Externalities,public goods and asymmetric information

Lecture5—Externalities Theodore Bergstrom,UCSBMarch31,2002c 1998Chapter5ExternalitiesA Model of One-sided PollutionEd smokes.Fiona,his neighbor,hates smoke.Ed and Fiona both love beans.Neither cares how many beans the other eats.Ed can get tobacco for free.Both havefixed incomes that can be used to buy beans.Ed’s utility function isU E(S,B E)and Fiona’s utility function isU F(S,B F)where S is the amount of smoking that Ed does and B E and B F are the amounts of beans consumed by Ed and Fiona respectively.The set of allocations available to Ed and Fiona consists of all the triples (S,B E,B F)such thatB E+B F=W E+W Fwhere W E and W F are the wealths of Ed and Fiona,measured in terms of the numeraire,beans.Smoke in a BoxThere is a nice way to show the set of possible allocations and the preferences of Ed and Fiona,using a diagram that looks like an Edgeworth box without a roof.The distance between the two vertical walls of the box in Figure5.1 is constructed to be W E+W F,which is the total amount of beans to be allocated between Ed and Fiona.A point in the box represents an allocation1in the following way.The horizontal distance of the point from the left side of the graph is beans for Ed.The distance from the right side is beans for Fiona.The vertical distance from the bottom of the graph is the total amount of smoking by Ed.Each point on the graph represents a feasible allocation since the sum of Ed’s and Fiona’s beans will always be W E +W F and since we have assumed that there is no resource constraint on Ed’s smoking.The point W 0on the horizontal axis represents the allocation in which Ed and Fiona consume their initial allocations of beans and there is no smoking.Figure 5.1:A One-Sided Externality0Beans for EdBeans for FionaS m o k i n g b y E d Ed’s indifference curves are the curves bulging out from the right side.They bend back on themselves because even for Ed,too much smoking is unpleasant.Fiona’s curves slope downwards away from the point 0.This gives her convex preferences and a preference for more beans and less smoke.Property RightsIf there were no restrictions on smoking and no bargains were made between Ed and Fiona,then Ed and Fiona would each spend their own wealth on their own beans and Ed would smoke an amount,S 0.But the allocationX =(S 0,W E ,W F )is not Pareto optimal.This can be seen by noticing that any point inside the football-shaped region whose tip is X designates a feasible allocation2that is Pareto superior to X.They would both be made better offif Fiona would give Ed some of her beans in return for which Ed would smoke less. It is easy to see that the Pareto optimal allocations are points of tangency between Ed’s and Fiona’s curves.Those Pareto optimal allocations which are better for both Ed and Fiona than the allocation X are represented by the points on the line segment,Y T.If Ed has a legal right to smoke as much as he likes and if Fiona and Ed bargain to reach a Pareto optimal point,the outcome would be somewhere on Y T.Alternatively,there might be a law that forbids Ed to smoke without Fiona’s consent.If no deal were struck,the outcome would be the allocation marked by W O on the box where there is no smoking and where Ed consumes W E and Fiona consumes W F.We see from Figure5.1that this allocation is not Pareto optimal.Both parties would benefit if Ed gave Fiona some beans in return for permission to smoke.The Pareto optimal allocations that are Pareto superior to the no-smoking allocation are represented by the line SZ in Figure5.1.The set of all Pareto optimal allocations includes the entire line ST as well as points of tangency beyond S and T.We notice that the optimal amount of smoke is different at different points on the curve ST that is chosen.Lindahl Equilibrium in a Smoky BoxIt is interesting tofind the Lindahl equilibrium in Ed and Fiona’s smoky box.Considerfirst the case where initial property rights allow no smoking. Let beans be the numeraire,with price1,let Ed’s Lindahl price for Ed’s smoking be p E and let Fiona’s Lindahl price for Ed’s smoking be p F.Recall that in Lindahl equilibrium,the allocation chosen must be an allocation that maximizes the the total value of output where public goods are evaluated at the sum of the Lindahl prices.Since smoking does not cost anything in terms of public goods,it must be that in Lindahl equilibrium,the amount of smoking S maximizes(p E+p F)S over all possible values of S.This is possible for afinite positive S only if p E+p F=0.1Thus we conclude that in Lindahl equilibrium,p F=−p E.When no smoking is allowed in the initial allocation,Ed’s Lindahl budget 1The logic here is similar to the reasoning that tells us that in competitive equilibrium afirm that operates under constant returns to scale can be maximizing profits with a finite positive output only if it is making zero profits.3Figure 5.2:Lindahl EquilibriumS m o k i n g b y E d Beans for Fionaconstraint must be B E +p E S ≤W E .(5.1)His budget line is a straight line passing through the the point W 0in Figure5.2,with slope −1/p E .Fiona’s Lindahl budget constraint isB F +p F S ≤W F .(5.2)Let W =W E +W F .Since Fiona’s consumption is measured from the right side of the box,her budget constraint can also be written as W −B E +p F S ≤W −W E ,which we see by rearranging terms is equivalent to B E −p F S ≥W E .In Lindahl equilibrium,we must have p F =−p E .Therefore Fiona’s budget constraint in equilibrium can be written asB E +p E S ≥W E .(5.3)Comparing the budget inequalities 5.1and 5.3,we see that in Lindahl equilibrium,Ed is confined to choosing a point that is on or below a bud-get line passing through the initial allocation W 0and Fiona is confined to choosing a point that is on or above the same budget line.If the price p E is arbitrarily chosen,there is no reason to suspect that Ed would choose the same allocation that Fiona would choose.But,just as in the case of competitive equilibrium,it is possible to show that under quite weak as-sumptions there will be at least one point where their choices coincide.We have drawn the dashed budget line in Figure 5.2to correspond to a price P E4at which Ed’s preferred allocation is the same as Fiona’s.This allocation is marked E N in thefigure.We see that in Lindahl equilibrium,Ed pays Fiona for permission to smoke.When Ed is paying the Lindahl equilibrium price,the amount of smoking that Ed demands is the same as the amount of smoking permission that Fiona is willing to grant at that price.In Lindahl equilibrium,Ed does not have to quit smoking altogether,but he smokes less than he would if he were free to smoke at no charge.An alternative way to assign property rights is to allow Ed to smoke as much as he wishes.Fiona,of course,may choose to bribe him to smoke less. The corresponding Lindahl equilibrium is found by choosing a budget line that passes through the point X in Figure5.2with the property that Ed’s favorite allocation from among those points that lie on or below this line is the same as Fiona’s favorite allocation from among those points that lie on or above the line.We have drawn such a line in Figure5.2and marked the resulting Lindahl equilibrium allocation as E S.In this Lindahl equilibrium, Fiona bribes Ed to reduce his smoking.The Lindahl price is the price at which Ed’s demand for smoking is equal to the supply of smoking permission that Fiona is willing to grant.In Lindahl equilibrium,Ed smokes less than he would if there were no charge for smoking,but he consumes more beans than he would without trade.What Is an Externality?Pigou’s ViewsEconomists are not entirely sure about how best to define externalities. Professor Arthur Cecil Pigou,one of the founders of modern publicfinance theory,devoted a chapter of his book The Economics of Welfare[?]to problems that most economists these days would call externalities.Pigou, however,doesn’t use the word“externalities”,he speaks of the divergence between social and private product.)According to Pigou:“Here the essence of the matter is that one person A,in the course of rendering some service,for which payment is made,to asecond person B,incidentally also renders services or disservicesto other persons(not producers of like services),of such a sortthat payment cannot be extracted from the benefited parties orcompensation enforced on behalf of the injured parties.”