The Invisible Hand and

Eric S. Maskin

The American Economic Review, Vol. 84, No. 2, Papers and Proceedings of the Hundred and Sixth Annual Meeting of the American Economic Association. (May, 1994), pp. 333-337.

Stable URL: http://links.jstor.org/sici?sici=0002-8282%28199405%2984%3A2%3C333%3ATIHAE%3E2.0.CO%3B2-P

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http://www.jstor.org Mon Mar 24 14:52:23 2008 The Invisible Hand and Externalities

When economists contemplate the invisi- that, in spite of externalities and incomplete ble hand at work, they generally think of information, private contractual agreements competitive markets. But there are some suffice to achieve efficiency, as long as no circumstances in which markets are not sup- agent is big enough to have significant mar- posed to operate well (i.e., in which the ket power. This conclusion must be quali- invisible hand is thought to falter). A lead- fied, however, with the proviso that, if the ing cause of market failure, many argue, is is "nonexcludable" (i.e., no one the presence of significant externalities. can be excluded from its effects), the gov- With such externalities, the first welfare ernment must intervene to prevent free-rid- theorem does not apply, and so competitive ing on the agreements. Intervention, in this equilibrium-if it exists at all-is not typi- case, amounts to establishing the right of an cally Pareto optimal. In the tradition of agent providing a positive external effect to A. C. Pigou (1932), the typical response to collect a fee for increasing the effect from this lack of optimality is for the government all who enjoy it, even if they are not parties to step in and introduce corrective policy, to a contract with the provider. Symmetri- usually in the form of taxes or subsidies. cally, providers of a negative externality can There is, of course, a strong anti- collect a fee for diminishing the effect from Pigouvian tradition, as well. Specifically, all their victims. In either case, however, the proponents of the Coase theorem (Ronald fee is set endogenously, that is, it is deter- Coase, 1960) have contended that, despite mined by the contractual arrangements externalities, unrestrained bargaining and rather than by the government. contracting ought to be sufficient to gener- This result for nonexcludable externali- ate an efficient outcome. (Indeed Coase's ties (which include pure public goods) pro- own celebrated example was a case of exter- vides support for a fairly laissez-faire stance nalities.) Thus, even if formal markets toward externalities but turns on an impor- themselves fail, the invisible hand neverthe- tant assumption, namely, that parties always less succeeds, and outside intervention or write contracts so as to maximize their so- design is not required. cial surplus (subject to incentive and indi- Recently, Joseph Farrell (1987) argued vidual-rationality constraints). I will return that, even when free bargaining is permit- to this assumption in the final section. ted, the laissez-faire conclusion inherent in the Coase theorem may founder if agents I. Bees and Trees have incomplete information about one an- other's relevant characteristics. I shall show, Let me invoke 's (1952) fa- however, that the problem that Farrell iden- mous example, that of the beekeeper and tified is due only to monopoly power and is the apple-grower, to illustrate the issues not peculiar to externalities. posed by externalities. When the bee- Indeed, in this paper, I shall take a modi- keeper's bees fly into the adjoining apple fied Coasian stance. I shall attempt to show orchard and pollinate the apple-grower's apple blossoms, they are conferring a posi- tive benefit on the apple-grower that the beekeeper cannot take advantage of directly *Department of , Harvard University, (i.e., a positive externality). The beekeeper's Cambridge, MA 02138. I thank the National Science inability to capture the value created by her Foundation for research support. bees means that she will tend to keep too 333 334 AEA PAPERS AND PROCEEDINGS MAY 1994 few of them from a social standpoint. But Farrell(1987) argued that this inefficiency there is a simple Coasian solution to this of negotiated agreements under incomplete problem, namely, the two parties can nego- information constitutes a counterexample to tiate a fee to be paid by the apple-grower to the Coase theorem. Indeed, he pointed out, the beekeeper to induce her to keep the there is a definite role for policy interven- efficient number of bees. If such a deal tion, since the government can restore ex comes off, there is no need for any outside ante efficiency by, for example, imposing a interference or corrective policy. scheme B la Claude d'Aspremont and Now, one potential stumbling block for a Louis-Andre Gerard-Varet (1979) (albeit at contract like this is that the apple-grower the cost of possibly leaving one of the two may be ignorant of the beekeeper's technol- parties worse off than were there no agree- ogy and so may not know the fee level that ment at all). would induce her to increase her operation The sort of inefficiency that the bee- by the marginal bee. Even so, if the apple- apple example illustrates is not at all special grower offered a fee f just equal to his to externalities. It is symptomatic of any marginal benefit, b, from the increase, ef- situation in which there is monopoly power ficiency would be attained, since the bee- and incomplete information. In the exam- keeper would accept f if (and only if) it ple, the apple-grower is a monopsonist in exceeded c, her marginal cost of beekeep- "pollination services" and is therefore able ing (net of the price at which she can sell to negotiate a fee for these services that is bees). But, in this case, the apple-grower's lower than his marginal benefit. Further- net marginal benefit b -f would be zero. more, the same would be true-and, there- What a rational apple-grower will do, there- fore, the same inefficiency would arise-if fore, is to "shade" his offer somewhat, that pollination services were an ordinary private is, to set f strictly less than b. This means good, and not an external effect created by that, if it turns out that b > c > f, then the beekeeping. additional bee will not be kept even though Because it is not evident that situations it would have been efficient (in the sense of entailing externalities are significantly more increasing social surplus) to do so. The same prone to the exercise of monopoly power logic works symmetrically for the case in than those involving purely private goods, a which it is the beekeeper who proposes f. fairer test of whether externalities pose a Her net payoff will be positive only if f is particular problem for the invisible hand is higher than c. Thus, if she is uncertain one in which monopoly power (but not in- about b, she may well set f higher than b, complete information) is kept out of the thereby preventing a deal even though b picture. exceeds c. In either case, there is positive probability that the outcome will not be efficient' (again, in the social surplus senseX2 same as ex ante efficiency (a contract is ex ante effi- cient if there is no other contract that makes both 'In fact, the same result also holds for range of parties better off in expectation, where the expectation intermediate cases in which the fee is jointly deter- is taken over both their "types," b being the apple- mined by the apple-grower and the beekeeper grower's type and c the beekeeper's). The rationale for (see Jean-Jacques Laffont and Maskin, 1979; Roger using the stronger concept is the supposition that situa- Myerson and Mark Satterthwaite, 1983). tions involving externalities occur repeatedly and that, 'whether the beekeeper or apple-grower sets the over time, agents are more or less symmetric with fee, however, the resulting contract is Pareto efficient respect to them. That is, in a dynamic economy, some- in the interim sense. That is, there is no other contract times an agent creates an externality, and sometimes for which it is common knowledge that both parties he is its beneficiary. Sometimes he is affected a great would be better off (otherwise, the fee-setter would deal by an externality, and sometimes only slightly. The propose such a contract). When I say that the contract presumption behind ex ante efficiency as a welfare is inefficient, therefore, I am invoking the stronger criterion is that all agents are basically the same in this concept of surplus-maximization, which here is the respect. VOL. 84 NO. 2 IMSIBLE-HAND THEORIES 335

