Discounting the future

Princeton University Press Discounting the Future Author(s): John Broome Source: Philosophy and Public Affairs, Vol. 23, No. 2 (Spring, 1994), pp. 128-156 Published by: Formerly published by Princeton University Press Stable URL: http://www.jstor.org/stable/2265483 Accessed: 15/09/2008 10:45 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=pup. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. Princeton University Press is collaborating with JSTOR to digitize, preserve and extend access to Philosophy and Public Affairs. http://www.jstor.org JOHN BROOME I. Discountingthe Future INTRODUCTION Shouldfuture goods be discounted?Should benefits that will come in the distantfuturecount forless in ourplanning than benefits that will come in the present or near future? I am not thinking of the plans made by an individualon her own behalf, but of plans made on behalfof the public as a whole, particularlyby governments.Shouldfuture goodsbe discounted by public authoritiesin their planning? In cost-benefit analysis and other applicationsof welfare economics, economists typicallydo count future goodsfor less than present goods. To manyphilosophersthis seems a reprehensiblepractice.How,they ask, can the mere date at which a good occurs make any difference to its value? Discounting seems to these philosophersa device for unjustly promoting ourowninterests at the expense of ourdescendants'.On the face of it, then, typicaleconomists and typicalphilosophersseem to disagree. But actually I think there is more misunderstandinghere than disagreement. Some economists doindeed disagreefundamentallywith some philosophers,but most economists and most philosopherswould be on the same side if they came to understandeach otherproperly.I hope this articlewill contribute to a mutualunderstanding.Myfirstpurposeis to tryand explain to philosophers what economists are doing when they discount the future and why they are doing it. The basic pointis verysimple.When economistsand philosophersthink of discounting, they typicallythink of discountingdifferentthings. Economists typically discount the sorts of goods that are bought and sold in markets,which I shall call commodities.Philosophersare typicallythinkThis paper was writtenwith the supportof the Economicand Social ResearchCouncil, under grantnumberR 000 23 3334. Some of the workwas done while I was a VisitingFellow at the Centre for AppliedEthics, Universityof BritishColumbia.I am gratefulto Wilfred Beckerman,Douglas MacLean,CarolPropper,and TylerCowenfor takingthe time to write veryhelpfulcomments,andtoJonathanEscottand StefanoVettorazziforsome useful points. 1129 Discounting the Future ing of a more fundamental good, people's well-being. There are sound reasons to discount most commodities,and there may well be sound reasons not to discount well-being. It is perfectlyconsistent to discount commodities and not well-being. However,it is also true thateconomistssometimes go toofarin discounting; they discount where they ought not. There is some justice in the complaintsof philosophers.A second purposeof this articleis to say where economists overstepthe mark. Section II describesthe idea of discountingwell-being, but only in order to distinguish it from the discounting of commodities.I shall not discuss whether well-being ought or ought not to be discounted; that is not the subject of this article.Sections Ill-V explainthe discounting of commodities and how it fits into the theoryof cost-benefitanalysis,and they explain what justification there is for it. Sections VI-VIII set limits to the justification. II. THE PURE METHOD OF EVALUATION In order to distinguish discounting commoditiesfrom discounting wellbeing, I shall start by explaining the idea of discounting well-being. Suppose some public authorityhas to evaluate various alternativeactions it might take. For instance, governmentsthese days face a choice between allowing the emission of greenhouse gases to continue unchecked, or doing something to limit it. Let us ignore the uncertaintythat in practice always surroundsthe results of an action; let us suppose we know what the results of each alternativeaction will be. So if a particular actionis taken,we knowhow historywill then unfold.Particularpeoplewill be born,live fora particulartime, and die. Eachpersonwho lives will have a particularlevel of well-beingat each time in her life. If a differentactionis taken, history will unfold differently.Figure I shows schematically two alternativehistories. Each half of the diagram shows one of them. The horizontalaxis shows time and the verticalaxis possible people. A vertical solidline marksthe present. Foreach personwho lives, a little graphshows her well-being from birth to death. Each half of the diagramrepresents a sort of two-dimensionalgrid,acrosswhich well-beingis distributed.Time is one dimension and people the other. Different actions distributewellbeing differentlyacross the grid;indeed they may lead to the existence of differentpeople. AlternativeA in Figure I represents what will happen if Philosophy & Public Affairs 130 A: business as usual B: respond greenhouse gases arenot controlled;alternativeB what will happenif they are. B shows peopleworseoff in the nearfuturethan they arein A, because of the cost of controllingthe gases. Butin the furtherfutureit shows more people living, and it shows them better off and longer lived. (I am not predicting that this will definitelybe the result of controllinggreenhouse gases; the diagramis only an illustration.) An action,then, leads to a particulardistributionof well-beingacrossthe two-dimensionalgridof people and times. If alternativeactions are open to us, we need to compare one distributionwith another in order to decide which actionis better.So we need to determinethe value of each distribution. Well-beingdistributedacross the gridmust somehow come together to determine the overallvalue of the distribution.We need to know how: how is well-being aggregatedacross the grid?How is it aggregatedacross people and acrosstime? Discountingis one partof this question:does wellbeing that comes later in time count for less in the aggregate than wellbeing that comes earlier?If later well-beingis discounted, I shall call this pure discounting. Purediscountingmeans discountingwell-being.A pure discountrateis the rateat which the value of well-beingdeclines as we look forwardin time from the present. I 31 Discounting the Future Economists often include pure discount rates in their theoreticalwork, allowinglater well-being to be counted for less than earlier.But not many economists actuallydefend pure discounting.Often they include discount rates only for the sake of generality.The rate can always be set to zero, so that later well-beingis not actuallydiscountedat all. FrankRamsey,wearing his economist'shat, decriedthe practiceof discountingwell-being, but neverthelessincluded discountfactorsin his work.He says: "Itis assumed that we do not discountlaterenjoymentsin comparisonwith earlierones, a practice which is ethicallyindefensible and arises merely from the weakness of imagination; we shall, however, . . . include such a rate of discount in some of our investigations."'So the fact that discount rates appearin their formulasdoes not show that economists approveof them. Some do, but I think more do not.2Mostphilosophersare opposedto pure discounting, and I thinkmany economistswouldbe on their side; I do not think this is a majorpointof disagreement.I shall not considerthe argumentsforand againstpure discountingin this paper.Butin orderto drawout the contrast with the type of discounting economists do in practice, I shall generally take for granted the majorityview that the pure discount rate should be zero: future well-being ought not to be discounted. Theoreticalwork is one thing. When they come to assessing real projects in practice,such as new roads or plans to controlgreenhouse gases, economists rarelydeal in well-being at all. The direct way to evaluate a practicalproject would be to work out the distributionof well-being that would result from it and then find its overallvalue by aggregating wellbeing across the two-dimensionalgrid.I shall call this the pure method of evaluation.In practiceit wouldbe verydifficult.It wouldrequireus, first,to workout how well off each personwill be at each time in her life, as a result of the project. Even setting uncertaintyaside, there are majordifficulties in this. Tobegin with, theremay be a fundamentaldifficultyin principle.In drawingFigure i, I tookit for grantedthat the well-being of a person at a time is a measurablequantity that can be comparedbetween people and i. FrankRamsey,"AMathematical Theoryof Saving,"Economic Journal 38(1928): 54349, reprintedin his Foundations: Essays in Philosophy, Logic, Mathematics and Economics, ed. D. H. Mellor(London:Routledgeand KeganPaul, 1978), p. 261. 