440 CHAPTER 13. GOVERNMENT AND THE INDIVIDUAL construct such a schedule given that it knows the customers’demand functions and, if we were to extend the argument to the case where there are di¤erent types of consumers, it can introduce a more complex version of the same charging structure as long as it can identify the type each consumer (see the argument on pages 333 –336). However this form of fee schedule is not the only way of setting up an e¢ cient payment system for the …rm or agency. Suppose the government allows the …rm to charge the price p 1 (equal to marginal cost of production) and then underwrites its losses by paying the …rm a subsidy equal in value to F 0 . By the same reasoning the …rm covers its costs: the subsidy can be …nanced by levying a tax on the population and it is clear that there is a welfare increase because the representative consumer is assured of the utility level  0 rather than   . The implementation in terms of a tax-…nanced subsidy combined with price regulation ap parently produces the same e¤ect as allowing the …rm the freedom to set a fee. With some extra caveats the argument can also be applied to the heterogeneous-consumer case. 10 Private information The assumption of perfect information that underlay these proposed e¢ cient solutions may be particularly inappropriate. The re are at least two respects in which this may be a poor way to model the situation facing such a …rm or public agency. First, the …rm may f ace di¤erent types of customers. It then has the now familiar problem of masquerading by high-valuation types as low-valuation types in order to acquire a more favourable contract for themselves, with a lower …xed charge. The analysis is essentially that outlined in section 11.2.4: it retains the essentially private and individualistic approach to …nding the e¢ cient solution. Second, the government in attempting to regulate the …rm may not be full informed about the …rm’s circumstances. Common sense suggests that in order to regulate it e¤ectively the government must have some information about the …rm’s cost function: otherwise how will it know whether or not the subsidy paid to cover F 0 is in fact an overpayment? However, imagine the situation confronting the government that is to award the right to supply good 1 subject to the price regulation and subsidy scheme that we have discussed. Although the government may be informed about the distribution of cost structures of the possible candidate …rms the speci…c information about the costs of any one particular …rm may be unobservable to the government: in other words the shape of  () in Figure 13.4 may be information that is private to the …rm. Figure 13.5 illustrates the case where there are two possibilities for the (x 1 ; x 2 )- trade-o¤: the larger, lightly shaded area corresponds to that in Figure 13.4 and the other depicts a case in which less of the infrastructure good 1 is obtained for any given sacri…ce of good 2. If there were perfect information about which of 10 Suppose, following note 3,that P h CV h were proposed as the objective function for the government, where CV h is the compensating varia tion of household h. Why might this prove unsatisfactory as a w elfare crit erion? 13.3. NONCONVEXITIES 441 Figure 13.5: Nonconvexity: uncertain trade o¤ the two cases were true then one could achieve an e¢ cient outcome either at x 0 (if the true situation were as in Figure 13.4) or at x 00 (if the true situation were as in the new, smaller, attainable set): in either case one uses the marginal-cost- price-plus-subsidy method of ensuring that a prod uc er of known cost operates e¢ ciently. However, under imperfect information about the producer’s type, this approach is not going to be implementable. 11 This conclusion about imperfect information should come as no surprise: it is just what we h ad in the case of the contracting model of section 12.6.3, for example. It can be handled using the principles of design that are by now fairly familiar. The designer here is of course the government and it attemp ts to maximise expected social welfare, where the expectation is taken over the various types of monopoly producer that the regulator may be confronting. This is a “second-best” maximisation problem because the regulator has to incorporate an incentive-compatibility constraint that ensures that a low-cost producer would not …nd it pro…table to masquerade as a high-cost producer: 11 Show that the low-e¢ cienc y type of …rm would like to pretend to the regulator that it is a high-e ¢ c iency type – see also Exercise 12.6 (page 427). 442 CHAPTER 13. GOVERNMENT AND THE INDIVIDUAL the detail of how it works in a speci…c model is contained in Exercise 12.6 (page 427). The outcome will be a multipart payment schedule that is contingent on output. Maximised soc ial welfare will be lower than the full inf ormation solution, but then that is just what we have come to expect from this type of model. The nonconvexity problem that undermines the operation of the unfettered free market can be solved without abandoning the approach that focuses on individual pro…t maximisation. However it usually requires some external in- tervention (the government regulator) to ensure that the producers stay solvent as well as operate e¢ ciently. 