11. Many Bees and Trees ability, (1) is very nearly the same as Imagine then that there are n beekeepers and n apple-growers and that the two groups are adjacent to one another. Each bee- keeper j (j= 1,...,n) is described by the cost c, that she incurs from keeping an where E -denotes the expectation with re- additional bee. The parameter ci is private spect to 8 and Pr denotes "probability of." information and, for concreteness, is as- Now, the solution to (2) is fi = 5-26. sumed to be an independent draw from the Hence, there exists a simple contract be- uniform distribution on [1,3]. Each apple- tween the apple-growers and beekeepers grower i is described by his utility function that is nearly efficient despite the incom- 8,x - x2, where x is the number of bees pleteness of information: first, each apple- from whose services the apple-grower bene- grower demands the level of pollination ser- fits. Like the ti's, the 8,'s are identical and vices he wishes at the price 5-26, and independently distributed according to the simultaneously each beekeeper proposes uniform distribution on [I, 31. whether she will keep an additional bee Assume, for the moment, that a bee- (i.e., be a "do-beekeeper") or not (i.e., be a keeper can control where her bee goes (i.e., "don't-beekeeper") if paid the price 5- whose blossoms it pollinates). This means 26. In view of the strong law, almost ev- that the beekeeper can exclude any apple- erybody will get to carry out his or her grower from enjoying the bee's external ef- proposal. However, to equate supply and fect unless he pays a fee. Under this as- demand, either a small fraction of do- sumption, pollination services turn out to beekeepers must be chosen at random and differ little from an ordinary private good proscribed from keeping an additional bee, (even though an apple-grower has no direct or else some don't-beekeepers must be se- control over x). Given the realizations of lected and compelled to keep an additional the 8,'s and cj's, the unique surplus-maxi- bee. mizing allocation of services can be de- Observe that no government intervention scribed as follows. For any "price" p, let at all is required to attain an efficient out- come here. It is worth noting why this is so. Even diehard Coasians acknowledge that there is an active role for government in dealing with externalities, namely, to estab- lish "property rights." But establishing a and property right in pollination services is not necessary because I have posited that bee- keepers have the power of exclusion. This ability prevents an apple-grower from free- riding on an agreement made by others. Since, as I will argue, the purpose of creat- Then, beekeeper j should keep s(c,,fi) ad- ing an ownership right in pollination ser- ditional bees, and apple-grower i should vices is precisely to curtail free-riding, such receive services equal to d(O,,fi), where fi a right is superfluous here. satisfies 111. The Nonexcludable Case