2. One economist who comes down firmlyagainst pure discounting is RobertSolow in "TheEconomicsof Resourcesor the Resourcesof Economics,"American Economic Review Papers and Proceedings 64 (1974): - I 4. On the otherhand,thereis a sustainedargumentin favor of pure discounting in ParthaDasgupta and GeoffreyHeal, Economic Theory and Exhaustible Resources (Cambridge: Cambridge University Press, 1979), pp. 255-82. 132 Philosophy & Public Affairs across times. This assumptionis open to serious doubts that economists know well. Besides, there is in any case the great practicaldifficultythat informationaboutpeople'swell-beingis hardto come by.A specialproblem is thatthe partsof a moderneconomyare so tightlyinterconnectedthat the effects of any economic actionwill be propagatedto everyonethroughout the economy. Remember that any economic project will have to be financed, perhaps by loans or taxes, and the financing will have its own complex repercussions. It would be impossiblein practiceto calculate all the effects on everyone. Workingout everyone'swell-beingat everytime wouldonly be the beginning of a pure evaluation. We would next have to aggregate all these amountsto arriveat the overallvalue of a project.Todo so, we wouldneed a theory of how this aggregationshould be done. This would be an ethical theory,and it would not be easy to arriveat. One componentof it would be the question of pure discounting:shouldfuturewell-beingbe discounted? This alone is hard to settle. Because of all these difficukies, economists have sensibly looked for a more practical method for evaluating projects. They want a shortcut through some of the difficulties.In particular,they want to avoidthe need fordifficultjudgments aboutwell-beingand how to aggregateit. It is only a shortcutthey are after.I think most economists would agree that the pure method would give the right answer if it could be applied.3The shortcutis not meant to supersede the pure method, but only to arriveat the right answer more easily.The eminent economistJoseph Stiglitz says as much: Anyprojectcan be viewed as a perturbationof the economyfromwhat it would have been had some other project been undertakeninstead. To determine whether the project should be undertaken,we first need to look at the levels of consumptionof all commoditiesby all individualsat all dates underthe twodifferentsituations.If allindividualsarebetteroff with the projectthan withoutit, then clearlyit should be adopted(if we adopt an individualisticsocial welfare function). If all individuals are worse off, then clearlyit should not be adopted.If some individualsare better off and others are worse off, whether we should adopt it or not depends criticallyon how we weight the gains and losses of different individuals.Although this is obviouslythe "correct"procedureto follow in evaluating projects, it is not a practicalone; the problemof benefit3. Stephen Marglin is one exception. See the quotation in Section VII. 133 Discounting the Future cost analysis is simply whether we can find reasonable shortcuts. In particular,we are presumed to have good informationconcerning the direct costs and benefits of a project,that is, its inputs and outputs.The question is, is there any simple way of relating the total effects, that is, the total changes in the vectors of consumption, to the direct effects?4 Economists have ended up taking a shortcut that leads them to deal in commoditiesratherthan well-being.It leads them to discount futurecommodities, but not necessarilyfuturewell-being. III. THE MARKET PRICE METHOD OF EVALUATION In making an evaluation,the instinct of economistsis to drawthe information they need fromthe market.In this section, I shall explain the thinking that supportsthis instinct at a generallevel. I shall applyit to discounting in Section V.5 The market-specifically prices-provides us with informationabout the values people attachto differentcommodities.Takethe two commodities labor and wine, for instance. Suppose laboris paid $Io per hour, and wine costs $5 per bottle.Each Sunday,in planningyourweek, you have to decide how much workto do that week and how much wine to buy.Having decided,you could alwayschange yourmind. Forinstance, you could work one hour more and buy two more bottles of wine, or you could work one hour less and buy two bottles fewer. But suppose you do not make these changes; you are in equilibrium-happy with yourplans. This shows that two bottles are worthjust as much to you as an hour of labor (or-as it appearsfromyourpointof view-an hourof leisure). Moreprecisely,if your purchases were to change by two bottles, given what you are already planning to buy,thatwouldbe worthjust as much to you as a change of one hour in yourleisure time. Economists say two bottlesof wine are worth as much to you as one hour of leisure at the margin. This expression means that an extra two bottles of wine, added to the bottles you alreadyplan 4. Joseph Stiglitz, "The Rate of Discount for Benefit-CostAnalysis and the Theory of Second Best,"in RobertLind,et al., Discounting for Time and Risk in Energy Policy (Washington: Resourcesfor the Future,I982), p. 156. 5. I shall ignore severalcomplications.In particular,I shallignore the differencebetween the interestratesfaced by consumersandproducers,which is caused by taxation.Thereis a moredetailedtreatmentin my Counting the Cost of Global Warming (Cambridge,UK:White Horse Press, 1992), chap. 3. 134 Philosophy & Public Affairs to buy, are worth an extra hour of leisure added to your planned leisure time. I have explained, then, that the relative price prevailing in the market between wine and leisure must be exactly the same as the relative value to you of the two commodities at the margin. If it was any different, you would change your plans; you would work less and buy less wine, or else you would work more and buy more wine. When you are in equilibrium, the relative price must match the relative value to you. For the same reason, the relative price of wine and labor must be the same as the relative value at the margin to anyone, and not just to you. But how can the relative value of wine and leisure be the same for everyone? Surely people differ in the values they attach to these things. The answer is that the prices are the same for everyone, and everyone adjusts themselves to the prices. Suppose you happen to value two bottles of wine above an hour of leisure. Then you will sign up for more work, earn some more money, and buy some more wine. If you still value two bottles of wine above an hour of leisure, you will sign up for more work still. But eventually, as you work longer and longer hours, the labor will begin to exhaust you, and you will have so much wine that its pleasures begin to pall. The value you attach to wine will fall, and the value you attach to leisure will rise. In saying this, I am assuming that wine and leisure have "diminishing marginal value" to you: the more of them you have the less you will value an extra unit. Economists generally make the plausible assumption that commodities have diminishing marginal value, and I adopt this assumption. You will reach an equilibrium where two bottles of wine are worth one hour of leisure to you at the margin. That is how your relative values at the margin come to match the relative prices in equilibrium. By the same process, so will everyone else's. Relative prices, then, measure people's relative values. What do I mean by relative values? If a person's aim in life is to maximize her well-being, the value to her of a commodity is the well-being she derives from it. In that case, prices measure the relative amounts of well-being that commodities bring her at the margin. This means they provide data for evaluations of just the sort we are looking for; as I described pure evaluations, the data needed are people's well-being, and we are looking for a shortcut to a pure evaluation. But suppose a person's aim is not to maximize her well-being. In that case, the value to her of a commodity will not be the well-being she derives from it. But no matter, many economists would say: people should 135 Discounting the Future be free to choose their own aims in life. If they happen not to pursue their own well-being, thatis theirbusiness. When it evaluatesa project,a public authorityshould use the values people attach to commodities, whatever the aims that underlie these values may be. There is a complication.Manyof the things that concern public authorities when they evaluateprojectsare not bought and sold on the market,so they do not have a price.6Examplesarepublic goodssuch as streetlighting and safety equipment installed in nuclear power stations. (Even though they are not marketed,I shall call these "commodities.")How can we find the value to peopleof a nonmarketedcommodity?Wecan use the price that people wouldbe willing to payforit if they had to, instead of its actualprice. A person might be willing to pay something to have streetlighting or safety equipment installed. The amount she is willing to pay for a commodity measures its value to her, comparedwith the value of other things she buys. It can be used as