Kenneth Arrow

"Among economic phenomena which have in some way been tied up with the existence of uncertainty, three classes may be distinguished: (1) those which by their very definition are concerned with uncertainty; (2) those which are not related to uncertainty by definition but nevertheless have no other conceivable explanation; (3) those whose relation to uncertainty is more remote and disputable."

"The businessman may be compared with two other types of individuals who are essentially concerned with behavior under uncertainty ― the scientist and the statistician. The scientist must choose, on the basis of limited information, among the innumerable logically conceivable laws of nature, a limited number. He cannot know whether his decisions are right or wrong, and, indeed, it is none too clear what is meant by those terms. There is a long history of attempts to reduce scientific method to system, including many which introduce probability theory, but it cannot be said that any great formal success has attended these efforts. If we were to compare the businessman to the scientist, we would be forced to the melancholy conclusion that little of a systematic nature can be said about the former’s decision-making processes. The statistician typically finds himself in situations more similar to that of the businessman. The problem of statistics can be formulated roughly as follows. It is known that one out of a number of hypotheses about a given situation is true. The statistician has the choice of one of a number of different experiments (a series of experiments can be regarded as a single experiment, so that drawing a sample of any size can be included in this schema), the outcome of any one of which is a random variable with a probability distribution depending on which of the unknown hypotheses is correct. On the basis of that outcome, the statistician must take some action (accept or reject a hypothesis, estimate the mean of a distribution to be some particular value, accept or reject a lot of goods, recommend a change in production methods, and so on), the consequences of which depend on the action taken and on the hypothesis that is actually true."

"Traditional welfare economics shows that there are certain of these combinations that will be preferred by all the voters, which permits us to eliminate the others without too much discussion. However, there will always remain an irreducible kernel of possibilities among which the choice rests on a combination or aggregation of individual ethical attitudes about distribution."

"Ever since I encountered Hicks’s Value and Capital while I was still a graduate student, I had the aim of completing and extending his vision of the economic system in its purest form. This was not because I believed that the economic world was perfectly competitive or that it was clearly self-equilibrating; after all, Chamberlin, Robinson, and Keynes were dominant intellectual influences, and I had the even more powerful influence of the facts of massive unemployment and large corporations. But the idea that the economic world was a general system, with all parts interdependent, seemed (and seems) to me to be an essential of good analysis. I regret what appears to be a revival of single-market thinking both among monetarists and among some of the younger empirical analysts. Then as now, the only game in town that offered a general system of economic interdependence was general competitive equilibrium, an idea to which the name of Leon Walras is imperishably linked. At least, such a system would provide a starting point for analysis of the market’s imperfections."

"L. Walras first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers and the equilibrium condition that supply equal demand on every market."

"Perhaps as important is the relation between the existence of solutions to a competitive equilibrium and the problems of normative or ."

"The government may be regarded as a decision-making entity. Among the decisions it makes are the formation of economic policy and the collection of economic-statistical information. In all modern nations the economic policies of the government are significant activities, if for no other reason than the high proportion of national income which passes through the Treasury; but of course in many countries much more ambitious economic planning is aimed at, though not necessarily achieved. Economic statistics, on the other hand, if one is to judge by expenditures, form only an insignificant proportion of a government's activities and are the least developed precisely in those underdeveloped countries which have the greatest felt needs for economic plans."

"Government economic policy, like almost any realistic decision problem, has two fundamental characteristics: it is sequential and it is uncertain."

"In view of the magnitude of an economic system, it would take only a very small percentage of improvement in economic stability or growth to make almost any conceivable data collection worthwhile. The situation is analogous to reported results of the use of linear programming in industry; the gains are small in proportion to previous profit levels but still very much larger than the costs of the programming. No country is adequate in respect to its data. In particular the underdeveloped countries, with their ambitious programs, might well ponder whether or not the marginal productivity of investment in better economic statistics is perhaps not higher than almost any conceivable alternative; they have more need and fewer data."