Suppose that beekeepers cannot control their bees. Symmetry then implies that each bee provides (in expectation) l/n units of If n is large, however, the strong law of pollination services to every apple-grower. large numbers implies that, with high prob- For surplus maximization, beekeeper j 336 AEA PAPERS AND PROCEEDINGS MAY 1994 should keep an additional bee as long as known to be (nearly) surplus-maximizing. Assume that the government requires any nonparticipating apple-grower to pay the same fee that is specified in the contract. Then any apple-grower prefers to sign the contract, since if he does so he pays the fee Thus, if n is large, it will be nearly efficient with less than probability 1, and his pollina- for beekeeper j to keep the additional bee tion services are the same whether or not he whenever cj < and for each apple-grower signs.3 I conclude, therefore, that the gov- to enjoy approximately iunits of pollina- ernment-instituted property right stops tion services in all. Notice that this approxi- free-riding. mate figure of is independent of any sin- I have been arguing the case of positive gle apple-grower's Oi. Therefore, if n is externalities, but a symmetric argument per- large, an incentive-compatible and efficient tains to negative externalities. For that mat- contract would require every apple-grower ter, the assumption that the 0,'s are inde- to pay approximately the same amount pendent draws can also be relaxed. When (which would come to at least iX % =&, the 8,'s are independent, the strong law since the average cost incurred by those implies that one does not need to collect beekeepers who keep an extra bee is 6,and information about the sample distribution approximately one-quarter of all beekeepers in order to approximate an efficient alloca- do so). An apple-grower, therefore, has a tion. When the 8,'s are correlated, this may strong incentive to refrain from signing any no longer be the case. However, if the con- agreement. By standing apart, he can avoid tract incorporates a modified "Groves paying anything and still enjoy approxi- scheme" (Theodore Groves, 1973), whereby mately the same level of pollination services a sample of apple-growers is selected and as when he participates. (Because the ap- each is induced to reveal his type, efficiency ple-grower does not appreciably affect the can again be (approximately) attained. efficient allocation of pollination services, the beekeepers and other apple-growers will IV. Surplus-Maximizing Contracts sign much the same agreement without him as with him). In other words, he can "free- I have been assuming that agents choose ride" on the other agents7contract. surplus-maximizing (or nearly surplus-maxi- This is where the government steps in. mizing) contracts. This may be criticized as What it can do is to endow beekeepers with being at odds with the large-numbers as- the property right to their bees7 pollination sumption; presumably efficient contracting services. Such a right entitles a beekeeper is more difficult with many agents. I am on to a fee from each apple-grower who enjoys comparatively safe ground with the case of pollination services. Now, of course, there is excludable externalities, since contracts no reason why the government should know there resemble ordinary Walrasian markets. the expected marginal benefit from these Moreover, it can be shown in this case that services, and so it may be unable to set the any sequence of interim-efficient, individu- fee appropriately. However, it can tie the ally rational contracts converges to the Wal- fee to the fee-structure specified in the rasian mechanism as n -+ w. contract. To be more concrete, suppose that, when n is large, agents sign a contract in which each beekeeper announces whether or not 3I am assuming here that, if the apple-grower does she is willing to keep an additional bee if not participate, the other agents will sign more or less paid the fee of 5, and a number of apple- the same contract: one that is (approximately) surplus- maximizing. These other agents may all gain, however, growers (approximately 75 percent) are se- from signing a contract that exploits the fact that his lected at random to pay a fee of $ each. fee is at their mercy. Of course, this will make the From the above analysis, this contract is apple-grower all the more willing to participate. VOL. 84 NO. 2 INVISIBLE-HAND THEORIES 337