a measure of value to her in place of marketprice. People'swillingness topayfora commodityis not as easy to find as a market price, but in practiceit can be workedout by variousmeans. How can prices, or willingness to pay,be used in evaluatinga project?A project uses some commoditiesas inputs and produces others as outputs. Think of one thatuses laboras input andproduceswine as output.Suppose this projectis profitableat marketprices. Thatis to say,if prices are $ I o for laborand $5 forwine, the projectproducesmorethan two bottlesof wine as output for every hour of labor used as input. Now, everyone assigns the same value to twobottlesas to one hour of laborat the margin. So everyone values the output of this project more than its input. Surely, then, the project is beneficial. This simple thought is the basis of cost-benefit analysis. To decide whether a projectis a goodidea (by which I mean it is better to do it than not), firstlist all the commoditiesthe projectwill use as inputs and all those it will produceas outputs.Valuethem all at marketprices or,failing that, at people'swillingness to pay for them. Call the value of an outputa "benefit" 6. A smaller complicationis this. I argued that the relativeprices of commoditieswill measure theirrelativevalues to a person,at the margin.But the argumentonly worksif the person buys or sells some amountof each commodity.If she chooses not to buy any of some commodity(and if she has none to sell), that commodity'spricedoes not indicateits value to her. Evidently,its valueto heris notmorethanits price,orelse she wouldbuysome, butit may be less than its price. Likethe complicationof nonmarketedcommodities,this complication can alsobe dealtwith by using the person'swillingnesstopayforthe commodityin placeof its price. 1I36 Philosophy & Public Affairs and the value of an input a "cost."If benefits exceed the costs, the project is profitable at market prices. In that case declare it a good idea. I shall call this the market price method for evaluating a project. It seems plausible, but there is a snag. We need to ask how the project will be operated. Who will supply the inputs and who will get the outputs? One possibility is that the costs are borne by the same people as receive the benefits. In the example, the labor might be done by the people who eventually receive the output of wine. Each of these people might be employed on the project and paid for her labor in wine. The pay could be more than two bottles per hour, since the project produces more than two bottles per hour. Since each person values two bottles more than one hour of leisure, each would be benefited by the exchange. (Assume each person works only a little time on the project, so that the change is marginal.) All these people would benefit, and no one would be harmed. Undoubtedly, the project operated this way would be a good idea. If it were operated this way, we could sidestep all the theoretical problems of aggregating wellbeing across a grid like Figure i. Since the project would make everyone better off, there would be no need to worry about aggregating well-being across people and time. But in practice the benefits of a project often come to people who have not borne the costs, or all of the costs. When a road is built, some people have to suffer the noise it makes, while other people benefit. I can only fit this possibility into my simple example by making an exaggerated assumption. Assume the labor is coerced, without pay, and the wine produced is distributed to people who have not done the work. Have we any reason to suppose that the benefit to these people is greater than the cost to the workers? No. We know how each person individually values wine compared with leisure; that information is given us by the market prices. It happens that everyone values two bottles of wine equally with one hour of leisure. But we do not know how one person values wine compared with how another person values leisure; market prices do not convey that information. It may be that the workers value their sacrificed leisure more than the beneficiaries value their extra wine. In general, if some people bear the costs of a project and others get the benefits, we cannot tell from market prices whether the project is a good idea or not. This is a fundamental difficulty in cost-benefit analysis. So long as a project harms some people and benefits others, valuing commodities by their market prices, or by willingness to pay, is not a reliable way to check whether the project is a good idea. The problem will be most severe if the I37 Discounting the Future people who are benefited are much better off, or much worse off, than the people who are harmed. When a person is in equilibrium, the price in money she pays for a commodity is the value of the commodity to her at the margin, divided by the value of money to her. For a given value of money, the price of a commodity is therefore a measure of the commodity's value to the person. Among people who are about equally well off, it is reasonable to assume the value of money to each of them is approximately the same. So among such people, prices may be reasonably good measures of values. On the other hand, money to a poor person is probably worth much more than money to a rich person. Between rich and poor, then, the prices of commodities are not good measures of their values. Of course, economists have ways of coping with this problem, which I shall not go into here. This article is concerned with the distribution of resources between the present and the future. For the sorts of projects I am interested in, the people who benefit will often not in practice be the ones who bear the costs; they may well be in different generations. Furthermore, they may not be equally well off, because future generations may be much richer, or much poorer, than us. So one might expect the problem I have mentioned to be particularly acute for projects that cross generations. But actually it is not. The reason is that, in a way, the market price method ignores future generations. Their well-being is only taken into account to the extent that it is valued by the present generation. This is a major weakness in the method, which I shall discuss in Section VII. But it does happen to cancel out the fundamental weakness I have been describing. When the market price method deals with intertemporal questions, it treats them as questions about how the present generation values future commodities compared with present commodities, not as questions about how the values of the present generation compare with the values of future generations. Distribution between rich and poor generations is not really at issue. Consequently, I think it is reasonable to set aside this most fundamental problem with the market price method, and concentrate on difficulties that are specific to discounting. IV. THE PRESENT PRICES OF FUTURE COMMODITIES Before I can explain how to apply the market price method to discounting, I need to introduce a useful theoretical device: the idea of dated commodities and their prices. Suppose I have $Ioo. I can use it to buy twenty bottles of wine at $5 each. Alternatively, I can put it in the bank. After a year I can get 138 Philosophy & Public Affairs the money out, with interest. If the interest rate is io%, I will have $iio. If wine has meanwhile gone up to $5.25, I can then buy twenty-one bottles of wine. So $ioo now will, in effect, buy me twenty-one bottles of wine in a year's time. We can think of wine in one year's time as a commodity on its that own, separate from wine now, and its present price is $4.75 ($100/21, is). This is what, in effect, I have to pay now in order to acquire a bottle of wine in a year's time. Since $4.75 iS less than $5, the present price of future wine is less than the present price of present wine. In general, a commodity at any date-a dated commodity-has a present price. From now on, when I speak of the price of a future commodity, I mean its present price unless I say otherwise. The percentage difference between the present price of a present commodity and the present price of the same commodity next year (I mean, for instance, the 1994 price of the commodity in I 995, not the I995 price of it) is called the commodity's own interest rate. In my example the own interest rate of wine is 5%. Commodities typically have positive own interest rates. That is to say, future commodities are typically cheaper in the present than present commodities. If you have a particular sum of money, you can generally buy more of a future commodity with it than you can of a present commodity, by keeping the money in a bank and earning interest. The only exceptions are commodities whose current price (for instance, the I 995 price of the commodity in 1995) increases through time as fast as, or faster than, the rate of interest at the bank. These commodities have own interest rates that are zero or negative. The relative price of commodities indicates the relative value people place on them. This is true among present commodities and also between present commodities and future commodities. In my example, the price of future wine, one year from now, is 5% below the price of present wine. Therefore, once people are in equilibrium-have made their plans, bought the amount of present wine they want, and set aside what they want in order to buy future wine-each person values present wine 5% above future wine at the margin. How can this be? Future commodities are generally cheaper than present commodities, which implies that most people value future commodities less than present ones. But why should a person value a commodity less just because she will possess it in 1995 rather than 1994? The answer to this question has two parts. The first is to explain why future commodities are generally cheaper than present ones anyway. 