13.4 Externalities Externalities imply a particular type of interdependence amongst economic agents; but we must be careful what kind of interdependence. Take the stan- dard multi-market model of the economy introduced in chapter 7. In a market economy there are bound to be interdependencies induced by the forces of com- petition. The demand for ice-cream goes up in the summer; as a result the wages of ice-cream vendors increase; as a result the wages of other workers increase; as a result up go the marginal costs of apple-growers, bicycle-repair …rms, car-parks, However the type of interdependency that is relevant here does not operate through the regular channels of the market: if it did then the economic issues involved would be much simpler. Instead the interdependency works by shifting one or more of the basic components of the model that we set for examining economic e¢ ciency: the production function  f or the utility function U h of other agents in the economy. The externality problem emerges in a number of guises; we had a glimpse of this in chapter 3 and in chapter 9 where the method for analysing e¢ cien cy was developed. Some of the standard versions of the externality issue are:  Networking e¤ects. Firms bene…t from each others’investment in certain capital and human resources that facilitate cooperation or otherwise lower other …rms’costs. This is the kind of phenomenon that in the aggregate may give rise to the increasing returns or “nonconvexity ” problem men- tioned in section 13.3.2.  Civic action. “Good citizenship”activity by some consumers may bene…t others –painting the house, for example.  Common-ownership resources. Suppose …rms have access to a resource where the ownership rights are vague or unde…ned –…shing grounds be- yond territorial waters, common land. A typical …rm may use the common- ownership resource as an input in a way that takes no account of indirect fact on other …rms’costs in accessing the resource –as the …shing grounds get depleted or the land is over-grazed. The phenomenon is epitomised as the “tragedy of the commons.” 13.4. EXTERNALITIES 443  Pollution. Actions by …rms or consumers may directly a¤ect others pro…ts or utility. The …rst pair of these are clearly activities that provide bene…ts to others and intuition suggests that individual agents pursuing their private interests may in some sense “underprovide.” The others are examples of negative or detrimental externality and the same intuitive reasoning suggests that private interests responding to market signals will lead to over-indulgence in the market activity that is producing the externality. However, is the intuition likely to be right here, or has it missed a key point about the market mechanism? We will address this by examining …rst the production case and then con - sumption : the essential di¤erence between them concerns not only the nature of the agents’ objectives and constraints but also the informational questions associated with the particular e xternality, as we shall see. Dealing …rst with production externalities enables us to develop a method of analysis and set of criteria for other types of externality and for introducing the issue of public goods. 13.4.1 Production externalities: the e¢ ciency problem The essence of the problem can be expressed in the form of a two-commodity model of a closed economy. Firm f’s pro d uc tion of good 1 causes a spillover e¤ect that impinges on the production costs of other …rms: the greater the activity the larger is this e¤ect. We will again assume that there is a single individual whose preferences are represented by a standard quasiconcave utility function. Equation (9.29) states the basic principle of the e¢ ciency condition with the production externality; for the consumer the relevant condition for a private good is (13.1); combining the two one has:  f 1  f 2 = U 1 U 2 + e f 21 (13.6) where e f 21 is the marginal valuation of the externality. The other two terms in (13.6) have essentially the same interpretation as in equations (13.1)–(13.4): they are the marginal cost of producing good 1 in terms of good 2 (left-hand side) and the the consumer’s willingness to pay for good 1 in terms of good 2 (right-hand side). We can exp loit the e¢ ciency condition (13.6) to provide a method of imple- mentation in a market economy. 