"Decision theory, as it has grown up in recent years, is a formalization of the problems involved in making optimal choices. In a certain sense — a very abstract sense, to be sure — it incorporates among others operations research, theoretical economics, and wide areas of statistics, among others."

"The formal structure of a decision problem in any area can be put into four parts: (1) the choice of an objective function defining the relative desirability of different outcomes; (2) specification of the policy alternatives which are available to the agent, or decision-maker, (3) specification of the model, that is, empirical relations that link the objective function, or the variables that enter into it, with the policy alternatives and possibly other variables; and (4) computational methods for choosing among the policy alternatives that one which performs best as measured by the objective function."

"Strictly speaking, decision theory really is concerned only with the fourth part of the division given above, that is, the determination of the computational methods for optimization. Given the determination of the other three factors―the objective function, the range of policy alternatives, and the model―the ideal picture is that someone, presumable the firm that hires the operations researcher, hands him, on a silver platter, an objective function. By talking to the engineers, or by looking into a few scientific laws, he determines the policy alternatives available and also the model."

"Speaking very broadly, almost any human action involves choice; the external environment delimits a range of possible actions at any given moment but does not usually reduce that range to a single alternative. The formulation of a theory of human action in some sphere as a theory of choice means its presentation as a functional relation associating with each possible range of alternatives a chosen one among them."

"Learning, as studied by psychologists, closely resembles sequential analysis in some aspects. Learning experiments usually consist of a series of trials in which the subject’s choices are sometimes rewarded and sometimes not. The individual, after making many choices, eventually begins to discriminate between the proper response and the improper one. At some point, presumably, he could terminate the experiment, at least in the sense of disregarding the further observations and making the same choice each time."

"Index numbers are, of course, desired for purposes other than to measure the cost of living. One obvious possibility is to consider some subset of cost-of- living items, such as food. The logic of the preceding argument goes through precisely provided we assume that the distribution of food expenditures in any period among different foods depends only on the total volume of food expenditures and is independent of the prices of other goods, for any given total volume of food expenditures. This does not deny substitution between foods and other commodities, but we assume that the total effect of this substitution is already reflected in the choice of a volume of food expenditures. In a broad way, similar considerations apply to the pricing of producers’ goods, which should be interpreted as reflecting indirectly consumers’ preferences. However, there is undoubtedly a good deal more in the detailed working out of the theory that has never been developed."

"In a capitalist democracy there are essentially two methods by which social choices can be made: voting, typically used to make ‘political’ decisions, and the market mechanism, typically used to make ‘economic’ decisions. In the emerging democracies with mixed economic systems Great Britain, France, and Scandinavia, the same two modes of making social choices prevail, though more scope is given to the method of voting and to decisions based directly or indirectly on it and less to the rule of the price mechanism. Elsewhere in the world, and even in smaller social units within the democracies, the social decisions are sometimes made by single individuals or small groups and sometimes (more and more rarely in this modern world) by a widely encompassing set of traditional rules for making the social choice in any given situation, for example, a religious code."

"In addition to ignoring game aspects of the problem of social choice, we will also assume in the present study that individual values are taken as data and are not capable of being altered by the nature of the decision process itself. This, of course, is the standard view in economic theory (though the unreality of this assumption has been asserted by such writers as Veblen, Professor J. M. Clark, and Knight) and also in the classical liberal creed. If individual values can themselves be affected by the method of social choice, it becomes much more difficult to learn what is meant by one method’s being preferable to another."

"The problem of measuring utility has frequently been compared with the problem of measuring temperature. This comparison is very apt. Operationally, the temperature of a body is the volume of a unit mass of a perfect gas placed in contact with it (provided the mass of the gas is small compared with the mass of the body). Why, it might be asked, was not the logarithm of the volume or perhaps the cube root of the volume of the gas used instead? The reason is simply that the general gas equation assumes a particularly simple form when temperature is defined in the way indicated. But there is no deeper significance."

"The concept of rationality used throughout this study is at the heart of modern economic analysis, and it cannot be denied that it has great intuitive appeal; but closer analysis reveals difficulties."