139 Discounting the Future Oddly enough, this has little to do with the values of the people who buy present and future commodities. It has to do with the economy's productive technology, not with its consumption. Technology is, in a particular sense, fertile. It is a fact of technology that, to speak roughly, present commodities can be converted into a greater quantity of future commodities, if we choose.7 Trees grow, for instance. If I fell my forests now, I shall harvest a particular quantity of timber. If I fell them next year, I shall harvest more. Let us say I shall harvest 5% more. The nature of my production process, then, gives me a choice between timber now and 5% more timber next year. This means that, when the economy is in equilibrium, the present price of next year's timber must be 5% below the price of this year's. If it were any higher, I would leave all my harvest to next year, and so would all my landowning colleagues. No timber would be put on the market this year. That would quickly drive up the price of this year's timber until it is 5% above the price of next year's. At that point I would begin harvesting again. Likewise, if the price of this year's timber rose higher than 5% above the price of next year's, the opposite would happen. The economy will only be in equilibrium when the price difference is 5%. On the scale of a whole economy, things are much the same. Each year, some of the goods produced by the economy are consumed and some are reinvested, and the division between investment and consumption can be varied. If fewer commodities are consumed this year, more can be invested. The result will be more commodities produced next year, and next year's increase will exceed the decrease in consumption this year. Just as timber this year can, in effect, be converted by the production process into a greater quantity of timber next year, commodities in general this year can be converted into a greater quantity of commodities next year. This is what I mean when I say technology is fertile. A consequence is that next year's commodities must be cheaper than this year's. If they were not, producers would increase their investment this year, in effect switching their production to next year's commodities instead of this year's. This would increase the price of this year's commodities relative to next year's, until an equilibrium is reached with future commodities cheaper than present ones. Most commodities will therefore have positive own interest rates. This is a necessary consequence of the fertility of technology. 7. Thereis a fulleraccountof technologicalfertilityin my TheMicroeconomicsof Capitalism (London:AcademicPress, I983), particularlypp. 36-37. 140 Philosophy & Public Affairs Not every commodity will have a positive own rate of interest, though; I shall mention exceptions in Section VI. Nor need it always be true that most commodities will have a positive rate. Our technology may not always be fertile. If, for example, runaway global warming damages our productive abilities, or our resources are exhausted, future commodities may become more expensive than present ones. Own rates of interest may become generally negative. Still, with our present fertile technology, they are generally positive. An economy's fertility may be affected to some extent by the decisions of consumers about saving. Suppose people decide to increase their savings, delaying some of their consumption to the future. In effect, they buy more future commodities in preference to present ones. This could raise the prices of future commodities compared with present ones, thereby reducing own interest rates. How could this happen? Only by causing a switch in the technical methods employed in the economy, to less-fertile methods. Here is a simple example. The change in consumers' behavior might induce the owners of forests to fell their trees at a more advanced age. But trees grow more slowly as they get older. So the change would cause the fertility of forestry to decline, and the equilibrium own interest rate of timber would be reduced. In ways like this, consumers might influence the fertility of technology. But for reasons I shall not go into here, I think their influence is small.8 It is a fair approximation to think of fertility, and hence interest rates, as given independently of decisions about saving. Tyler Cowen and Derek Parfit, on the other hand, stress the influence of savings on interest rates and suggest it is crucial to the argument about discounting.9 I think not. My approximation is helpful for thinking about the problem, but it is not essential for the argument. We are concerned with interest rates established in the market, because these rates indicate the relative values people attach to present and future commodities. The important question is whether or not these rates are generally positive, because a positive rate implies that future commodities have a lower value than present ones. Insofar as savings influence interest rates, interest rates in the market will be determined by the mutual interaction of technology on the one hand and consumers' decisions about saving on the other. 8. Ibid. 9. TylerCowenand DerekParfit,"Againstthe SocialDiscount Rate,"in PeterLaslettand James S. Fishkin, ed., Justice Between Age Groups and Generations (New Haven: Yale UniversityPress, 1992), pp. 144-6I, esp. I5I. 141 Discounting the Future In present conditions, own interest rates will certainly emerge from this interaction generally positive. That is all that matters.'0 If interest rates are positive, people attach less value to future commodities than to present ones. The second part of the answer to the question I posed earlier is to explain how this can happen. The explanation is that people must adjust themselves to the prices they face. Suppose next year's wine is as valuable to you as present wine. If it is cheaper than present wine, you will save your money and buy next year's wine rather than this year's. As you do this, and so find yourself with less wine this year, you will find you value this year's wine more and are less keen on buying yet more future wine. When you are in equilibrium, the relative values you attach to present and future wine at the margin must match their relative prices. Everyone will be in the same position. We shall all adjust our relative values, at the margin, to each commodity's own rate of interest. The process is exactly the same as the one I described in Section III for undated commodities. This may still be mysterious. Even after adjustment, how can future wine be less valuable to ybu than present wine? Just because it comes in the future, how can that make it less valuable? I can think of three possible explanations. One is that the benefit you expect to get from wine declines with your advancing years: for any given quantity of wine, you expect to enjoy it less the older you are. I shall ignore this possibility in order to concentrate on the other two explanations, which I think are more imporIo. Cowenand Parfitdo not suggest marketrates will be zero, but they do claim interest rates will be zeroat the "optimum," when savingsin the societyareat the level they shouldbe at. This is because they do not believein discountingfuturecommodities;they take present and future commoditiesto have the same value. So long as futurecommoditiesare cheaper than present commodities,they think savings are not as high as they should be. Savings should be increased,which means that more future commoditiesshould be consumed instead of presentones. They thinkthatincreasingsavingsshouldeventuallybringthe priceof future commoditiesup to the level of present ones. That is to say,interest rates should be broughtdownto zero.Butthis is mistaken.Underpresentenvironmentalconditions,interest rates cannot generallybe zero at the optimum.Supposewe grantthat savingsare at present toolow If they areincreased,this will increasethe rateof growthof the worldeconomy.Long beforeinterestratesaredrivendownto zero,the increasedsavingswill bringabouta positive rateof growthin percapitaincome:peoplewill be gettingricheras timepasses. (Indeed,that may well be so already,even