[?],page183.5Pigou offers a list of examples of beneficial externalities,including the fol-lowing...Maintenance of a private forest may improve the environment for neighbors,lamps erected at the doors of private houses may illuminate the street,pollution abatement activities offirms improve air quality,re-sources devoted to fundamental research may in unexpected ways improve production processes.Pigou also lists some harmful externalities,“the game-preserving activities of one occupier involve the overrunning of a neighbor’s land by rabbits,”a factory in a residential neighborhood destroys the ameni-ties of neighboring sites,motor cars congest and wear out roads,manufac-turers produce noxious smoke as a biproduct.Pigou suggests that appropriate taxes and subsidies may be useful for achieving efficiency in a competitive economy with externalities.2According to Pigou:“When competition rules and social and private net product at the margin diverge,it is theoretically possible to put mattersright by imposition of a tax or the grant of a subsidy.”[?],page381.Modern economists frequently refer to such interventions as“Pigovian”taxes or subsidies.Externalities and Missing MarketsWalter P.Heller and David Starrett[?]propose and then(partially)re-nounce a definition that would seem to reasonably capture the“external-ity”found in the Ed-Fiona example and the examples suggest by Pigou. According to Heller and Starrett:“An externality is frequently defined to occur whenever a decision variable of one economic agent enters into the utilityfunction or production function of another.We shall argue thatthis is not a very useful definition,at least until the institutionalframework is given.”To understand Heller and Starett’s point,it may be helpful to consider an example.Suppose that persons A and B both pick berries from a common berry-patch.As it happens,the more berries that B picks,the more difficult 2Pigou acknowledges that in practice,correction of externalities by means of taxes and subsidies may be difficult or impossible,and he discusses the alternative of using publicly-managedfirms as an alternative.6it is for A tofind berries and the harder A has to work to pick any given number of berries.In this case,A will care about the number of berries that B picks.According to our proposed definition,B’s berry-picking generates an externality on A.If,on the other hand,the berry patch is owned by an owner who hires A and B to pick berries for an hourly wage and also sells berries to them,then the economy can be readily modelled as one in which there are no externalities;that is,neither A nor B cares about the berry-picking activities or the berry consumption of the other.As Heller and Starr suggest,“one of the prime attributes of the market system is that it isolates one individual from the influence of others’behavior(assuming of course that prices are taken by everyone as given.)”Heller and Starr suggest that the definition proposed at the beginning of this paragraph should be modified to apply only if interdependencies exist in the framework of a competitive market system.Thus they propose to describe externalities as follows:“...one can think of externalities as nearly synonymous with nonexistence of markets.We define an externality to be a situ-ation in which the private economy lacks sufficient incentives tocreate a potential market in some good and the nonexistence ofmarkets results in losses in Pareto efficiency.”Heller and Starrett suggest that when we observe situtations with appar-ent externalities,it is useful to focus our attention on the more fundamental question of why it is that the situation lacks markets which would eliminate the externality.Heller and Starr suggest the relevant considerations in this way.“We propose(roughly)that situations usually identified with “externality”have more fundamental explanations in terms of1)difficulties in defining private property(2)noncompetitivebehavior(3)absence of relevant economic information,or(4)nonconvexities in transaction sets.”Creating Markets for Externality PermitsThe Case of One Polluter and One VictimLet us pursue Heller and Starrett’s suggestion that the externality in the case of Ed and Fiona might correspond to a“missing”market.In order to7construct this market,however,we are going to have to introduce some legalinstitutions.In particular,let us suppose that the“government”introducesa new commodity called“smoking permits”along with a law that requiresthat for each unit of smoke that a person produces,he has to to presentone smoking permit.The government prints afixed supply¯S of smoking permits and distributes them in some way between Ed and Fiona.Although Fiona will not want to use a smoking ticket for permission tosmoke,she will be willing to pay something for smoking tickets because sheknows that there is afixed supply of tickets and that every ticket that sheacquires is one that Ed will not be able to use.If,for example,Fiona keepsall of the smoking tickets,then Ed will not be able to smoke at all.We now have an economy with two private commodities,beans andsmoking tickets.In our previous discussion,we defined Ed’s and Fiona’sutility functions U E(S,B E)and U F(S,B F)with the variable S represent-ing Ed’s smoking appearing in both people’s utility functions.With theintroduction of smoking permits,we can convert this economy into one withprivate goods only.In particular,if Ed always uses his smoking permits toget permission to smoke,his utility when he has S E smoking permits will be ˜U E(S E,B E)=U E(S E,B E).If Fiona buys S F smoking permits and hides them in her sock drawer,then Ed will have only¯S−S F permits and hence will produce only¯S−S F units of smoke.In this case,Fiona’s utility will be ˜U F(S F,B F)=U(¯S−S F,B F),which depends only on her own consumption of beans and her own consumption of smoking permits.The economy that we have constructed in this way is a standard two-person,two-commodity pure exchange economy—the kind of economy that is found in Edgeworth boxes in all good intermediate price theory texts.Let us now draw an Edgeworth box for this economy.This box turnsout to look exactly like the Edgeworth box that we drew in Figures5.1and5.2except that we now put a roof on the Edgworth box.In particular,thebox will be¯S units high,where¯S is the initial supply of tickets.Before going further with our Edgeworth box construction,we need todecide who gets the smoking tickets initially.As you might guess,the ques-tion of to whom the permits are assigned initially is exactly the same ques-tion of property rights that we addressed in the case of Lindahl equilibrium.One possibility is that we assign a property right to clean air to Fiona.Thiscould be accomplished by giving all of the smoking permits to Fiona ini-tially.In this case the initial endowment corresponds to the point W0in theEdgeworth box.Alternatively,we could have given Ed an initial right tosmoke as much as he wishes,given his initial holdings of beans.We couldaccomplish this assignment of rights by giving Ed an initial holding of per-8Figure5.3:A Market for Smoking PermitsBeans for Fionamits equal to the amount of smoking he would choose if he could