"If the total number of alternatives is two, the method of majority decision is a social welfare function which satisfies Conditions 2–5 and yields a social ordering of the two alternatives for every set of individual orderings."

"If there are at least three alternatives which the members of the society are free to order in any way, then every social welfare function satisfying Conditions 2 and 8 and yielding a social ordering satisfying Axioms I and II must be either imposed or dictatorial."

"The idealist doctrine then may be summed up by saying that each individual has two orderings, one which governs him in his everyday actions, and one which would be relevant under some ideal conditions and which is in some sense truer than the first ordering. It is the latter which is considered relevant to social choice, and it is assumed that there is complete unanimity with regard to the truer individual ordering."

"From the point of view of seeking a consensus of the moral imperative of individuals, such consensus being assumed to exist, the problem of choosing an electoral or other choice mechanism, or, more broadly, of choosing a social structure, assumes an entirely different form from that discussed in the greater part of this study."

"In this aspect, the case for democracy rests on the argument that free discussion and expression of opinion are the most suitable techniques of arriving at the moral imperative implicitly common to all. Voting, from this point of view, is not a device whereby each individual expresses his personal interests, but rather where each individual gives his opinion of the general will."

"Invention is here interpreted broadly as the production of knowledge. From the viewpoint of welfare economics, the determination of optimal resource allocation for invention will depend on the technological characteristics of the invention process and the nature of the market for knowledge."

"In an ideal socialist economy, the reward for invention would be completely separated from any charge to the users of information. In a free enterprise economy, inventive activity is supported by using the invention to create property rights; precisely to the extent that it is successful, there is an underutilization of the information."

"To sum up, we expect a free enterprise economy to underinvest in invention and research (as compared with an ideal) because it is risky, because the product can be appropriated only to a limited extent, and because of increasing returns in use. This underinvestment will be greater for more basic research. Further, to the extent that a firm succeeds in engrossing the economic value of its inventive activity, there will be an underutilization of that information as compared with an ideal allocation."

"If the government and other nonprofit institutions are to compensate for the underallocation of resources to invention by private enterprise, two problems arise: how shall the amount of resources devoted to invention be determined, and how shall efficiency in their use be encouraged? These problems arise whenever the government finds it necessary to engage in economic activities because indivisibilities prevent the private economy from performing adequately (highways, bridges, reclamation projects, for example), but the determination of the relative magnitudes is even more difficult here."

"The choice among these alternatives in any given case depends on the degree of difficulty consumers have in making the choice unaided, and on the consequences of errors of judgment. It is the general social consensus, clearly, that the laissez-faire solution for medicine is intolerable. The certification proposal never seems to have been discussed seriously."

"According to this point of view, knowledge is, so to speak, a by-product of production or of investment. In research, on the contrary, it can be said that knowledge is the primary product. The distinction between products and by-products is not important for ordinary goods, because in a competitive regime the marginal costs of the two must be equal. But since knowledge does not have the normal properties of an economic good, it is necessary to study each mode of its production."

"To conclude, I argue that the government should not display risk aversion in its behavior. Hence, the proper procedure is to compute the expected values of benefits and costs, and discount them at a riskless rate, contrary to the view of Hirshleifer (1964, p. 85). Suppose the future to be unknown; it is known that one of a set of states will prevail, and their probabilities are known (or believed in). A given state means a complete description of all production possibilities, so that all uncertainties are resolved when the state is known. To summarize some earlier discussions (Arrow, 1964b; Deberu, 1959, chap 7; Hrishleifer, 1964, pp. 80-85), we can achieve an optimal allocation if we imagine markets in all possible commodity-options, a commodity-option being an obligation to deliver a fixed amount of a given commodity if, and only if, a given state prevails."

"The fundamental fact which causes the need for discussing public values at all is that all significant actions involve joint participation of many individuals. Even the apparently simplest act of individual decision involves the participation of a whole society. It is important to note that this observation tells us all non-trivial actions are essentially the property of society as a whole, not of individuals. It is quite customary to think of each individual as being able to undertake actions on his own (e.g., decisions of consumption, produc- tion, and exchange, moving from place to place, forming and dissolving families). Formally, a social action is then taken to be the resultant of all individual actions. In other words, any social action is thought of as being factored into a sequence of individual actions."