13.4.2 Corrective taxes Given that the consumer(s) are maximising utility in a free market (13.6) could be interpreted as a simple rule for setting corrective taxes. We simply need to rede…ne the components as ~p 1 ~p 2 = p 1 p 2  t (13.7) 444 CHAPTER 13. GOVERNMENT AND THE INDIVIDUAL where the ~ps denote pro duc er prices, the ps are consumer prices, and t is a tax on the output of polluters. If we arrange things so that t = e f 21 then we have a corrective tax that imposes the value of the marginal externality on the one generating it. Note that, by de…nition, this tax is positive if the externality is deleterious (as in the case of pollution), but that t is negative (a subsidy to the …rm producing good 1) if the externality is bene…cial. 12 It is clear that although there could be informational problems with this neat solution, including the question of de…ning the boundaries between taxable and nontaxable commodities and the problem of enforcement, it has the advantage of simplicity in that requires only a relatively minor modi…cation of the market mechanism. 13.4.3 Production externalities: Private solutions However, does the government need to get involved at all with corrective taxes or subsidies? Perhaps if the interests of the various …rms involved in an externality are correctly modelled then outside intervention by the government may be irrelevant. Internalisation through reorganisation In some cases, where the production externality impinges only on one or a few other …rms an industrial organisation solution can be sought. A merger of the “victim”…rm with the …rm generating the externality would change the nature of the problem. What had been two separate decision-making entities relying on market signals become two component plants of a single …rm A rational manager of the combined …rm would recognise the interdepen den cies amongst the plants and allow for this in making decisions on net outputs for th e combined …rm. The merger has thus “internalised”the externality. Of course this leaves open the question of whether a large organisation would be e¢ ciently organised internally to take account of the richer information that becomes available from the merger of the erstwhile separate …rms. Internalisation through a pseudo-market However, changes in the industrial structure may not be necessary to do the job of internalisation. It could be that self interested but enlightened managers of the …rm can extend the operation of the market. To see the argument h ere take the case where there are just two …rms: …rm 1 is a polluter and …rm 2 the victim. We assume that both …rms are fully informed about technological possibilities and production activities, including the impact of the externality: this information assumption is important. We also assume 12 Does this imply that the “polluter pays”? [See footnote questions 20 and 22 in chapter 9.] 13.4. EXTERNALITIES 445 that there is no legal or other restraint on the activities of …rm 1, the polluter. So it would appear that …rm 2 would have to su¤er a loss of pro…ts that, ceteris paribus, becomes larger as …rm 1 increases its output. The key to the private solution is for …rm 2 (the victim) to make an o¤er of a side-payment or bribe to …rm 1. The bribe is an amount that is made conditional upon the amount of output that …rm 1 generates: the greater the pollution, the smaller is the bribe; so we model the bribe as a decreasing function  () having as argument the polluter’s output. The scheme can be implemented because we assume that the pollution activity is common knowledge. How should  be determined? We can treat it as one more c ontrol variable for …rm 2, and so the optimisation problem is max fq 2 ;g n X i=1  p i q 2 i      2  2  q 2 ; q 1 1  (13.8) The …rst-order conditions are: p i   2  2 i  q 2 ; q 1 1  = 0 (13.9) 1 +  2 d 2  q 2 ; q 1 1  dq 1 1 dq 1 1 d = 0 (13.10) Using the de…nition of the externality we can write (13.10) as 1 +  2  2 2  q 2 ; q 1 1  e 1 21 dq 1 1 d = 0 (13.11) which, in view of (13.9), implies d dq 1 1 =  2  2 2  q 2 ; q 1 1  e 1 21 = p 2 e 1 21 (13.12) Now look at the problem from the point of view of …rm 1. Once the victim …rm makes its o¤er of a conditional bribe, …rm 1 should take account of it. So its pro…ts must look like this max fq 1 g n X i=1  p i q 1 i  + (q 1 1 )   1  1  q 1  (13.13) – there is explicit recognition in (13.13) that the size of the sidepayment will depend upon q 1 1 , which is under …rm 1’s direct control. The …rst-order conditions for …rm 1’s problem are then given by p 1 q 1 i + d(q 1 1 ) dq 1 1   1  1 1  q 1  = 0 (13.14) p 2   1  1 2  q 1  = 0 (13.15) which, taking into account (13.12), imply  1 1  1 2 = p 1 p 2 + e 1 21 : (13.16) 446 CHAPTER 13. GOVERNMENT AND THE INDIVIDUAL Figure 13.6: A fundamental nonconvexity Remarkably we seem to have come to the same e¢ cient solution as would have been reached by an optimally designed pollution tax –see equations (13.6) and (13.7). What is more this apparently e¢ cient outcome can be obtained even if the legal system assigned rights to the victim rather than the perpetra- tor. It appears, therefore, that if there is perfect information, costless enforce- ment and meaningful negotiation is possible, that e¢ cient an outcome can be attained through a purely private mechanism. In e¤ect the set of markets has been augmented by the creation of a pseudo-market in pollution rights, and the appropriate pricing of these rights plays the central role in implementing the e¢ cient allocation. This extension of the market has e¤ectively internalised the externality by placing an implicit price on it that the producer of the externality cannot a¤ord to ignore. However, there may yet be problems:  If a polluter is allowed to sell rights to pollute inde…nitely then it is pos- sible that the process might go on until …rm 2 go es out of business. In which case the feasible set will look like that illustrated in Figure 13.6. However, if this occurs it is then clear that reliance on the extended mar- ket mechanism will not work for the very same reason that we encounter in section 13.3: the pricing of pollution rights leads one to point ^q rather than the e¢ cient point ~q. One may have transformed the externality-type problem of market failure into a nonconvexity-type problem.  