smoke freely and by giving the rest of the permits to Fiona.In this case the initial allocation corresponds to the point X in the Edgeworth box.It would also be possible in principle to allocate initial holdings of permits in any other way such that the total number of permits adds to¯S.In Figure5.3,we have shown the competitive equilibrium budget lines and the competitive equilibrium allocations E N and E S corresponding to the two different initial allocations W0and X.Notice that these correspond exactly to the Lindahl equilibria in our previous discussion.You may also wonder what decides the total number¯S of smoking per-mits to be issued.In part,the answer is indeterminant.If we start from a situation in which¯S permits are issued and where in the resulting competi-tive equilibrium Fiona chooses to hold some permits,then we notice that if the government issued more permits,but gave them all to Fiona,the out-come would not be changed at all.Of course if the government wants to give Ed the right to produce at least S units of smoke,it will have to supply at least¯S permits.Having shown the way in which markets can“privatize”the smoking externality in our model of Ed and Fiona,it is useful to return to the focus suggested by Heller and Starrett.Why did it seem natural for us to model the effects of Ed’s smoking on Fiona,without immediately assigning owner-ship rights and without introducing a corresponding market for transfer of9such rights?It may be fruitful to turn this question around and ask why it seemed entirely natural to assign initial property rights to beans.Certainly it is physically possible for Ed to steal Fiona’s beans and vice versa.In many societies,but certainly not in all,institutions and norms have evolved that make theft relatively rare.It is possible in principle to regard inflicting tobacco smoke on another person without that person’s permission as the legal and moral equivalent of theft.Indeed norms in the United States ap-pear to be shifting in that direction.This is undoubtedly in part a response to relatively new scientific information about actual damage that smokers inflict on non-smokers and in part due to an increase in the proportion of non-smokers in the population.As Heller and Starrett point out,even where market equilibrium exist,as in the case of Ed and Fiona,introduction of market institutions is likely to have costs.If there is to be a market,then somehow Ed has to be prevented from smoking without a permit.For violations to be enforceable,they must be relatively cheaply observable.In realistic circumstances,it may not be so easy to tell whether Ed is secretly puffing a cigar,or whether the nasty smell that plagues Fiona comes instead from a burning tire or aflatulent canine.A fundamental difficulty in the establishment of property rights in the face of“externalities”is that it is easy for people to claim damage from the actions of others and difficult to verify that actual damage has been done. It would certainly be impractical to force everyone to buy permission for each publicly observable action that he or she might take.In every society, people are willing to accept occasional annoyance from others without com-pensation,knowing that some of their own actions will also cause offense.It seems to me that a free society must be one whose members are relatively tolerant of annoyance that does not cause objectively measurable harm.As science develops new methods of detecting,measuring,and pricing harmful externalities,however,new market forms and new forms of property rights are quite likely to evolve.Conspicuous examples of this kind include mar-kets for emissions of pollutants into the air and water,and for congestion of highways,streets and other public areas.The Case of Many Polluters and Many VictimsSuppose that instead of just two people,Ed and Fiona,we have a community in which there are many polluters and many pollution victims.We will not assume that polluters and pollutees are separate people,but allow the possibility recognized by Walt Kelly’s Pogo,who said“We have met the10enemy and it is us.”In this economy,there are n consumers,m private goods,and k non-private activities .Consumer i cares about i ’s own vector of private goods x i but does not care about the private goods consumption of others.Consumers also care about their own vectors of non-private activities as well as the sum of the vectors of non-private activities of others.Thus Consumer i has a utility function u i (x i ,,y i ,z )where y i is the vector of non-private activities performed by i and where z = n s =1y s .For simplicity of notation,let us confine our attention to a pure exchange economy without production of private goods.Each consumer i has an ini-tial endowment vector of private goods,ˆx i and we define ˆx = n i =1x i .3This formulation account for pollution activities in the following way.Consumer i may take pleasure in releasing pollutant j but,holding constant his own release of pollutant,every consumer may regard the total amount of pol-lutant j in the atmosphere as a “bad”.In this case,u i is an increasing function of y ij ,but a decreasing function of z j = n s =1y sj .Suppose that for each polluting activity j ,the government issues a fixed number ˆz j trans-ferable permits,where consumer i is given ˆz ij permits and where we define ˆz j = n i =1ˆz ij .Consumers are allowed to trade these permits for private goods or for other kinds of tickets.A consumer is not allowed to release more pollution than the amount for which he has permits.The formulation can also account for positive externalities.For example,there may be a service activity,like picking up trash or beautifying the environment,which is unpleasant to perform,but where the total amount of this activity perform is regarded as a good by all consumers.For such an activity,j ,u i would be a decreasing function of the amount y ij of the service performed by i but an increasing function of the total amount z j of service j that is performed by community members.The government could issue an initial endowment of marketable service obligations,such that the holder of each unit of obligations is required to perform a corresponding unit of the service.With this assignment of property rights,the total amount of each non-private activity that will be performed must equal the total number of per-mits or obligations for that activity that are issued by the government.Trades of permits and obligations will determine the ultimate distribution3This model can be interpreted as a production economy,in which we allow some consumers to own firms (or parts of firms).These consumers may engage in “production”which is treated as negative consumption of output goods,along with positive consumption of input goods.The consumers’budget equations then apply to net purchases positive or negative.11of non-private activities,but will not affect the vector ˆz of total amounts of pollution and of service activities.In the resulting economy,each consumer’s utility takes the form u i (x i ,y i ,ˆz )where ˆz is fixed.The only variables that i chooses are x i and y i .When ˆz is held constant,nobody other than person i cares about either x i or y i .Thus when ˆz is fixed,we have a model that is formally the same as a pure exchange model with private goods only where any feasible allocation of x ’s and y ’s must satisfy the equations n i =1x i =ˆx i and n i =1y i =ˆz .As is well known from competitive equilibrium theory,a competitive equilibrium will exist for this economy if all individuals have continuous,convex preferences and if a few other relatively weak technical assumptions are satisfied.If,however,the vector of permits and obligations ˆz is arbitrar-ily selected,there is no reason to expect that the outcome will be Pareto optimal.Although the competitive equilibrium with ˆz ,may not be the op-timal,it will be true that this outcome will be Pareto optimal conditional on the aggregate vector ˆz .That is to say,any allocation that is Pareto su-perior to this competitive equilibrium must either be infeasible or must be one in which the aggregate vector of non-private activities is different from ˆz .To say this yet another way,although this competitive equilibrium may not have the right total amount of non-private activities,allocation of these activities among individuals is done efficiently.One Pollutant,Many Polluters,and Many PolluteesTo focus our attention,let us consider a special case of the model we have just discussed.There are n consumers,one private good and one non-private pollution activity.Each person’s utility function is of the form u i (x i ,y i ,z )where x i is i ’s private consumption,y i is the amount of pollution that i produces and z = n i =1y i is the total amount of pollution produced in the community.The function u i is an increasing function of its first two arguments and a decreasing function of its third argument.