Equivalence of Tariffs and Quotas Under Foreign Supply ...



qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmEquivalence of Tariffs and Quotas Under Foreign Supply MonopolyEcon 567 Project 13/18/2013Fei Zhan & Can HuangTable of ContentI. INTRODUCTIONThis model examines the equivalence of tariffs and quotas in their protective effects with monopolistic supply from abroad, in the development of practical commercial policies by analyzing the "Voluntary Export Restrictions."The paper based on the previous research of Jagdish Bhagwati, which concluded that an import tariff and a corresponding quota produce identical discrepancy between foreign and domestic prices. Hirofumi Shibata improved the model by introducing a monopoly element into the foreign supply, this does not create different domestic prices whether a given import level is permitted by a tariff or by a quota as concluded.By constructing the model, we tested separately the two conditions: when an import tariff is charged and when a quota is allocated. By setting the constraints and adopting the “Solver” in Microsoft Excel, we achieved the same results for both conditions. The import ratio set by government when a tariff is imposed equals the one when quota is allocated.II. MODEL GENERAL ASSUMPTIONS (a) Monopoly in foreign supply.(b) Perfect competition in domestic production.(c) A quota which was allocated so as to ensure perfect competition among the quota holders.(d) An import ratio is set by government(e) Import market is in balance.VARIABLES AND PARAMETERS Parameters a10b0.5c20j-0.5e3f0.25g5Variables for model with tariff EndogenousDefinitionInitial valuesSddomestic supply 14Pddomestic price8Ddomestic demand16Dfdemand for import 2SfForeign Supply2Rtax revenue collected by the government0ttax0himport ratio target set by the government 0.14 Variables for model with quotaEndogenousDefinitionInitial valuesSdqdomestic supply 14Dqdomestic demand16Dfqdemand for import 2Pdqdomestic price8SfqForeign supply2hqimport ratio target set by the government 0.14BASIC EQUATIONS AND EXPLANATIONS(a) Equations and explanations for model with tariffEquationsNotesSd=a+bPddomestic supply D=c+jPddomestic demandDf=D-Sd=(c-a)+(j-b)Pddemand for import equals domestic demand minus domestic supplyDf=Sfimport market clearance C=e+gSf+fSf^2cost function of foreign producerdC/dSf=(1/(1+t))(d(PdSf)/dSf)g+2fSf=(1/(1+t))(Pd+ Sf/(j-b))marginal cost equals marginal revenue after tariff?R=(t/1+t)PdSftax revenue collected by the governmenth=Sf/Sdimport ratio target set by the government Name the equations from top to bottom (1) to (8). Equation (1) and (2) state that the domestic supply and domestic demand are each a function of domestic price; in equation (3), the difference between total demand and domestic supply equals the net demand available to the foreign monopolist and in equation (4) this difference clears market by equalizing to foreign supply; equation (5) that total cost of foreign supply is a function of the level of production; equation (6) that marginal revenue from foreign sale is equated by the monopolist to his marginal cost; and equation (7) that imported tariff collected by government equals the tariff revenue per unit multiplied by the foreign supply; equation (8) shows that an import ration is set by proportion foreign supply to domestic supply.We have eight equations and eight unknowns: SD, D, DF, SF, PD, R, h, and t. Set each initial values and constraint the equations to zero, we can determine the remaining values and target value of h by using solver. Accordingly, corresponding to every t, there will be some level of imports, SF, and domestic price, PD.(b) Equations and explanations for model with quotaEquationsNotesSdq=a+bPdqdomestic supply Dq=c+jPdqdomestic demandDfq=Dq-Sdq=(c-a)+(j-b)Pdqdemand for import equals domestic demand minus domestic supplyDfq=Sfqimport market clearance Cq=e+gSfq+fSfq^2cost function of foreign producerdCq/dSfq=(d(PdqSfq)/dSfq) OR dCq/dSfq<(d(PdqSfq)/dSfq) ie: g+2fSfq=(Pdq+ Sfq/(j-b)) OR g+2fSfq<(Pdq+ Sfq/(j-b))marginal cost equals/less than marginal revenue after tariffeffective quota: less thanineffective quota: equalhq=Sfq/Sdqimport ratio target set by the government All the same, we name the equations from top to bottom (1) to (7). Except for (6), all other equations are exactly the same and have the same meanings with their corresponding ones in equations of model under tariff charges. This case with quota states that the maximizing equilibrium condition for the monopolist when a quota is set; the equality sign holds if the monopolist sells less than the quota (i.e., the quota becomes ineffective), and the inequality if he sells the maximum amount set by the quota. In this case, there are thus seven equations and six unknowns: SD, D, DF, SF, PD, and h. The import level which will maximize the foreign monopolist's profits is thus determined.After equations are set, we can begin set constraints and use solver to solve for the values of h and examine if the import ratios in the above two cases will be equal or not. = 3 \* ROMAN III. MODELING RESULTS AND