with savings at their present low level.) Consequently,the marginalvalue of commoditiesto people will be declining;as people get richer,they attach less value to extracommodities.Futurecommoditieswill be less valuablethan presentones, then. Commoditiesought to be discounted,that is to say,even at the optimum.Cowenand Parfitcannot legitimatelytake it for grantedthat they shouldnot be. 142 Philosophy & Public Affairs tant. I shall assume that, at any time in your life, a particular quantity of wine will bring you the same well-being as it would at any other time. The next possibility is illustrated by the indifference-curve diagram in Figure 2. Here I assume your aim is to maximize your own well-being. This means, among other things, that you do not discount your own future wellbeing compared with your present well-being; both count the same in your present values. Since I have already assumed that a particular quantity of wine brings you the same well-being in the future as in the present, your indifference curves must be symmetrical about the 450 line-the dotted line in the diagram. Your "budget line" in the diagram shows the options that are available to you, given whatever you have available to spend on wine. Your options are not symmetrical, because future wine is cheaper than present wine. This means the budget line is steeper than 45'. Out of all the options available to you on the budget line, you choose the one that puts you on the highest possible indifference curve. This is where an indifference curve touches the budget line. The diagram shows you will buy more future wine than present wine. This is how you end up valuing future wine less at the margin than present wine. All along, I have been assuming wine has a diminishing marginal value: the more of it you have, the less well-being an extra bottle will bring you. Since you have more future wine, you value extra bottles of it less. Wine will presumably have a positive own interest rate throughout your life. Consequently, wine at later dates must always be less valuable to you at the margin than wine at earlier dates. If the explanation I have just given of how this happens is the right one, you must buy progressively more and more wine as your life continues. This point will become important in Section VIII. The third possible explanation is illustrated in Figure 3. Here you yourself discount your future well-being; you value it less than your present well-being. Let us call this imprudence on your part. Imprudence skews your indifference curves toward present wine; the curves are not symmetrical about the 450 line, but steeper. Your budget line still has the same slope as before. In equilibrium you must value future wine less than present wine, since its price is less. If you are imprudent, that may happen even if you buy the same amounts of present and future wine. That is what the diagram shows: the point of tangency between the budget line and the highest indifference curve you can reach lies on the 450 line. This will Discounting the Future 143 2 FIGURE next year's wine \ equilibrium , indifference \ \ u r v e~~~~~~cuvs budget line this year's wine happen only by coincidence, because your degree of imprudence happens to match the own interest rate of wine. But it certainly can happen. V. DISCOUNTING IN THE MARKET PRICE METHOD Now back to cost-benefit analysis. In Section III, I described how the prices of commodities can be used in cost-benefit analysis. To evaluate a project, list the commodities it uses as inputs and the commodities it produces as outputs and evaluate them all at their market prices. Since market prices indicate their relative values to people, this seems a good basis for judging whether or not the project is a good idea. Exactly the same idea extends to projects that have inputs and outputs at different dates. All the inputs and outputs can be evaluated at their market prices. In this case, these are the present prices of dated commodities. They measure the relative values of the dated commodities to people, so Philosophy & Public Affairs 144 FIGURE next year's wine 3 \ this year's wine they seem a goodbasisforcost-benefitanalysis.Generally,futurecommodities have lower present prices than present commodities. This process consequently discounts future commodities;it values them less than present commodities.This methodprovidesa basis fordiscounting,then. The discount is appliedto commodities,and not to well-being. This is just the marketprice method of evaluationappliedto the present and the future. Its great advantageis that the informationit needs comes from the market. I said in Section II that economists were looking for a shortcutthrough the difficultiesof the pure method. This is it. There is no need to inquirehow much well-beingeach personderivesfromthe project. Nor is there any need to engage in philosophical analysis to work out appropriatediscount factors for future well-being. The market price method cuts through all that. Its discount factors come from the market like any other prices; they are simply the prices of future commodities comparedwith present ones. It may well be that future well-being ought not to be discounted at all. Even so, the marketwill value futurecommodi- 145 Discounting the Future ties belowpresentones. So, if we are going to calculatewith commoditiesat all, future commoditiesought to be discounted. There are, to be sure, some major,valid objections to the market price method. I shall come to them soon. ButI thinkit is a mistake to object to the generalidea of using this shortcutto evaluateprojects.In his discussion of discounting in Reasons and Persons, Derek Parfitraises several accurate objectionsto the marketprice method," but I think he underestimatesthe method'svalue. He says: It may be in several ways more convenient, or elegant, to calculate opportunitycosts using a SocialDiscount Rate. Butthe conclusions that are established by such calculationscould be re-expressedin a temporallyneutralway.When describingthe effects of future policies, economists could state what futurebenefits and costs there would be, at different times, in a way that used no discount rate. The arguments that appealto opportunitycosts could be fully statedin these terms. I believe that, on any importantquestions that we need to decide, this would be a better, because less misleading, descriptionof the alternatives.'2 Beforerespondingto this remark,let me explainthe idea of an "opportunity cost."The opportunitycost of something is what we could have instead, if we choose not to havethis thing. The opportunitycost of timbertodayis the timberwe could have next year if the trees were not felled today.Because trees grow,this opportunitycost is a greateramount of timber next year. That is why today'stimberis more expensive than next year'stimber;you have to give up a greateramount of next year'stimberto get it. In general, because technologyis fertile,the opportunitycost of commoditiestodayis a greaterquantityof commoditiesnext year.That is why commoditiestoday are more expensive than commodities next year-why next year's commodities are discounted, that is. The opportunitycosts of commodities are embedded in their prices. A cost-benefitanalystwould simplyvalue next year'stimberbelowthis year's in her calculations,next year'sconcrete belowthis year's,and so on, taking her valuationsfrommarketprices. Whatwould Parfithave her do instead? He would have her trace through the economy all the effects on people's i i. Derek Parfit, Reasons and Persons (Oxford: Oxford University Press, i984), pp. 480-86. I 2. Ibid., p. 484. 146 Philosophy & Public Affairs well-being, at each time in the future, of using timber and concrete at particulardates. He would then have her add up these amounts of wellbeing, withoutdiscountingfuturewell-being.Parfit,in fact, wouldlike the economistto use the pure method of evaluation,withoutdiscounting wellbeing. But this would be a tremendouslydifficultoperation,and normally pointless.The point of using prices is that, in a sense, they encapsulate all that informationaboutthe effects on people'swell-beingin an easily manageableand observableform.The marketpricemethod is a shortcutto the pure method, and it is a hundred times more practical. In his discussion, Parfitconcentrates on difficult cases where a costbenefit analystwould be wrong to discount a particularfuturecommodity. The existence of a stretchof beautifulcountrysideis one of his examples of a commodity,and Parfitis right that this one ought not to be discounted. I shall mention these cases in Section VI. The difficult cases lead Parfitto forgetall the mundane cases where the discountingof futurecommodities is legitimate, and the only practicalway of proceeding. Furthermore,as I shall explain in Section VI, even in these difficultcases the marketprice method would get the right answerif it was properlyapplied.This method actuallytells us not to discount the futureexistence of a stretchof beautiful countryside. Parfit raises a