(To be continued...)We will show that unlike in the case of Ed and Fiona,if we introducing just one kind of pollution permit allocates production efficiently among pol-luters but won’t lead to efficient total amount of pollution.If we introduce separate permissions for each pollutee we have thin markets,no reason to expect competitive c.e.to happen even though it exists.12Exercises5.1Suppose that Ed’s utility function is U E(B E,S)=B E S for0≤S≤4,and U(B E,S)=0for S>4.Suppose that Fiona’s utility function is U F(B F,S)=B F−S2.Assume that the initial allocations of beans are W Eand W F,where W E+W F=16.a).Sketch an Edgeworth diagram,showing Ed’s and Fiona’s preferencesover possible allocations.b).Write algebraic expression(s)to describe all of the Pareto optimalallocations for Ed and Fiona.c).Write an equation for the utility possibility frontier and sketch it.d).Find the Lindahl equilibrium prices and quantities as a function ofW E where initial property rights forbid smoking.e).Find the Lindahl equilibrium prices and quantities as a function ofW E where initial property rights allow one to smoke as much as onewishes.5.2Jim and Tammy are partners in business and in Life.As is all toocommon in this imperfect world,each has a little habit that annoys the other.Jim’s habit,we will call Activity X and Tammy’s habit,activity Y. Let x be the amount of activity X that Jim pursues and y be the amount of activity Y that Tammy pursues.Jim must choose an amount of activity X between0and50.Tammy must choose an amount of activity Y between0 and100.Let c J be the amount of private goods that Jim consumes and let c T be the amount of private goods that Tammy consumes.Jim and Tammy have only$1,000,000per year to spend on consumption goods.Jim’s habit costs$40per unit.Tammy’s habit also costs$100per unit.Jim’s utility function isU J=c J+500ln x−20yand Tammy’s utility function isU T=c T+500ln y−10x.a).Find the set of Pareto optimal allocations of money and activities inthis partnership.13b).Suppose that Jim has a contractual right to half of the family incomeand Tammy has a contractual right to the other half.c).If they make no bargains about how much of the externality generatingactivities to perform,how much x will Jim choose and how much y will Tammy choose?d).Find Lindahl equilibrium prices and quantities if the initial propertyrights specify that neither activity X nor activity Y can be performed without ones partner’s consent.e).Find Lindahl equilibrium prices and quantities if Jim has a right toperform X as much as he is able to and Tammy has a right to perform activity Y as much as she is able to.5.3The cottagers on the shores of Lake Invidious are an unsavoury bunch. There are100of them and they live in a circle around the lake.Each cottager has two neighbors,one on his right and one on his left.There is only one commodity and they all consume it on their front lawns in full view of their two neighbors.Each cottager likes to consume the commodity,but is envious of consumption by the neighbor on his left.Nobody cares what the neighbor on his right is doing.Every consumer has a utility function U(c,l)=c−l2,where c is her own consumption and l is consumption by her neighbor on the left.a).Suppose that every consumer owns1unit of the consumption goodand consumes it.Calculate the utility of each individual.b).Suppose that every consumer consumes only3/4of a unit.What willbe the utility of each of them?c).What is the best possible consumption if all are to consume the sameamount?d).Suppose that everybody around the lake is consuming1unit,can anytwo persons make themselves both better offeither by redistributing consumption between them or by throwing something away?e).How about a group of three persons?f).How large is the smallest group that could cooperate to benefit all ofits members.14。

Chapter3Allocation and Distribution The undisputed standard graduate publicfinance textbook when I was in graduate school was Richard Musgrave’s The Theory of Public Finance[2]. In this book,Musgrave proposes that the main economic functions of govern-ment can be divided among three branches,the Allocation,the Distribution, and the Stabilization Branches of government.The job of the Allocation Branch is to“secure adjustments in the allocation of resources”.The job of the Distribution Branch is to“secure adjustments in the distribution of income and wealth”,and the job of the Stabilization Branch is to secure “economic stabilization”.Musgrave suggests that we think of each branch as run by a“man-ager”who is instructed to“plan his job on the assumption that the other two branches will perform their functions properly.”Thus the Allocation Branch proceeds on the“assumption of full employment of resources and that the proper distribution of income has been secured.”The distribution branch assumes that“a full-employment income is available for distribution and that the satisfaction of public wants is taken care of.”Similarly for the Stabilization Branch–(but I’m afraid my class never got as far as the stabilization part of Musgrave’s book.)Musgrave’s proposed division of labor was and is an attractive one.A good part of the appeal of this separation is that it approximately coin-cides with lines of specialization in the academic world.The Stabilization Branch could be staffed by macroeconomists,the Allocation Branch by mi-croeconomists and the Distribution Branch by welfare economists,ethical philosophers,and perhaps a few stray theologians and political scientists. The macroeconomists and microeconomists would never have to communi-cate directly and the microeconomists would rarely have to communicate2Chapter3.Allocation and Distribution with the Distribution m´e lange.1In this lecture we consider the relation between the Allocation Branch and the Distribution Branch.In case utility is quasi-linear,this relation is especially simple.In fact,the Allocation Branch can get its job done while paying almost no attention to the actions of the Distribution Branch.As you recall from our discussion in the last chapter,if there is quasilinear utility, then so long as the Allocation Branch knows that the Distribution Branch is not going to be so cold-hearted as to leave some consumers with zero private goods,there is a unique Pareto optimal amount of public goods.All the Allocation Branch needs to do is to solve for the Pareto optimal quantity of public goods and provide it.But in general,the Allocation Branch will not be able to determine the right amount of public goods to supply unless it knows what the Distribution Branch is doing.This makes life more complicated,but does not