The argument implicitly supposes that transactions costs are negligible: the bribe is negotiated and paid with no more fuss than a conventional 13.4. EXTERNALITIES 447 market transaction; the quid pro quo of the reduction in the polluting activity is veri…ed with no more fuss than checking the quality of goods in the market. But it is not hard to think of situations where this assumption just will not do. For example, where there are many potential perpetrators and victims, isolating the p articular polluter involved, implementing the bribe and monitoring the actions contingent on the bribe may be di¢ cult.  Each …rm is supposed to be well informed about the cost functions of others in order to implement the optimal bribe function. This assump- tion could seem rather unsatisfactory in view of the regulation problem highlighted in section 13.3.4: will a competitor know a rival’s costs better than the government? 13.4.4 Consumption externalities We can use some of the production-externality analysis to handle external e¤ects in consumption as well. Now, in contrast to the case considered above, we take the situation where production takes place without externality, but there may be interdependencies between agents’utility functions. Good 1 is some commodity that a¤ects the utility of other people either negatively (tobacco?) or positively (deodorant?) and good 2 is just a basket of other goods. Using the basic e¢ ciency principles from equation (9.34) and (13.2) we get U h 1 U h 2 =  1  2  e h 21 (13.17) where e h 21 is the marginal externality generated by h in consuming good 1 (val- ued in terms of good 2) obtained from equation (9.33): at an e¢ cient allocation each household’s marginal willingness to pay for good 1 shou ld just equal the marginal cost of producing good adjusted by the value of the marginal exter- nality. Again we might think of a modi…ed market solution using a corrective tax. So, reasoning as before, equation (13.17) would lead to p 1 p 2 = ~p 1 ~p 2 + t (13.18) where p 1 p 2 again represents the consu mer’price ratio, ~p 1 ~p 2 is the producer’s price ratio and t = e h 21 (13.19) is the required corrective tax. 13 To follow through on the example used in the e¢ ciency on discussion on page 250 the implication of (13.18) and (13.19) is that if smoking generates a negative externality (e h 21 < 0) then there should be a positive corrective tax on smoking equal to the value of the marginal externality. The tax can be seen as a 13 On this basis should deodorant and perfume be subs idised? 448 CHAPTER 13. GOVERNMENT AND THE INDIVIDUAL way of incorporating the social costs of a negative externality in with the private cost of supplying the consumer with the good that generates the externality. However, it is clear that in the case of consumption externalities the problems of information and measurement might be fairly intractable. In some cases (as with smoking) it may be true that there is independent in formation on the damage to other peoples’health so that the value of the marginal externality is common knowledge. But in many cases the informational problems will be at least as great as those associated with knowing …rms’costs in the production- externality model. Given the heterogeneity of tastes it may be impossible for someone to provide accurate and veri…able information about the externality; it may even be impossible to determine in which direction (positive or negative) the externality works! In the light of this people may have an incentive to misrepresent their preferences 14 –a problem that emerges more sharply in the analysis of public goods –section 13.6 below. 13.4.5 Externalities: assessment Can all the various types of externality be satisfactorily handled through the workings of private interests? This central question that we have addressed in this section resolves into the questions: can the externality be internalised? If so, how? In some cases the answer appears to be positive, but the workings of the market need to be adjusted appropriately. These cases cover situations where the e¢ cient outcome can be sustained by a corrective tax that drives a wedge between consumer and producer prices. Some versions of internalisation rely on explicitly superseding the conventional market mechanism by merging separate production entities. Internalisation may be trickier in situations where agents voluntarily set up their own extended market or where the problem of imper- fect information means that it is impossible to prevent agents misrepresenting preferences or costs. 