related point. He mentions, as a legitimate reason for valuingfuturecommoditiesbelowpresent ones, thatour successors will be better off than us. Being better off, they will derive less well-being from extra commodities than we will; this is the law of diminishing marginal value. So it is better,at the margin, for commoditiesto come to us than to them. However,says Parfit,the reason future commodities are less valuable is not that they exist in the future. It is that they are coming to people who are better off. It is deceptive to say we are discounting for time.'3 In the theory I have developed so far, I have not yet mentioned our successors. Nevertheless, the situationdepictedin Figure 2 allows me to say something about Parfit'spoint. That figure shows a person who consumes more wine next year than this year, because next year's wine is cheaper than this year's. Since most commoditiesare cheaper next year than this, she will consume moreof most commoditiesnext yearthan this. In a sense, she is betteroff next year because she has a greaterconsumption then. Consequently,the marginalvalue to her of all these commodities I3. Ibid. 147 Discounting the Future is less next year than this. Her situationmimics within her single life the relationbetween us and our successors that Parfittalks about. So we can use this example to examine Parfit'spoint. Future commodities are discounted comparedwith present ones: they have a lower present price. Correspondingly,the value to people of future commoditiesis less than the value of present ones. Is the discount a discount for time? Parfitsays no: since futurecommoditiesare discounted because people have more future commodities than present ones, it is misleading to say the discount is for time. But I do not think it is misleading. It is commoditieswe are discounting, not well-being. Dated commodities areidentifiedby theirdates, and it happens that futurecommodities are cheaper than present ones. This can reasonablybe called a discount fortime. Whatcauses futurecommoditiesto be cheaperthanpresent ones is anothermatter.Eveningphone calls arediscountedcomparedwith daytimephone calls. The cause of this discountis thatfewerpeople use the phone in the evening; there is less pressure on the phone company's resources, so each call costs less to provide.Nevertheless, the discount is for the time you make the cill. It is evening calls that the phone company markets at a discount, not calls when fewer people are using the phone. As I explained in Section IV, the fertilityof the economy's productive system is the chief cause of why futurecommoditiesare cheaper.The fact that people, like the person in Figure 2, end up assigning a lowervalue to future commodities than present ones is more an effect than a cause. People arrange their affairs so as to consume more in the future, and consequentlythey end up assigning less value to futurecommoditiesat the margin. But even if it was a cause, the discount would still be for time. Commoditiesare discounted by their own interests rates, and an interest rate is a discount for time. VI. COMMODITIES THAT SHOULD NOT BE DISCOUNTED I have explained the thinking that underliesthe marketprice method and said what is right aboutit. Now I come to what is wrong with it. A lot of sound objections have been raised, but I shall only mention three here.'4 The first objectionis not to the theoryof the marketprice method, but to I 4. There is a fuller catalogin my Counting the Cost of GlobalWarming,pp. 60-92. Philosophy & Public Affairs 148 the way the method is applied.I explained that a commodityin the future normallyhas a lowerprice than in the present. It is discounted, that is to say,and the appropriatediscount is given by its own interest rate. According to the theory,each commodityshouldbe discountedat its own rate. But in practiceall commoditiesare generallylumped togetherand discounted at the same rate. Normally,they are all discountedat something called the "real"interestrate, which is a weighted averageof the own interestrates of variouscommodities. This may be an acceptableapproximationfor most commodities. Most commodities are produced within the economic system, and most have similar own interest rates, determined principallyby the fertility of the technology.But some commodities have quite different rates. These include nonreproduciblescarce resources, which are not producedat all. I explainedin Section IV that most present commoditiescan, in a sense, be convertedinto a greaterquantityof futurecommodities.Thatis why future commoditiesare generallycheaper than present ones. But this is true only of commodities that are produced within the economic system. Scarce resources cannot be convertedinto a greaterquantityof futureresources, and they therefore have own interest rates of zero or thereabouts.'5It followsthat they ought not to be discounted,even accordingto the theoryof the marketprice method. DerekParfitgives an example: a stretch of beautiful countrysidethat might be destroyedto buildan airport.6 The value of this scarce resource will remain the same throughtime; it will not decline like the value of producedcommodities.It ought not to be discounted, and the theory underlying the market price method says it ought not to be discounted. Parfit mentions another type of commodity that ought not to be discounted. Some industrialplants cause congenital deformitiesamong people born in their neighborhoods.In valuing the plants, cost-benefit analystsoften discountdeformitiesthatwill happenin the distantfuture;they give them less significance than present ones. But Parfit says that is a mistake.A deformitycaused at one timeis just as badas a deformitycaused at another.It leads to the same loss of well-being, and since Parfitbelieves i5. This is known among economists as the "Hotellingrule,"because it appearsin H. Hotelling, "The Economics of Exhaustible Resources,"Journal of Political Economy 39 (193I): I37-75. i6. Parfit, Reasons and Persons, p. 483. 149 Discounting the Future well-beingought not to be discounted,he believes deformitiesought not to be discounted either.'7 Let us grant the premise that well-being ought not to be discounted. Then I am sure Parfitis right that deformitiesought not to be discounted. But this example is theoreticallytricky,and more needs to be said aboutit. Some commoditiesrepresent a constant quantityof well-being whenever they occur;let us call them constant-well-beingcommodities.Deformities are a negative constant-well-beingcommodity.Fortheoreticalpurposes,it is easier to work with positive commodities,so let us work with the converse of deformities:the positive commodityof saving people from deformities. Saving people's lives is plausibly another example of a constantwell-being commodity;on average,savingone person'slife in one hundred years will presumablyaddjust as much well-being to the worldas saving one person'slife now.Grantedthat well-beingought not to be discounted, constant-well-beingcommoditiesought not to be discounted. Some constant-well-beingcommoditiesare scarce resources, but some are not. Lifesavingis not, for instance. Lifesavingis actually a produced commodity.People'slives are savedby carein hospitals,by installing safety devices in factories,by propagandaagainst smoking, and in many other ways; these are all ways in which the commodityof lifesavingis produced by the economy.Furthermore,lifesavingparticipatesin the general fertility of the productivesystem. It is like timber:a quantityof lifesavingin the present can be convertedinto a greaterquantityin the future.Wecan, if we I 7. Parfitmakesa concessionhe oughtnot to make. He pointsoutthatwe can compensate for some deformitiesby providingthe victim with commoditiesas compensation.We must compensatefor present deformitieswith present commodities.But we can compensatefor future deformitiesby setting up a fund now to buy futurecommodities.The fund will grow overtime with interest. Since the fund will grow,it will be cheaperto compensateforfuture deformitiesthan present ones. Providedwe set up the fund, says Parfit,this is a reason for valuingfuturedeformitiesless thanpresentones. Butthereis a mistakein thisreasoning.The fund earns interestbecause futurecommodities,in general,are cheaperin the present than present ones. Thatis whatinterestis: it is the fact thatfuturecommoditiesarecheaperin the present than present commodities.In equilibrium,they are thereforeless valuable than present ones; they bringless benefit at the margin.A present deformitywill require some quantityof present commoditiesas compensation.A futuredeformitywill requirea greater quantityof futurecommodities,becausethe futuredeformityis just as badas the presentone, but the future commoditiesare less valuable.The fund earns interest just as quickly as commoditiesdeclinein value,so it willjust be abletoprovidecompensationto the same value wheneverit is spent. Consequently,futuredeformitiescan only be compensatedforat exactly the same present cost as presentdeformities. 