necessarily mean that we must abandon Musgrave’s program of divisional separation. Recall that Musgrave’s suggestion was not that each branch should ignore the actions of the others,but rather that each branch should assume that the other branches“will perform their functions properly”.Let’s see how this goes in an explicit example.A Case where The Allocation Branch Needs to Know What the Distribution Branch is DoingWe return to Claude and Dorothy,but now suppose that they both have Cobb–Douglas utility functions.In particular:U C(X C,Y)=X C Y2(3.1)U D(X D,Y)=X D Y(3.2) Suppose that p x=p y=1.A little calculation shows the Samuelsoncondition to be2X CY+X DY=1(3.3)1At the time when Musgrave’s book was written,publicfinance economists paid little attention to the problem of how the Allocation Branch was tofind out the utility functions of consumers who would be willing to tell the truth about their preferences only if it was in their interest.Perhaps if Musgrave were writing this book today,he would add an Investigative branch,or to make it sound a little less sinister,an Econometric Survey Research branch.WHEN CAN THE ALLOCATION BRANCH IGNORE DISTRIBUTION?3 or equivalently:2X C+X D=Y.(3.4) This equation together with the family budget equation,X C+X D+Y=W(3.5) gives us two equations in the three unknowns,X C,X D,and Y.There is not enough information in equations3.4and3.5to solve uniquely for Y, without postulating something about the distribution(X C,X D)of income between Claude and Dorothy.Indeed if we use equation3.5to eliminate X D from equation3.4,wefind that the efficiency conditions are satisfied for any choice of Y and X C such that Y=X C/2+W/2.This means that the optimal amount of Y depends on how the private goods are divided between Claude and Dorothy.The more generously the Distribution Branch chooses to treat Claude relative to Dorothy,the more public good the Allocation Branch should supply.If the Allocation Branch knows the rule according to which the Distribu-tion Branch is going to operate,then in typical cases it can solve uniquely for the right amount of public good.For our example,the rule used by the Distributive branch adds one more equation to the two equations with which the Allocation Branch has to work.Suppose,for instance,that the Distribution Branch decides that Claude and Dorothy should always have equal incomes.Then in addition to equations A and B,we haveX C=X D.(3.6) Solving the system of equations3.4,3.5,and3.6,wefind that Y=3W and5X C=X D=W/5.When can the Allocation Branch Ignore Distribu-tion?We showed that when Claude and Dorothy have quasi-linear utility func-tions,there is a unique amount of public goods that satisfies the Samuel-son condition.This fact generalizes to the case of many consumers,all of whom have quasilinear utility functions.While quasilinear utility functions are very easy to work with,the assumption of quasilinear utility in public goods is not very realistic.If preferences are quasi-linear,then a consumer’s marginal rate of substitution between public and private goods must be in-dependent of wealth.If this assumption held in the real world,we would4Chapter3.Allocation and Distribution expect tofind that rich communities would choose the same menu of public goods as poor communities.We would also expect to see that within a given community,if the rich are taxed at a higher rate than the poor,then the rich would always favor less public goods than the poor.As we will see later,both of these conclusions are strongly refuted by available empirical evidence.As we have seen,when there is quasilinear utility,there is a unique Pareto optimal amount,Y∗of public good corresponding to allocations in which both consumers get positive amounts of the private good.This makes it very easy to calculate the utility possibility frontier.Since the supply of public good is Y∗,we know that along this part of the utility possibility frontier,Claude’s utility can be expressed as U C(X C,Y∗)=X C+f C(Y∗) and Dorothy’s utility is U D(X D,Y∗)=X D+f D(Y∗).Therefore it must be that on the utility possibility frontier,U C+U D=X C+X D+f C(Y∗)+ f D(Y∗).After the public good has been paid for,the amount of the family income that is left to be distributed between Claude and Dorothy is W−p Y Y∗.So it must be that U C+U D=W−p Y Y∗+f C(Y∗)+f D(Y∗). Since the right side of this expression is a constant,the part of the utility possibility frontier that is achievable with positive private consumptions for both persons will be a straight line with slope-1.It turns out,however,that there is an interesting class of preferences, broader than the class of quasilinear preferences,for which the Pareto opti-mal amount of public goods does not change when income is redistributed among consumers.Before examining a more general class of utility func-tions that have this property,we will look at one specific example where preferences are not quasilinear,but where there is a unique Y that satisfies the Samuelson conditions.The Case of Identical Cobb-Douglas UtilitiesSuppose that there are n consumers,each of whom has a utility function of the form:U(X i,Y)=Xαi Yβ.(3.7) whereα>0andβ>0.Suppose also that this economy begins with a total endowment of W units of private good and no public goods,but it is possible to produce public goods at a constant cost of c units of private good per unit of public good.Then an allocation(X1,...,X n,Y)≥0is feasible if and only ifX+cY=W(3.8)WHEN CAN THE ALLOCATION BRANCH IGNORE DISTRIBUTION?5 where X= n i=1X i s The Samuelson necessary condition for a Pareto optimal allocation requires that the sum of the marginal rates of substitution between public and private goods equals the marginal cost of public goods. Consumer i’s marginal rate of substitution between public and private goodsisαβX i Y.The sum of the marginal rates of substitution over all consumers is:α1−αni=1X iY=αβXY.(3.9)Therefore the Samuelson condition can be written:αβXY=c.(3.10)We see that in this case,the sum of marginal rates of substitution depends only on the total amount X of private consumption.Thus any redistribution of income that leaves total private consumption unchanged will have no effect on the sum of marginal rates of substitution.Although each individual marginal rates of substitution depend on individual private consumption, we see that the sum of these marginal rates of substitution is not changed if private consumption is redistributed while X remains constant.Solving the simultaneous equations3.8and3.10,wefind that the unique value of Y s that satisfies the Samuelson necessary condition for an efficient allocation is¯Y=αα+βWc(3.11)Since the sum of the marginal rates of substitution depends only on the total amount of private consumption and not on who gets it,any allocation (X1,...,X n,¯Y)≥0such thatX i=W−c¯Y=βα+βW(3.12)will be feasible and satisfy the Samuelson condition.marginal rate of substitution curves without making about income dis-tribution we can draw a“sum of the marginal distribution.6Chapter3.Allocation and DistributionMore General ResultsBergstrom and Cornes[1]found a more general class of utility functions for which the Pareto efficient amount of public goods is independent of the distribution of private goods.Suppose that there is a single private good and k public goods.Let X i denote the amount of private goods consumed by individual i and let Y=Y1,...,Y k)be the vector of public goods.The Bergstrom-Cornes family of utility functions take the following form for each consumer i:U i(X i,Y)=A(Y)X i+B i(Y).(3.13) Notice that each individual has the same function A(·),but that the func-tions B i(·)can differ from person to person.Samuelson ConditionsIf there is just one public good and utility functions take this form,then the marginal rate of substitution of each consumer i between the public good and the private good is seen to be:MRS i(X i,Y)=A (Y)A(Y)X i+B i(Y)A(Y).