There are two problems with nonexclud- d'Aspremont, Claude and GCrard-Varet, Louis- able externalities. First, as I have shown, AndrC. "Incentives and Incomplete Infor- the surplus-maximizing contract does not mation." Journal of Public Economics, resemble a Walrasian mechanism (at least February 1979, 11(1), pp. 25-45. on the demand side). Second, there are Farrell, Joseph. "Information and the Coase many interim-efficient and individually ra- Theorem." Journal of Economic Perspec- tional allocations even in the large-numbers tives, Fall 1987, 1(2), pp. 113-29. case (to see this, note that the left-hand Groves, Theodore. "Incentives in Teams." side of condition (3), which weights all Econometrica, July 1973, 41(4), pp. apple-growers equally and corresponds to 617-31. surplus-maximization, can be rewritten with Laffont, Jean-Jacques and Maskin, Eric. "A unequal weights, in which case it corre- Different Approach to Expected Utility sponds to some other interim-efficient allo- Maximization Mechanisms," in J. J. Laf- cation). One would have to argue that sur- font, ed., Aggregation and revelation of plus-maximization has some special salience preferences. Amsterdam: North-Holland, for agents to single it out. Of course, this is 1979, pp. 289-308. one role that institutions and traditions play Meade, James. "External Economies and -to select one equilibrium from among Diseconomies in a Competitive Situa- many. tion." Economic Journal, March 1952, 62(245), pp. 54-67. Myerson, Roger and Satterthwaite, Mark. "Ef- REFERENCES ficient Mechanisms for Bilateral Trading." Journal of Economic Theory, April 1983, Coase, Ronald. "The Problem of Social Cost." 29(2), pp. 265-81. Journal of Law and Economics, October Pigou, A. C. The economics of welfare. Lon- 1960, 3(1), pp. 1-44. don: Macmillan, 1932. http://www.jstor.org

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You have printed the following article: The Invisible Hand and Externalities Eric S. Maskin The American Economic Review, Vol. 84, No. 2, Papers and Proceedings of the Hundred and Sixth Annual Meeting of the American Economic Association. (May, 1994), pp. 333-337. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28199405%2984%3A2%3C333%3ATIHAE%3E2.0.CO%3B2-P

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References

The Problem of Social Cost R. H. Coase Journal of Law and Economics, Vol. 3. (Oct., 1960), pp. 1-44. Stable URL: http://links.jstor.org/sici?sici=0022-2186%28196010%293%3C1%3ATPOSC%3E2.0.CO%3B2-F

Information and the Coase Theorem Joseph Farrell The Journal of Economic Perspectives, Vol. 1, No. 2. (Autumn, 1987), pp. 113-129. Stable URL: http://links.jstor.org/sici?sici=0895-3309%28198723%291%3A2%3C113%3AIATCT%3E2.0.CO%3B2-L

Incentives in Teams Theodore Groves Econometrica, Vol. 41, No. 4. (Jul., 1973), pp. 617-631. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28197307%2941%3A4%3C617%3AIIT%3E2.0.CO%3B2-E

External Economies and Diseconomies in a Competitive Situation J. E. Meade The Economic Journal, Vol. 62, No. 245. (Mar., 1952), pp. 54-67. Stable URL: http://links.jstor.org/sici?sici=0013-0133%28195203%2962%3A245%3C54%3AEEADIA%3E2.0.CO%3B2-O