"To conclude, then, we must in a general theory take as our unit a social action, that is, an action involving a large proportion or the entire domain of society. At the most basic axiomatic level, individual actions play little role. The need for a system of public values then becomes evident; actions being collective or interpersonal in nature, so must the choice among them. A public or social value system is essentially a logical necessity."

"The only rational defense of what may be termed a liberal position, or perhaps more precisely a principle of limited social preference, is that it is itself a value judgment. In other words, an individual may have as part of his value structure precisely that he does not think it proper to influence consequences outside a limited realm. This is a perfectly coherent position, but I find it difficult to insist that this judgment is of such overriding importance that it outweighs all other considerations. Personally, my values are such that I am willing to go very far indeed in the direction of respect for the means by which others choose to derive their satisfactions."

"I interpret moral obligation as the carrying out of agreements which may, however, be implicit. Thus, a society in which everyone immediately executed his aggressive impulses would be untenable. Therefore, there is an agreement that I will refrain from aggressive actions, which in themselves give me satisfaction, in return for your not taking aggressive action against me. However, conscious agreements to achieve these ends are much too costly in terms of information and bargaining. Therefore, as societies have evolved they have found it economical to make these agreements at an unconscious, implicit level. Internalized feelings of guilt and right are essentially unconscious equivalents of agreements that represent social decisions."

"In this case of unrestricted income distribution, the dimensionality of the issue space is the same as the number of individuals. Thus, as Tullock argues, political resolution of distributional issues is apt to be possible only if only a few parameters of the income distribution are under consideration, not the whole distribution. Why this restriction of the scope of choice should occur is not easy to explain on simple economic grounds. On the other hand, the restriction does conform to the long-standing view of writers on ethics, of whom Kant is perhaps most conspicuous, that decisions on distribution ought to be made as if by an impartial observer, who considers then only the mean, a measure of inequality, and perhaps one or two further parameters characterizing the income distribution, but not specifically who gets what. If voters acted like Kantian judges, they might still differ, but the chances of coming to an agreement by majority decision would be much greater than if voters consulted egoistic values only. Does this suggest that ethics may have survival value for political systems and therefore descriptive as well as prescriptive significance?"

"There are two approaches to a theory of general equilibrium in an imperfectly competitive environment; most writers who touch on public policy questions implicitly accept one or the other of these prototheories without always recognizing that they have made such a choice. One assumes that all transactions are made according to the price system, that is, the same price is charged for all units of the same commodity; this is the monopolistic competition approach. The alternative approach assumes unrestricted bargaining; this is the game theory approach. The first might be deemed appropriate if the costs of bargaining were high relative to the costs of ordinary pricing, while the second assumes costless bargaining."

"Because the costs of transmission are nonnegligible, even situations which are basically certain become uncertain for the individual; the typical economic agent simply cannot acquire in a meaningful sense the knowledge of all possible prices, even where they are each somewhere available. Markets are thus costly to use, and therefore the multiplication of markets, as for contingent claims as suggested above, becomes inhibited."

"I want, however, to conclude by calling attention to a less visible form of social action: norms of social behavior, including ethical and moral codes. I suggest as one possible interpretation that they are reactions of society to compensate for market failures. It is useful for individuals to have some trust in each other's word. In the absence of trust it would become very costly to arrange for alternative sanctions and guarantees, and many opportunities for mutually beneficial cooperation would have to be, foregone."

"It is difficult to conceive of buying trust in any direct way (though it can happen indirectly, for example, a trusted employee will be paid more as being more valuable); indeed, there seems to be some inconsistency in the very concept. Nonmarket action might take the form of a mutual agreement. But the arrangement of these agreements and especially their continued extension to new individuals entering the social fabric can be costly. As an alternative, society may proceed by internalization of these norms to the achievement of the desired agreement on an unconscious level."