(3.14)Summing Equation3.13over all i and rearranging terms slightly,wefind that the Samuelson condition can be written asA (Y) A(Y)X+ni=1B i(Y)A(Y)=c.(3.15)where X= n i=1X i.Thus we see that the sum of the marginal rates of substitution depends only on the aggregate amount of consumption and on the amount of private goods and does not depend on the distribution of the private goods among individuals.We can use the feasibility condition X+cY=W to eliminate the variable X from Equation3.15.Then we have:A (Y) A(Y)(W−cY)+ni=1B i(Y)A(Y)=c.(3.16)The only variable in Equation3.16is Y.From the previous lecture we know that(if utility is continuously differentiable)the Samuelson conditionWHEN CAN THE ALLOCATION BRANCH IGNORE DISTRIBUTION?7 is necessary for an interior Pareto optimum and that if utility functions are also quasiconcave,then the Samuelson condition together with the feasibility equation is sufficient for an allocation to be Pareto efficient.Therefore we can conclude that at any interior Pareto optima,the amount of public goods must solve Equation3.16.We also know that if Equation3.16is satisfied for Y=¯Y,then every allocation(X1,...,X n,¯Y)such that X i=W−cY and such that X i>0for all i is Pareto optimal.A Non-calculus TreatmentWe haven’t yet answered the question of when there is a unique value of Y that satisfies Equation3.16.Nor have we worked out the story of what happens at boundary solutions.We could approach the uniqueness ques-tions with calculus arguments and the boundary solutions with Kuhn-Tucker methods,but I think it is more instructive to take a different approach.We can use simpler arguments based on addition,multiplication,some inequal-ities and some simple geometry of convex sets.Let us begin by extending our discussion to a more general set of feasible allocation than we have considered previously.Specifically,let us assume that there is some closed bounded subset F of the Euclidean plane such that the set of feasible allocations consists of all allocations(X1,...,X n,Y)such that( X i,Y)∈F.2Preferences that can be represented by utility functions of the Bergstrom-Cornes form as in Equation3.13all have the same linear coefficient for private consumption.Therefore,the sum of individual utilities is determined by the amount Y of public goods and the total amount X of private goods consumed and does not depend on how the private goods are divided among individuals.Specifically,we haveni=1U i(X i,Y)=A(Y)X+ni=1B i(Y)(3.17)where X= n i=1X i.Now consider the combination(¯X,¯Y)of public goods and aggregate private good output that maximizes the sum of utilities subject to the feasi-bility constraint,(X,Y)∈F.3Why should we be interested in the feasible 2In the special case where there is afixed initial endowment of private goods and public goods are produced from private goods at constant cost of c per unit,the set F is {(X,Y)|X+cY=W}.3A standard mathematical result(known as the Weierstrass theorem)tells us that if8Chapter3.Allocation and Distribution outcome that maximizes the sum of utilities?Because any allocation that maximizes the sum of utilities must be Pareto optimal.(I leave this as an exercise for you to prove.)The sum of utilities will be the same at all allocations in which the amount of public goods is¯Y and the total amount of the private good is ¯X although,of course,different allocations of the same total amount ofprivate goods will lead to different distributions of utility.But since(¯X,¯Y) maximizes the sum of utilities over all feasible allocations,it must be that every allocation in which the amount of public goods is¯Y and the total amount of a private goods is¯X is Pareto optimal.We can state this result more formally.Proposition1Suppose that preferences of all consumers can be repre-sented by utility functions of the form U i(X i,Y)=A(Y)X i+B i(Y)and suppose that(¯X,¯Y)maximizes A(Y)X+ i B i(Y)over the set of all fea-sible combinations of X and Y,where X= i X i.Then every allocation (X 1,...,X n,¯Y)such that X i=¯X is Pareto optimal.Proposition1tells us that we canfind a whole lot of Pareto optima by choosing¯X and¯Y to maximize A(Y)X+ B i(Y)subject to(X,Y)∈F and then distributing the total amount¯X of private goods in any way that adds up.This theorem does not,however,tell us whether¯Y is the only possible amount of public goods in a Pareto optimum,or even if¯Y is the only possible amount of public goods at an interior Pareto optimum.Figure3,which will look familiar to you from consumer theory will give you a good idea of how to answer these questions.The crosshatched region in Figure3shows the set of feasible allocations F.We have drawn two level curves(indifference curves) and for the function A(Y)X+ B i(Y). Notice that we have drawn the set F as a convex set and we have also drawn the level curves to be convex toward the origin,in such a way that the set of points above each level curve is a convex set with noflat edges.A standard result in consumer theory is that this is appropriate if and only if the function A(Y)X+ B i(Y)is a strictly quasi-concave function.The picture shows the indifference curve to be the highest indifference curve that touches the feasible set F.The point of tangency is the point(¯X,¯Y).The line shown as ab is tangent both to the set F and to the set{(X,Y)|A(Y)X+ B i(Y)≥A(¯Y)¯X+ B i(¯Y}at the one and only point(¯X,¯Y)belonging to both sets. the feasible set is a non-empty closed bounded set in afinite-dimensional space and if the function to be maximized is continuous then there is at least one point in the feasible set that maximizes the function over the feasible set.Therefore so there always is at least one (¯X,¯Y)that solves this constrained maximization problem.WHEN CAN THE ALLOCATION BRANCH IGNORE DISTRIBUTION?9 Figure3.1:Maximizing the Sum of UtilitiesXLooking set F is closed, bounded and convex and the function A(Y)X+ B i(Y)is a strictly quasi-concave function,that there is exactly one quantity¯Y of public goods that corresponds to an outcome which maximizes the sum of utilities.Bergstrom and Cornes are able to show that when this is true,in any Pareto optimal allocation that gives a positive amount of private goods to each consumer, the amount of public goods must be the unique quantity¯Y that maximizes the sum of utilities.Proposition2Suppose that preferences of all consumers can be repre-sented by strictly quasiconcave utility functions of the form U i(X i,Y)= A(Y)X i+B i(Y)and that the set F of feasible combinations of aggregate output and public good supply is closed,convex and bounded.Then there is a unique quantity of public goods¯Y such that in every Pareto optimal allocation in which each consumer has a positive amount of private goods, the amount of public goods must be¯Y.Although any allocation that maximizes the sum of utilities must be Pareto optimal,(You will be asked to prove this in an exercise),it is not in general true that every Pareto optimum maximizes the sum of utilities. Example3.1,shows why this is the case.Example3.2shows why we need the convexity assumption for Proposition2.10Chapter 3.Allocation and Distribution Example 3.1Suppose that there are two persons,1and 2,and that each consumer i has utility function U i (X ,Y )=X i +√.Public goods can be produced from private goods at a cost of 1unit of private goods per unit of public goods and there are initially 3units of private goods which can either be used to produce public goods or can be distributed between persons 1and 2.Thus the set of feasible allocations is {(X 1,X 2,Y )≥0|X 1+X 2+Y ≤3}.The sum of utilities is U 1(X 1,Y )+U 2(X 2,Y )=X 1+X 2+2√Y which is equal to X +2√where X =X 1+X 2.Thus we would