150 Philosophy & Public Affairs choose, use fewer resources on lifesaving today,invest them productively, and so have greaterresources availablenext year, which we could use to save more lives next year. Because present timbercan be convertedinto a greater quantity of future timber, future timber must be cheaper than present timber in equilibrium. Timber is therefore discounted. Surely, therefore, the same should be true of lifesaving. Future lifesaving is cheaper than present lifesaving; so lifesaving should be discounted. But this contradictsmy earlierremarkthatit shouldnot be discountedbecause it is a constant-well-beingcommodity.So there is a puzzle. Which is right? The answer is that the earlier remark was right: if lifesaving is a constant-well-beingcommodity,it should not be discounted. Lifesavingin the futurewill make the same contributionto well-beingas lifesavingin the present. Certainly,futurelifesavingis cheaper than present lifesaving, but this is not a reason for valuing it less. The marketprices of commodities only have a role in valuationsbecause they measure the relativevalues of commoditiesto people.In equilibrium,they will do so, and up to now I have been assuming the economy is in equilibrium.But if lifesaving produces constant well-being and yet is cheaper in the future, we evidently do not have an equilibrium.With ordinarycommodities like timber, there is a market that will move to equilibriumif it is working smoothly.But with lifesaving there is no such market.Nor is there one for savingpeople from deformities.We have no reason to discount these commoditiesat an interest rate that has been establishedin the marketformarketedcommodities. There is more to the puzzle, though. If we can convert a quantity of lifesaving now into a greaterquantitynext year,and if lifesavingnext year is just as valuableas lifesavingnow,the conclusion we have to drawis that lifesaving should be deferred.We should withdrawresources fromlifesaving today,and apply them to saving more lives next year. We should also defer lifesaving next yearin orderto save yet more lives the year after.We should deferlifesavingthe yearafterin orderto savestill morethe yearafter that, and so on. We will end up postponingall lifesaving to the indefinite future, which never comes. So, we will end up saving no lives at all. If lifesaving produces constant well-being and yet its price declines with time, this is the conclusion we must draw.But it is a ridiculous one. We have a paradox. Here is one possible solution. Lifesaving may not be a constant-wellbeing commodity.Undoubtedly,savingsome people'slives addsmorewellbeing to the world than saving other people's. Saving a twenty-year-old Discounting the Future '5' with a long and happy future ahead of her adds more to well-being than saving a ninety-year-oldwith little left to look forwardto. We may expect that, by and large, a society will first direct its resources to saving the people with most well-being to gain. As it progressesin its ability to save lives, it will start to save people with less and less to gain. In the future, therefore,where more lives are being saved,life-savingwill, by and large, produce less well-being at the margin. Therefore, the more lifesaving is deferredto the future, the less well-beingit will produceon averageat the margin. Eventually,as lifesavingis deferred,there will come a point where the lowerprice of futurelifesavingis matched by its lowerbenefit in terms of well-being. Afterthat,it wouldbe wrong to defer any morelifesaving.At that point, future lifesaving is on average genuinely less valuable than present lifesaving. Lifesavingshould then be discounted. It is possiblethatwe arein this positionalready.If we are,lifesavingis not a constant-well-being commodity,and it should be discounted. But we have no reason to think this is so, because there is no market that can be expected to make it so. Wecannotrely on a marketinterestrate. Allwe can do is considerdirectlywhat well-beingwill result fromlifesaving at different dates. If we conclude that lifesaving will lead to the same amount of well-being at everydate, as I assumed earlier,it should not be discounted. The same goes for saving people from deformities. VII. DISENFRANCHISED GENERATIONS My second objectionto the marketprice method is that for many projects most of the interested parties are not represented in the market. Many projects will affect future generations for centuries or millennia ahead. Nuclear waste will remain dangerous for many thousands of years, and projects for disposing of it must take account of that. Attempts to control global warming will bring their main benefits more than a century from now. But the only people whose values are registeredin marketprices are those who are alive now. This is surely a very serious gap. One thing might lead you to disagree.I suggested in Section IV that the main determinantof interestratesis the economy'stechnology,specifically its fertility.If this is correct,then interestrateswouldnot be much different even if, in some way, future generations came to be represented in the market. Imagine a trust for future generationswas set up, able to borrow money against the potentialearningsof futuregenerationsand empowered 152 Philosophy & Public Affairs to buy resources for their use. Once the economy settled down to a new equilibrium,interests rates would not have changed much. So is the disenfranchisementof future generationsa significantfault in the market price method of evaluation, or is it not? If enfranchisement would not make much difference to interest rates, then surely not: the marketprice methoduses interestrates that areaboutcorrect.Butactually this reasoning is erroneous.Interestrates would be aboutthe same in the new equilibrium,after the economy had settled down. But just after the new trust was set up, the economy would be very far from equilibrium. From the trust'spoint of view-representing future generations-future commoditieswould be much more valuablethan they seem to us who are participatingin the marketnow. The trust would use its funds to transfer many more resources to the future. It would buy up future commodities, makingthem moreexpensive and reducing theirown interestrates.When the new equilibriumwas achieved, their prices would dropagain to their originallevel, and interest rates would be restored.But in the meantime many resources would have been transferredawayfrom us for the use of futuregenerations.It is only the disenfranchisementof future generations that gives us the share of the world'sresources that we have. With things as they are, then, in our present equilibrium,if we came to take account of the interests of future generations, we would use lower interest rates. We would discount the future less than we do now in the market.If public authoritiestookaccount of the interests of future generations, they would use lowerinterests rates than marketrates in their decision making. This would transferresources forwardin time for the use of futurepeople. Shouldpublic authoritiesact this way?A. C. Pigou thought they should. He wrote: Butthereis wide agreementthat the State shouldprotectthe interests of the futurein some degreeagainstthe effects of ourirrationaldiscounting and of our preference for ourselves over our descendants. The whole in the United States is based on this conmovementfor "conservation" viction. It is the clear duty of Government,which is the trustee for unborn generationsas well as forits present citizens, to watch over,and, if need be, by legislative enactment, to defend, the exhaustible natural resources of the countryfromrash and reckless spoliation.I8 i8. A. C. Pigou,The Economics of Welfare, 4th ed. (London:Macmillan,I932), pp. 29-30. 