"Despite the favorable properties of the price system, I am no unrestrained admirer of it. Some of its limits in the urban context will be stressed below. It is not possible, however, to understand the city as an economic problem without first understanding the virtues of the free market system in performing its role of allocating resources."

"The case for equality may be made on other than utilitarian grounds; thus J. Rawls has, argued for maximizing the minimum utility, rather than the sum of utilities, as an ethical criterion, and this criterion would tend toward output equality and therefore strong input progressivity."

"Dynamic analysis may have deeper implications if we depart from the analysis of stationary states. The frim must now serve some additional roles. In the absence of futures markets, the firm must serve as a forecaster and as a bearer of uncertainty. Further, from a general equilibrium point of view, the forecasts of others become relevant to the evaluation of the firm's shares and therefore possibly of the firm's behavior."

"In any case the empirical evidence can only be made meaningful with at least a minimum of theoretical analysis."

"Property systems are in general not completely self-enforcing. They depend for their definition upon a constellation of legal procedures, both civil and criminal. The course of the law itself cannot be regarded as subject to the price system. The judges and the police may indeed be paid, but the system itself would disappear if on each occasion they were to sell their services and decisions. Thus the definition of property rights based on the price system depends precisely on the lack of universality of private property and of the price system. This ties in with the third hypothesis put forward in section I. The price system is not, and perhaps in some basic sense cannot be, universal. To the extent that it is incomplete, it must be supplemented by an implicit or explicit social contract. Thus one might loosely say that the categorical imperative and the price system are essential complements."

"While economic theory in general may be defined as the theory of how an economic condition or an economic development is determined within an institutional framework, the deals with how to judge whether one condition can be said to be better in some way than another and whether it is possible, by altering the institutional framework, to achieve a better condition than the present one."

"Nevertheless, when all due allowances are made, the coherence of individual economic decisions is remarkable. As incomes rise and demands shift, for example, from food to clothing and housing, the labor force and productive facilities follow suit. Similarly, and even more surprising to the layman, there is a mutual interaction between shifts in technology and the allocation of the labor force. As technology improves exogenously, through innovations, the labor made redundant does not become permanently unemployed but finds its place in the economy. It is truly amazing that the lessons of both theory and more than a century of history are still so misunderstood. On the other hand, a growing accumulation of instruments of production raises real wages and in turn induces a rise in the prices of labor-intensive commodities relative to those which use little labor. All these phenomena show that by and large and in the long view of history, the economic system adjusts with a considerable degree of smoothness and indeed of rationality to changes in the fundamental facts within which it operates."

"My own interest first centered on the relations between Pareto efficiency and competitive equilibrium. In particular, there was considerable discussion among economists in the late 1940’s about the inefficiencies resulting from rent control and different proposals for arriving at the efficiency benefits of a free market by one or another transition route. Part of the informal efficiency arguments hinged on the idea that under rent control people were buying the wrong kind of housing, say, excessively large apartments. It struck me that an individual bought only one kind of housing, not several. The individual optima were at corners, and therefore one could not equate marginal rates of substitution by going over to a free market. Yet diagrammatic analysis of simple cases suggested to me that the traditional identification of competitive equilibrium and Pareto efficiency was correct but could not be proved by the local techniques of the differential calculus."

"In fact, is is not a mere empirical accident that not all the contingent markets needed for efficiency exist but a necessary fact with deep implications for the workings and structure of economic institutions. Roughly speaking, information about particular events, even after they have occurred, is not spread evenly throughout the population. Two people cannot enter into a contract contingent on the occurrence of a certain event or state if only one of them in fact will know that the event has occurred. A particular example of this is sometimes known as “moral hazard” in the insurance and economic literature. The very existence of insurance will change individual behavior in the direction of less care in avoiding risks."

"There is no need to enlarge upon the importance of a realistic theory explaining how individuals choose among alternate courses of action when the consequences of their actions are incompletely known to them. It is no exaggeration to say that every choice made by human beings would meet this description if attention were paid to the ultimate implications."