maximize the sum of utilities by maximizing X +2√subject to X +Y ≤3.The solution to this constrained maximization problem is Y =1and X =3.Any allocation (X 1,X 2,1)≥0such that X 1+X 2=2is a Pareto optimum.In Figure 3,we draw the utility possibility set.We start by finding the utility distributions that maximize the sum of utilities and in which Y =1and X 1+X 2=2.At the allocation (2,0,1),where Person 1gets all of the private goods,we have U 1=2+1=3and U 2=0+1=1.This is the point A .If Person 2gets all of the private goods,then U 1=0+1=1and U 2=2+1=3.This is the point B .Any point on the line AB can be achieved by supplying 1unit of public goods and dividing 2units of private goods between Persons 1and 2in some proportions.Figure 3.2:A Utility PossibilitySetU 1Now maximize the sum of utilities.Consider,for example,the point that maximizes Person 1’sWHEN CAN THE ALLOCATION BRANCH IGNOREDISTRIBUTION?11utility subject to the feasibility constraint X 1+X 2+Y =3.Since Person 1has no interest in Person 2’s consumption,we will find this point by maximizing U 1(X 1,Y )=X 1+√subject to X 1+Y =3.This is a standard consumer theory problem.If you set the marginal rate of substitution equal to the relative prices,you will find that the solution is Y =1/4and X 1=234.With this allocation,U 1=314and U 2=1/2.This is the point C on Figure 3.Notice that when Person 1controls all of the resources and maximizes his own utility,he still leaves some crumbs for Person 2,by providing public goods though he provides them from purely selfish motives.The curved line segment CA comprises the utility distributions that result from allocations (W −Y,0,Y )where Y is varied over the interval [1/2,1].An exactly symmetric argument will find the segment DB of the utility possibility frontier that corresponds to allocations in which Person 2gets no private goods.The utility possibility frontier,which is the northeast boundary of the utility possibility set,is the curve CABD .There are also some boundary points of the utility possibility set that are not Pareto optimal.The curve segment CE consists of the distributions of utility corresponding to alloca-tions (W −Y,0,Y )where Y is varied over the interval [0,1/2].At these allocations,Person 1has all of the private goods and the amount of pub-lic goods is less than the amount that Person 1would prefer to supply for himself.Symmetrically,there is the curve segment DF in which Person 2has all of the private goods and the amount of public goods is less than 1/2.Finally,every utility distribution in the interior of the region could be achieved by means of an allocation in which X 1+X 2+Y <3.In this example,we see that at every Pareto optimal allocation in which each consumer gets a positive amount of private goods the amount of public goods must be Y =1,which is the amount that maximizes the sum of utilities.Example 3.2Suppose that as in Example 3.1,there are two persons,1and 2,and each person i has utility function U i (X ,Y )=X i +√Y .As in the previous example,public goods can be produced from private goods at a cost of 1unit of private goods per unit of public goods and there are initially 3units of private goods.But in this example,the amount of public goods supplied must be either Y =0or Y =1/4.In this case the set of possible allocations is not a convex set.The utility possibility set includes the two lines AB and CD .Points on12Chapter3.Allocation and Distribution Figure3.3:A Non-convex Utility Possibility SetU1the line AB show all of the utility distributions that are possible when Y=1 and2units of private goods are divided between the persons1and2.Points on the line CD show the utility distributions that are possible when Y=1/4 units of private goods are divided between the persons1and2.The and234cross-hatched area shows the entire utility possibility set.(Points that are not on AB of CD are obtained by wasting some of the private goods.)The utility possibility frontier consists of the three line segments AB,CE,and DF.The Pareto optimal allocations on the line segments CE and DF are reached with Y=1/4rather than Y=1,even though Y=1maximizes the sum of utilities.Moreover,except for the endpoints C and D,points on these lines correspond to allocations in which both persons get a positive amount of public goods.EXERCISES13 Exercises3.1Suppose in the example where Claude and Dorothy have utility func-tions X C Y2and X D Y respectively,the Distribution Branch has the rule that X C=2X D.Solve for the Pareto optimal choice of Y by the Allocation Branch.3.2Whereα>0andβ>0,show that if all consumers have identical Cobb-Douglas utility functions Xαi Yβthen these same preferences can also be represented by a utility function of the form A(Y)X i+B i(Y).What are the functions A(Y)and B i(Y)?Hint:What monotonic transformation of the Cobb-Douglas func-tions will give a utility function of the Bergstrom-Cornes form?3.3Consider an economy with three individuals,each of whom has a utility function:Y X i.Public goods can be produced from private goods at a cost of one unit of private goods per unit of public goods,and there is an initial allocation of W units of private goods.Describe and sketch the entire utility possibility set.3.4Consider an economy with two individuals.Person i has utility function Y(X i+k i)where k i>0.Public goods can be produced from private goods at a cost of one unit of private goods per unit of public goods,and there is an initial allocation of W units of private goods.a).Find the unique amount of public goods that satisfies the Samuelsoncondition.b).Show that there are some Pareto optima that do not satisfy the Samuel-son condition and that have a different amount of public goods. c).Describe the utility possibility set and the utility possibility frontier.Sketch the way it would look,qualitatively.d).Suppose that one or both of the k i’s are pare the quan-tity of public goods at Pareto optimal outcomes that do not satisfy the Samuelson conditions with those at Pareto optimal outcomes that do.Interpret your result.14Chapter3.Allocation and Distribution 3.5Consider an economy with n individuals where individual i has utility function U i(X i,Y)=Yα(X i+βi Y+γi),where0<α<1, iβi=0,and γi>0for all i.Assume that public goods can be produced from private goods at a cost of one unit of private goods per unit of public goods,and that there is an initial allocation of W units of private goods.Find the unique quantity of Y that satisfies the Samuelson conditions.3.6Prove the following results which are claimed in the text of the lecture:a).An allocation that maximizes the sum of individual utilities over allfeasible allocations must be Pareto optimal.b).Where a i>0for all i=1,...,n,any allocation that maximizes thesumni=1a i U i(X i,Y)of individual utilities over all feasible allocations must be Pareto opti-mal.Hint:Consider an allocation that is feasible and Pareto superiorto the allocation that solves your maximization problem.What istrue of the sum or weighted sum of the utilities in this allocation?Can this allocation be feasible?Why not?3.7In Example3.1,find the allocation that maximizes2U1(X1,Y)+ U2(X2,Y)subject to the feasibility constraint.Hint:Can X2be positive in an allocation that maximizes thisexpression?3.8There are two consumers and one public good.Person1always prefers more of the public good to less.Person2’s preferences are more subtle. Their utility functions are given byU1(X1,Y)=(1+X1)YU2(X2,Y)=X2Y−12Y2.The feasible allocations are those such that X1+X2+Y=W.a).Are these utility functions of the Bergstrom-Cornes form?EXERCISES15 b).Draw some sample indifference curves for Person2between privateand public goods.How would you describe Person2’s attitude toward public goods?c).Find the allocations that maximize the sum of utilities.Take care