13.5 Public consumption Check out Table 9.2 (page 236) once more. It gives four special cases on the public-private spectrum of goods. We have examined two of these (those on the left of the table, corresponding to “Rival”goods); it is now time to look at the analysis of the case in the top-right-hand corner, marked with an enigmatic “?”. This special case is “public consumption” in the sense that the good lacks the rivalness property – making it available for an extra person to consume involves no extra resources. But it is not truly “public”because we assume that it is excludable. It is interesting half-way house on the way to disc uss ing the topic of public goods in section 13.6. Fortunately we can deal with the issues that it raises in comparatively short order. 14 Provide an example to show this based on foot note question 13. 13.5. PUBLIC CONSUMPTION 449 13.5.1 Nonrivalness and e¢ ciency conditions So, let us think through the provision of a good that exhibits the characteristic of non-rivalness but yet is excludable –pay-for-view TV, for example. The ex- cludability property means that you can charge for the good; and so an e¢ cient allocation could be implementable through some type of market mechanism. How should the price be set and can we rely on the free market to set it? Let good 1 be the non-rival good and good 2 a basket of all other goods. The argument of sec tion 9.3.4 implies that the e¢ cient allocation must satisfy 15 n h X h=1 U h 1 (x h ) U h 2 (x h ) =  1  2 (13.20) This immediately suggests an implementation method. Because the good is assumed to be excludable we can introduce a charge p h for each agent h that is the price (for that agent) for the right to consume good 1, denominated in terms of good 2. The condition (13.20) then gives n h X h=1 p h =  1  2 (13.21) Each consumer is set a price that corresponds to his marginal willingness-to-pay for the service supplied; each could be cut o¤ if he does not pay; the sum of these prices totals the marginal cost of supply of the service. 16 Two di¢ culties with this allocation rule suggest themselves:  The assumption of perfect excludability in this case is a strong one –things will go wrong if individual consumers’marginal willingness to pay cannot be readily observed.  It is often the case that this type of go od is to be supplied not by a col- lection of competitive …rms but by just one, or a few, large producers. So there may also be a problem of monopoly supply that requires regulation, as discussed in section 13.3.4. However there is a commonly-encountered institution that, it could be ar- gued, is designed precisely to supply such non-rival goods. 13.5.2 Club goods The club can be seen as a d evice that does exactly that job. Through its mem- bership rules it implements an e¤ective exclusion mechanism. Let us analyse a simple version of a club that provides good 1. 15 Explain why. 16 What is the marginal unit of the product that is being supplied in the TV example? [...]... goods see Andreoni (1 988 ) and Bergstrom et al (1 986 ) For approaches that relax the dominantstrategy requirement for the implementation of public goods see Groves and Ledyard (1977) (Nash equilibria) and d’ Aspremont and Gérard-Varet (1979) (a Bayesian approach) The provision-point mechanism and money-back guarantees are dealt with in Bagnoli and Lipman (1 989 ) and Palfrey and Rosenthal (1 984 ) The use... 13.9 Reading notes The standard reference on market “failure” is Bator (19 58) Hotelling (19 38) provides an early treatment of the nonconvexity (“increasing returns” issue ) On the analysis of regulation of …rms see Baron and Myerson (1 982 ), Demsetz (19 68) and La¤ont and Tirole (1993) The classic treatment of the market approach to externalities is in Meade (1952) and Buchanan and Stubblebine (1962) The... compensated-demand elasticities of the di¤ erent types of commodities 3 2 Explain 3 3 Show why [Hint: use Roy’ identity] s this [Hint: Use the symmetry of substitution e¤ects.] 13 .8 CONCLUSION: ECONOMIC PRESCRIPTIONS Meat, …sh, dairy products and fats Fruits and vegetables Drink and Tobacco Household running expenses Durable goods Other goods and services 13 .8 = 1:025 11.1 8. 2 10.1 5.3 5.6 6.2 = 1:05 27 .8 18. 6... 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Show that the above assumptions on  imply that C is incr easing and convex in x 1 and is nondecreasing in N. 18 Explain why. 13.6. PUBLIC GOODS 451 in. alternatives,  and if  is de…ned for possible pro…les of utility functions,  and if  is non-manipulable in the sense that it is implementable in dom- inant strategies, 4 58 CHAPTER 13. GOVERNMENT AND. …rst with production externalities enables us to develop a method of analysis and set of criteria for other types of externality and for introducing the issue of public goods. 13.4.1 Production externalities: