October 24, 2006Theorem of the Second Best and Principle of TargetingThe theoretical argumen t in favor of liberal trade is based on ideas con-cerning the efficiency of market outcomes, and o n the P rinciple of Com para-tiveAdvantage. ThisPrincipleimpliesthatunderfreetradeandgiventhatdomestic mark ets are not distorted, a country exports commodities that itcan produce relativ ely more cheaply than its partners. “Mor e cheaply” isunderstood in terms of “opportunity costs” rather than in terms of dollarsor labor hours. I review the meaning of opportunit y cost using a two-commodity example. Then I discuss the Theory of the Second Best and thePrinciple of Targeting.Suppose that food and steel are the only two commodities. In thissetting, the opportunit y cost of steel is simply the number of units of foodthat the economy must sacrifice in ord er to ob tain one m o re un it of steel. Theeconomy converts food in to steel b y reallocating factors of production fromthe food to the steel sector. Firm s that use the factors of production, andwork er s and land-o w ners who supply these factors, m axim ize their profits,utility, or ren t. In an undistorted competitive equilibrium, it is not possibleto increase output of one com m odity without decreasing output of the othercom m odit y : the allocation of factors is efficient. The opportunity cost ofsteel equals the equilib rium re la tive price of steel,pspfwhere psis the nominalprice of steel and pfis the nomin a l price of food .If t wo economies have different equilibrium re la tive prices in autarky, thenone economy necessarily ha s a lo wer equilibr ium relative price of steel. Tha teconom y has a lo wer opportunity cost of steel — a comparativ e advantage insteel — and it exports steel in a free trade equilibrium. When the equilibriumtrade price differs from the autarkic prices, trade increases total income inboth of the countries. The income of owners of any particular factor ofproduction might fall as a consequence of trade. In general, some agentsgain and some lose when relativ e prices c hange. Ho wev er, the income lossof one group is less than the gain of other groups, so total national incomeincreases with trade. In this case, it is possible for the winners to compensatethe losers, so that all are better off as a consequence of trade. (O f course, ifthe winners do not actually compensate the losers, the latter are worse off.)1The conclusion that trade increases national income depends on the as-sum ption that the economies are “undistorted”. A nything that causes theeconom y to be at an inefficient equilibrium can be view ed as a distortion,including imperfect competition, missing markets (e.g. absence of insur ancemar kets) or governm ent policies that restrict trade (e.g. tariffs).The Theory of the Second Best states that if there are two or more marketimperfections (distortions), correcting one of them may either increase or de-crease w elfar e. For example, if there are t wo tariffs, eliminating one may notincrease w elfa re. A pessimistic interpretation of this theory is that it impliesthat economic theory allow s us to reach no conclusion about real world mar-kets, since w e know that these are subject to man y imperfections/distortions.Amoremoderateinterpretationisthatwecannotuncriticallyuseeconomictheory to conclude that a particular reform, suc h as trade liberalization,necessarily impro ves efficiency.Here is a simple example of the theory of the second best. Imaginean economy in which there are only two market failures, both of whic h arepresent in a particular sector. The first failure is that production of thecommodity damages the environment, but the producer does not pa y forthis dam ag e (i.e. there is a negativ e en viro nmen tal externalit y ) . The secondfailure is that the industry is oligopolistic rather than competitiv e. These t womar ket imperfections cut in opposite directions. The first causes the mark etoutcom e to result in excessiv e production , from the standpoin t of society.The second causes the market outcome to result in too little production , sinceoligopolists (t y pically ) sell at a point where price is greater than ma rgina lcost. A t this level of generality, we do not know whether there is too little ortoomuchproductiononbalance. Wecannot conclude that welfare w ould behigher if we remo ve one of the im perfections, e.g., b y forcing the oligopoliststo produce where price equals marginal cost in order to mimic the competitiv eoutcom e. The salien t feature of this example is that each distortion affectsthe welfare cost of the other distortion.Now we consider a differen t example. In this case (as abo ve) productioncreates pollution, wh ich causes damages that (in the absence of a policyin terven tion ) firms do not internalize. (That is, firms do not bear the cost ofthe pollution unless a go vernm e nt policy forces them to bear this cost, e.g. b ytaxing them.) This externality is the first distortion, or m arket failure. Thesecond distortion is "policy induced": w e begin with a go vernmen t policythatimpedesfreetrade. Inthiscase,the theorem of the second best tellsus that trade liberalization might either increase or lo wer welfare, because2the liberalization takes place in the presence of the other (env iro nm ental)distortion.Figures 1 - 5 illustrate this example of the theory of the second best, usinga partial equilibrium trade model. We first consider the effect of pollutionin a closed economy; then we introduce trade. Suppose that each unit ofproduction causes an amoun t of pollution that results in γ dollars w orth ofdamage. (All costs and benefits are measured in dollars in this examp le.)The private margina l cost curve (PM C ) is the supply curve in the absenceof taxes. T he social margin al cost curv e (SM C ) is equal to PMC + γ;thissa ys that the cost to societ y of an additional unit of output is equal to thesum of private costs (e.g., the costs of capital and labor needed to producean additional unit) and pollution costs. In the absence of en vironmenta lregulation, the competitive level of output is Qcand the competitive price ispc. The optimal tax is γ. In the closed economy, it does not matter if thistax w ere levied on producers or consumers. Either tax has exactly the sameeffect on the price that consumers pay and producers receive. T he optima llevel of outpu t is Qs, where the social margin al costs in tersect the demandcurv
View Full Document
Unlocking...