todistinguish the case where W is large enough for there to be an interior solution from the case where it is not.d).In the case where W=4,find all of the Pareto optimal allocations anddraw the utility possibility set and show the utility possibility frontier.e).In the case where W=4,find all of the Pareto optimal allocations anddraw the utility possibility set and show the utility possibility frontier.f).In the case where W=1/2,find all of the Pareto optimal allocationsand draw the utility possibility frontier.g).In the case where W=3/2,find all of the Pareto optimal allocationsand draw the utility possibility frontier.h).For what values,if any,of W are there Pareto optimal allocations inwhich both consumers consume some private goods and where the sum of utilities over the set of feasible allocations is not maximized.3.9The graph of an indifference curve for the utility function U(X,Y)has the equation U(X,Y)=u for some constant u.Suppose that U(X,Y)= A(Y)X+B i(Y)and that you graph indifference curves with Y on the hor-izontal axis and X on the vertical axis.Write an expression for the slope of the indifference curve as a function of Y and the utility u on that curve. What conditions on the functions A and B i imply that indifference curves have diminishing marginal rate of substitution as in standard convex pref-erences?What conditions are needed if there is diminishing marginal rate of substitution for all values of u?3.10Bergstrom and Cornes prove that under fairly weak assumptions rep-resentability of preferences in the functional form A(Y)X i+B i(y)is both necessary and sufficient for it to be true that regardless of the level of aggre-gate income starting from a Pareto optimal allocations in which both con-sumers have some private goods,if one leaves the amount of public goods unchanged and redistributes private goods to reach another allocation in which all consumers have some private goods,the resulting outcome will also be Pareto optimal.This exercise shows that the“necessity”part of this。

Chapter 20Externalities and Public Goods299.In the case of a negative externality, the social marginal cost will*a.exceed the private marginal cost.b.be equal to private marginal cost.c.fall short of private marginal cost.d.bear no significant relation to private marginal cost.300.A perfectly competitive steel mill that produces large amounts of a pollution (a negativeexternality) will, from a social point of view, producea.too little steel.b.the socially optimal quantity of steel.*c.too much steel.d.too much steel only if it installs pollution control equipment.301.Each of the following provides incentives to reduce a negative externality excepta.merger with affected firms.*b.subsidizing consumption of the good being produced.c.bargaining among firms.d.taxation of the externality.302.To reach an economically efficient output level, the size of an excise tax imposed on afirm generating a negative externality should bea.t he firm’s marginal cost.b.the social marginal cost.* c.the difference between the social marginal cost and the firm’s marginal cost.d.the sum of the social marginal cost and the firm’s marginal cost.303.Which of the following “externalities” doesnotdistort the allocation of resources?I.An individual’s unwillingness to cut his or her own lawn in an otherwiseimmaculately kept neighborhood.II.Smoke produced in an area by a new firm, which raises the costs of otherfirms.III.A new firm’s bidding up skilled wages in an area, therebyraising costs forother firms.IV.An individual’s unwillingness to obtain job training, thereby lowering thetotal GNP.Possible choices:a.I, III, and IV*b.III and IVc.III onlyd.IV only304.In perfect competition, environmental externalities need not distort the allocation ofresources providing*a.transaction costs are zero.b.average costs are constant for all output levels.c.firms install pollution control equipment.d.the government sets realistic pollution standards.305.In drilling a new oil well in an existing oil field, the fact that output on existing wells isreduced means thata.existing wells have negatively slopedMCcurves.b.existing wells and new wells are owned by different people.c.existing wells and new wells are owned by the same people.*d.there is a discrepancy between private and social marginal costs.306.Bargaining costs are generally high in cases involving environmental externalitiesbecausea.there are strong incentives to be a free rider.b.many individuals may be affected by the externalities.c.it is difficult to measure the costs of the externalities.*d.All of the above307.Externalities between two firms can be “internalized” if:I.The two firms merge.II.Bargaining costs are zero.III.The externalities affect each firm equally.IV.Marginal costs for both firms are constant.Which statement(s) correctly complete the sentence?a.Only IIb.All except III*c.I and II, but not III and IVd.I and IV, but not II and III308.If bargaining is costless and an externality exists,a.an efficient outcome may be reached depending on which party is assignedproperty rights.* b.an efficient outcome will be reached regardless of which party is assignedproperty rights.c.an efficient outcome will not be reached without government intervention.d.an efficient outcome can never be reached.180309.If bargaining is costless, the assignment of property rights for an externalitya.has no impact on the possibility of an efficient outcome and no distributionalimpact.* b.has no impact on the possibility of an efficient outcome but does have adistributional impact.c.does have an impact on the possibility of an efficient outcome but has nodistributional impact.d.does have an impact on the possibility of an efficient outcome and does have adistributional impact.310.A nonexclusive good is a gooda.that is sold in various markets.* b.where it is impossible to keep people from enjoying the benefits it provides.c.that is produced by a perfectly competitive firm.d.that is produced at the lowest possible cost.311.A non-rival good is a good thata.is produced by a monopoly.b.is produced by a cartel.*c.can provide benefits to additional users at a zero marginal cost.d.is sold in a single market.312.Left to their own, private markets tend to*a.underallocate resources to public goods.b.allocate the economically efficient amount of resources to publicgoods.c.overallocate resources to public goods.313.Perfectly competitive markets will tend to underallocate resources to nonexclusive publicgoods becausea.these goods are produced under conditions of increasing returns to scale.*b.no single individual can appropriate the total benefits provided by the purchase ofsuch goods.c.these goods are best produced under conditions of monopoly.d.no private producer can provide the capital necessary to produce such goods.314.Efficient production of a public good requiresa.that individuals pay for such goods according to benefits received.b.that each individual’sMRSbe equal to theRPTof public goods for private goods.*c.that the sum of individuals’MRSs be equal to theRPTof public goods for privategoods.d.that governments produce at the low point of the average cost curve for the publicgood.181315.The “free-rider problem” of public goods refers toa.individuals’ refusal to pay taxes.* b.individuals’ attempts to hide their preferences for collective goods and to avoidpaying for them.c.individuals’ over-use of collective goods.d.the inelasticity of individuals’ demands for public goods.316.Society’s demand curve for a public gooda.* b.c.d.182is given by the horizontal summation of individual demand curves.is given by the vertical summation of individual demand curves.cannot be derived from individual demand curves due to the nature of a publicgood.is given by the average citizen’s individual demand curve.。