domestic production, must always




P, MR MC

McD

pQ =PT c

PF / RN El l N \

0 XQ XT CQ=CT X, C

FIGURE 3 The quota AG is chosen so that the monopolist's profit-maximizing price will be the same as with a tariff which results in imports of BC

result in a lower welfare cost than a price-equivalent tariff. In the case illustrated in Figure 3, the saving of BEFG results from substitution of imports for higher-cost domestic production. The revenue generated by auction of import licenses also exceeds the revenue from the price-equivalent tariff.

Import-equivalence

As noted earlier, a quota results in less domestic production and a higher price than an import-equivalent tariff. For the objective of limiting imports to a fixed level, a tariff results in a lower welfare cost to the community, since the additional domestic productioni thus induced is worth more than its cost to consumers. This case is illustrated in Figure 4. The additional welfare cost from use of a quota in place of the import-equivalent tariff is measured by ABC. This cost is higher, the more elastic are domestic marginal cost and demand. (The cost is independent of the world price of the protected good, since imports are held fixed.)




P, MR MC

MCD

pQAF

PF

I I ~~~~~~~~~D PF~

~ ~ ( It ) =P

Xs \

0 XQ XT CQ CT X,C

FIGURE 4 The tariff rate t is chosen so that the same level of imports results as under the quota (AF = BG)

Summary and conclusions

This paper extends the usual analysis of protection to take into account the underlying objectives of the policy. A monopoly in domestic production is assumed throughout. Where the objective of protection is to fix domestic price, an import quota results in a lower welfare cost than a tariff which achieves the same objective. A quota may also provide a less costly means of fixing profits at a predetermined level than a comparable tariff. These results are particularly interesting because quotas are often assumed to be especially undesirable where domestic production is monopolized.14 In contrast, where expansion of domestic output or limiting imports is the objective, a tariff achieves the result at lower resource cost.

The aim of this analysis is not to condone protection, but rather to take a more realistic view of the problems surrounding commercial policy -realistic in that the model includes the purposes of protection. A more complete analysis would seek to explain the formation of these objectives in terms of

14See, for example, Kindleberger (1968, 134).




economic and political variables.15 A fuller understanding of protectionism may be the first step toward achieving trade liberalization.

References

Bhagwati, J. N. "On the Equivalence of Tariffs and Quotas." In R. E. Baldwin, et al., Trade Growth and the Balance of Payments -Essays tit Honor of Gottfried Haberler (Chicago, 1965), 53-67. Bhagwati, J. N. and T. N. Srinivasan. "Optimal Intervention to Achieve Non- Economic Objectives." Review of Economic Studies 36 (Jan. 1969), 27-38. Harberger, A. C. "Three Basic Postulates for Applied Welfare Economics: An Interpretive Essay." The Jottrnal of Economic Literature 9 (Sept. 1971), 785-97. Johnson, H. G. "The Cost of Protection and the Scientific Tariff." Journal of Political Economy 68 (Aug. 1960), 327-45. Kindleberger, C. P. International Economics (Homewood, Illinois, 1968). McCulloch, R. and H. G. Johnson. "A Note on Proportionally-Distributed Quotas." American Economic Review 63 (Sept. 1973), 726-32. McPherson, C. "Tariff Structures and Political Exchange." Unpublished (University of Chicago, 1971). Shibata, H. "A Note on the Equivalence of Tariffs and Quotas." American Economic Review 58 (Mar. 1968), 137-42.

'5McPherson (1971) attempts to explairn tariff structures as the outcome of rational be- haviour in a political context.



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