ANALYSIS Constraining the equations and setting initial values for endogenous variables, we get the value of government-set import ratios in both cases with the help of solver. As can be seen below, the procedure of tariff case is:Constraint to zeroequation valueEndogenousFinal viable valuesInitial viable values00Sd14.634146341400Pd9.268292683800D15.365853661600Df0.73170731723.38891E-100Sf0.7317073172-4.94462E-090R8.01470985502.58994E-130t0.5909090910?h0.05 0.14 ???target h???0.05??And for the case with quota, it illustrated as follows:Constraint to zeroequation valueEndogenousFinal viable valuesInitial viable values00Sdq14.634147251400Pdq9.268294504800Dq15.365852751600Dfq0.73170549621.27566E-070Sfq0.7317054962-3.170736261<=0hq0.050.14???target hq???0.05??Hence, the target import ratio set by government under the case of imposing an import tariff equals the target import ratio when quota is allocated. Therefore, an import tariff and a corresponding quota produce identical divergence between foreign and domestic prices is proved. Additionally, the domestic prices are kept the same in both cases since tariff and quota permit same level of imports as can be seen from the result boxes.Further more, the equilibriums in the two systems are illustrated in an dynamic form in figure 1. Source: A Note on the Equivalence of Tariffs and QuotasFigure 1In this figure we place first a tariff rate that generates an import level; then we set the identical import level as a quota and illustrate that the same domestic price is generated but higher price for the foreign monopolist. In the tariff system, because tax rate is MK divided by KQ, it shifts the net demand for the monopolist downwards to GH and marginal revenue of monopolist to GL. Equilibrium exists at J where the marginal cost line intersects marginal revenue line for the monopolist, so that export of monopolist totals OQ, the domestic price is at OA while the monopolist's c.i.f. price is at OB. In the quota system, we adopted the same import level OQ as the quota. EI, as the corresponding marginal revenue, becomes discontinuous at I. Equilibrium exists where the marginal cost schedule for the monopolist cuts the demand curve below I so that the monopolist exports exactly the same volume set by the quota and the domestic price is at OA which in turn becomes the monopolist's c.i.f. price. In the case marginal cost line crosses the marginal revenue curve between E and I, the monopolist cannot use all the quota allocated, which intern pushes the domestic price higher than OA. However, the marginal cost line will never cut the marginal revenue schedule between E and I, as long as the quota is set at the same import level under the positive tariff system, because at the monopolist's equilibrium export level reached under a positive tariff (OQ in Figure 1), the monopolist's marginal cost (QJ) definitely be smaller than the monopolist's marginal revenue that would exist if there were no tariff (QI). Thus we have shown that conditions of foreign supply make no difference for the equivalence of tariffs and quotas in protective effect, under the condition of perfect competition in domestic production and among quota holders. = 4 \* ROMAN IV. IMPLICATION FOR POLICIESThe demonstration here has implication on the “Voluntary Export Restriction” policy. The system was employed by Japan, Hong Kong, and South Korea in their exports, chiefly of textile products, to the United States, Canada, and other European countries. In this system, the exporting and importing country negotiate about the quantity of specific commodities allowed to enter into the importing country. In one condition that they fail to make an agreement, the importing country will impose a tariff on the commodities in question. In other condition, if the two countries agree on the volume of imports, the exporting country will promise to voluntarily administer the de facto import quota agreed upon, while the importing country concedes the non-use of tariffs. This type of policy has its own rationality based on our analysis above. Firstly, for protection purpose, the tariff and quota are equally effective for the policy maker of the importing country. Secondly, for the monopolist of the exporting country, quota is preferred to tariff if some kind of trade restriction is inevitable. Facing the restriction by quota, they can manage to obtain some part of the quota rent through the formation of cartel. Whereas in the restriction of tariff, the same part of revenue will be collected by the government of importing country. Therefore, from the perspective of both the importing country and the exporting country, the Voluntary Export Restriction Policy is preferred to the explicit tariff restriction. ReferenceJ. BHAGWATI, "On the Equivalence of Tariffs and Quotas," in R. E. Bald- win and others, editors, Trade, Growth, and the Balance of Payments- Essays in Honor of Gottfried Haberler, Chicago 1965. J. BHAGWATI, "More on the Equivalence of Tariffs and Quotas," Am. Econ. Rev., this issue, 142-46 ................
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