153 Discounting the Future On the other hand, some people think a public authorityshould adoptthe values of its constituents. In a democracy,they think,public authoritiesare responsibleto their electorate,which does not include generationsnot yet born. No doubt the present generationcares aboutfuture generations to some extent, and wishes to leave resources for their use. The value the present generation attaches to the well-being of future generations will have been embodiedin presentinterestrates, andit wouldbe wrong to give any furthervalue to future generations.Stephen Marglintakes this view. He says: "Iwant the government'ssocialwelfarefunction to reflectonly the preferences of present individuals.Whateverelse democratictheorymay or may not imply, I consider it axiomatic that a democratic government reflects only the preferencesof the individualswho arepresentlymembers of the bodypolitic."'9Marglinand Pigouare arguingaboutwhat the job of a governmentis-an argumentin politicalphilosophythat I do not wish to join. I shall say something else instead.20 Besides the question of what a governmentought to do, there is the separatequestion of which Qfits actions would have the best results. It is quite possiblethat the actiona governmentought to takeis not the one that would have the best results. Forinstance, a governmentmight have a duty to do what its electorate wants, and its electorate might want it to do something that wouldnot have the best results. In this paperI concentrate on the question of what wouldhave the best results. That was the question I posed in Section II. The problem I laid out was to compare alternative distributions of well-being across present and future people, to decide which is better. The market price method of evaluation came up as a possible shortcuttowardachieving this aim. It was intended to avoidthe verydifficultprocessof comparingpeople'swell-beingdirectly,butwas still meant to determine which distributionof well-being is better, weighing together the well-beingof differentpeople at differenttimes. Marglinsuggests, though, that a government's"socialwelfarefunction"should reflect ig. S. A. Marglin,"The Social Rate of Discount and the OptimalRate of Investment," QuarterlyJournalof Economics77 (I963): 97. I wouldbe misrepresentingMarglinif I did not point out that although he thinks the governmentshould base its decisions on the preferencesof the presentgeneration,he does not thinkit shoulduse marketinterestratesin its calculations.Because of something called the "isolationparadox,"he thinks the market rate does not properlymeasure what the present generationwould like to leave to its successors. I cannot go into the detailsof the isolationparadoxhere. 20. The pointis developedin moredetailin my WeighingGoods(Oxford:Blackwell,i 99 i), chap. 7. Parfitmakes a similarpoint in Reasons and Persons,pp. 480-8I. 154 Philosophy & Public Affairs only the preferences of the individualswho are presently members of the bodypolitic.He sees the socialwelfarefunction as playinga particularrole in a democraticpoliticalprocess:helping to determinewhat a government ought to do. He does not suggest the social welfarefunction measures the actualvalue of the alternativedistributions.So his aim is differentfromthe one I have been pursuing in this paper. I have been looking for a way of aggregatingpeople'swell-being to determine the overallvalue of alternative distributions,and for thatpurposethe well-beingof futuregenerations needs to be included. VIII. IMPRUDENCE Marketprices indicate the relativevalues people set on differentcommodities. In Section III, I discussed what "values"means in this context. I said that if a person aims to maximize her well-being, the value of a commodity to her is the well-being she will derive from it. If people generally aim to maximize their well-being, tben, market prices will indicate what wellbeing people expect to get from commodities.Prices will be some sort of a measure of well-being, and the market price method of evaluation has some chance of approximatingthe pure method. Butif people do not aim to maximize theirwell-being, this will not be so. Imprudenceis an importantinstance. When I say a personis imprudent,I mean she discounts her own future well-being; she does not attach as much value to her futurewell-being as she does to her present well-being. Figure 3 shows indifferencecurvesfor an imprudentperson. In the example I used for that diagram,futurewine is 5%cheaper than present wine. In equilibriumthe person must adjust her relative values to prices. She thereforevalues futurewine 5%less than present wine, at the margin. But that does not mean an extrabottleof wine in the futurewouldbringher 5% less well-being than an extra bottle in the present. As it happens, in the example I assumed it would bring her exactly the same well-being. So although futurewine is discounted by 5%on the market,it does not bring 5%less well-being. The discount rate does not measure well-being. In general, if people are imprudent, the market prices of commodities will not properlyrepresent the commodities'effects on well-being. The marketprice method of evaluationwill thereforenot correctlyindicate the results that would be reached by the pure method. Marketinterest rates will discount the future too quickly. 155 Discounting the Future Whatis to be done aboutthis? In Section III, I saidthatmany economists would say "nomatter."If people are imprudent,that is up to them. It is not the job of a public authorityto overrulepeople's own decision making in these matters. So imprudence gives no reason to use a lowerdiscount rate on commodities than the market'srate. Many economists believe that, if people are imprudent,this is a reason for the governmentto be imprudent too. On the other hand, Pigou thought otherwise. In the passage I quoted in Section VII, he says the governmentshould protect the interests of the future, not only against our preference for ourselves over future generations, but also against our own "irrationaldiscounting." Once again, I shall decline to enter an argument about the job of the government;that is a matterforpoliticaltheory.In this article,I have been asking what actionwouldhavethe best results. The puremethodof evaluation was intended to answer this question, and the market price method was intended as a shortcutto the puremethod.If peopleareimprudent,the marketprice method will fail as a shortcut,because marketprices will not measure people'swell-being. Marketinterest rates will not correctlyindicate which action will have the best results. The practicalimportanceof this point depends on whether people are typicallyimprudent.I know of no convincingevidence aboutthat, one way or the other.2'But it is theoreticallyimportantfor the followingreason. In Section IV,I explainedthat, forreasons of technology,futurecommodities would generallybe cheaperin the marketthan present ones. This implies that consumers,when they arein equilibrium,must valuefuturecommodities less than present ones at the margin. I asked how that could happen, and I mentioned only two possible explanationsof importance.The firstis that the person might plan to consume more commodities in the future than in the present. This makes futurecommoditiesless valuableto her at the margin, because of theirdiminishingmarginalvalue. Extracommodities will bring her less well-being in the future than in the present. So in this case future commoditiesought definitely to be discounted in public evaluations;the positivemarketinterest rates constitutea genuine reason for discounting. Butthis case can only occurif the personis increasing her consumption over time. It can only occur in a society generally if the economy is growing,so thatpeople'sconsumptionis generallyincreasing. 2I. MancurOlson and MartinBailey,in "PositiveTime Preference," Journal of Political Economy 89 (I98I): I-25, claim to have evidence that people are imprudent, but their argumentis seriouslyflawed.See my Counting the Cost of GlobalWarming,p. i ion.2I. 156 Philosophy & Public Affairs In a static economy, this cannot be the explanationof why people value future commoditiesless than present ones. In a static economy,only the second possible explanationis available,and that is imprudence. But if imprudence is the explanation,the fact that interest rates are positive in the marketdoes not indicate that present commoditiesproducemorewellbeing than future commodities.If well-being ought not to be discounted, marketinterestratesdo not give us a goodreasonfordiscountingcommodities in public decisions. When it comes down to it, if well-being ought not to be discounted, the only justification there can be for discounting commoditiesis that future commoditiesproduceless well-beingthan present ones. And that will only plausiblybe the case if peoplewill be betteroffin the future.Whateverhappens, technologywill almostalwaysensure that interest rates are positive, but these positiverateswilljustify discountingonlyif the economyis growing. This is a severelimitationon ourright to discountfuturecommodities. IX. CONCLUSION Within the market price method of evaluation, there are some good grounds for discounting future commodities. The method itself has its attractions, and it is much more practical than the pure method. But there are also some sound objections to the market price method. The most serious is that it does not take properaccount of the well-being of future generations. We cannot put our faith in the market price method in circumstances where the objections are important.It is certainlyunreliablefor evaluating long-term projects that have large effects on future generations. For instance, it is useless forprojectsaimed at mitigatingglobalwarming.For these projects, I think we have no alternativebut to fall back on the pure method; no shortcutis available.We shall have to do our best to estimate the effects the projects will have on people's well-being. Then we shall have to decide whether future well-being should be discounted. I have avoided that question in this article. The market price method skirts around it, by fixing attention on the discounting of commodities. But it cannot be avoidedin the end.22 22. My own tentative views about it are given in Counting the Cost of Global Warming, pp. 94-I08.