Commodity Bundles Research Articles

The Household's Decision to Accept or Reject a Conditional Transfer Offer

Households deemed by society to have insufficient resources to purchase an adequate commodity bundle are often offered aid (i.e., additional resources) conditional upon the households' purchasing a given level of some commodity (e.g., food, fuel, or housing). Such conditional transfers attempt to modify the households' normal behavior, i.e., if the households would normally purchase the required level of the designated commodity upon receipt of the transfer, the constraint would not be necessary. How these incentives and constraints interact to affect the households' behavior determines in large part the number and type of eligibles aided by the program, aggregate program costs (given payment levels), and the types of commodity bundles purchased by the recipient households. Clearly, understanding the decision to accept or reject a conditional transfer offer has widespread implications for the costs of the transfer program, the impact on eligible households, and the attainment of society's objectives. Numerous studies have investigated the size and distribution of recipient benefits in conditional transfer programs [1; 3; 6; 8; 9; 14; 16; 21]. To this author's knowledge, however, no analysis has estimated a model of the household's decision to participate in a conditional transfer program using household data and a theoretically appropriate measure for the household's net gain.' To overcome this gap in our understanding of the household's

Mosak's Equality and the Theory of Duality

Slutsky in the interpretation of the substitution matrix in the Fundamental Equation of Value Theory.2 Slutsky's interpretation involves a compensation of the change in real income caused by a price change .that makes possible the purchase of the same quantities of all the goods that had formerly been bought,13 while Hicks' compensation keeps the consumer on the same utility level as before the price change.4 It is known that when the price change is infinitesimal, the Hicks substitution matrix is equal to the Slutsky matrix. We will call this Mosak's Equality. Mosak's Equality has played an important role in index number theory. The price index that truly reflects the welfare change should be based on the Hicksian compensation. Such an index is difficult to compute, however, because utility levels are not observable. Instead, the Laspeyres index is widely adopted in practice. This index is based on the Slutsky compensation, since it indicates the change in income that would be needed in the current year in order to buy the commodity bundle bought in the base year. Mosak's Equality reveals that for small price changes the Laspeyres index is a good approximation to the ideal index.5 Despite its practical importance, Mosak's Equality has been given only a rather cumbersome proof.6 The aim of the present paper is to give a new proof of Mosak's Equality based on the principles of duality theory. Like the duality proofs of many other theorems, this proof is simpler and more transparent than the traditional one.

Commodity Bundling by Single-Product Monopolies

CONSIDER two products that have independent demands in the sense that all individual buyers consider them neither substitutes nor complements. Then, if the two products are priced separately, the demand for either is independent of the price of the other. In his classic analysis of block booking of feature films, George Stigler shows that it may be profitable for a monopoly seller of two such products to bundle them by requiring a buyer to take both in order to get either.' His work provides a rationale for tying arrangements that does not depend on technological or other dependencies among the products involved.2 Adams and Yellen extend the analysis of multiproduct monopoly with independent demands.3 They discuss two different bundling strategies: pure bundling, in which the seller only offers the products in fixed proportions; and mixed bundling, in which buyers may either buy the products separately or purchase a bundle with fixed proportions of each. In this note, I consider a single-product monopoly and investigate the profit and welfare implications of bundling its product for some other

Arbitrage and equilibrium in economies with infinitely many commodities

An ‘arbitrage opportunity’ for a class of agents is a commodity bundle that will increase the utility of any of the agents and that has non-positive price. The non-existence of ‘arbitrage opportunities’ is necessary and sufficient for the existence of an economic equilibrium. A bundle is ‘priced by arbitrage’ if there is a unique price that it can command without causing an ‘arbitrage opportunity’ to exist. For economies that have infinitely many commodities, appropriate notions of ‘arbitrage opportunities’ and ‘bundles priced by arbitrage’ depend on the continuity of agents’ preferences. This paper develops these notions, thereby providing a foundation for recent work in financial theory concerning arbitrage in continuous-time models of securities markets.

Preferences under Certainty and Uncertainty: A Note

A recent article by Blackorby et al. (1977) attempts to provide a set of sufficient conditions for the expected utility hypothesis. In their derivation they manage to take the sting out of the most objectionable aspect of the original von Neuman-Morgenstern assumptions-the continuity postulate over lottery bundles. They suggest that this postulate requires only the recognition of the fact that any irrational real number can be approximated arbitrarily closely by rational numbers. However, the proof of the expected utility hypothesis offered by these authors is incorrect. Suppose there are S states of nature and n commodities. A commodity bundle in state s can be represented by Xs = (Xs, ..., Xs) and all contingent commodities by X = (X1, ..., Xs). Treating X as an nS dimensional commodity bundle with additivity over states and equal subjective probabilities, Blackorby et al. show that

Commodity-Choice Behavior with Pigeons as Subjects

Starting from an initial (baseline) budget line, income-compensated price changes always resulted in substitution effects consistent with the Slutsky-Hicks theory. This behavior cannot be explained by a simple random-behavior model. Similar changes in relative prices that did not originate from the initial (baseline) budget line resulted in "undersubstitution effects": The composition of consumption changed in the expected direction, but the magnitude of change was not large enough to be consistent with the initial commodity bundle chosen. These undersubstitution effects are not explainable by shifting preference patterns or anchoring effects found in inconsistent choice sequences with human subjects.

Relative Deprivation and the Gini Coefficient: Reply

In their comment, John Hey and Peter Lambert (henceforth H & L) provide an alternative motivation for the representation of the theory of relative deprivation by the Gini coefficient. They also derive additional results that interpret other familiar Lorenz curve properties within the framework of relative deprivation theory. I would like to comment on three points: the alternative motivation, the extension of the relation into the utility space, and the use of the satisfaction rather than the deprivation function. First, it should be noted that the motivation of my note and that provided by H & L lead to the same representation, and technically speaking the difference is only in the order of integration. The difference between the two approaches is in the interpretation given to the results. H & L assume that each individual compares his income with that of each of the other individuals in his reference group. This means that for each pair of incomes, the intervening income distribution is irrelevant. In each comparison, the intensity of deprivation (satisfaction) is the difference in income. Summing the intensities over the entire society gives aggregate deprivation. According to my approach there are no individual comparisons. Each unit of income represents an ability to consume a bundle of commodities. The value of having a specific bundle (a unit of income) is a function of the scarcity of this bundle in the reference group, and the deprivation felt by an individual is the sum of the values of the bundles in the reference group that he is not able to consume (see Yitzhaki [1979]). The second point is related to H & L's use of Kakwani's [1977] results in order to define the deprivation function in terms of the utility function. Since the utility function is not known, this extension appears to be of only theoretical value. On the other hand, if instead of using 1 F( ) as an index of scarcity the index [1 F( )Ev, v > 0 is used, then the satisfaction function would have the following properties: If v = 0, then S = ,u, where At is the mean income, and S is the aggregate satisfaction. If v = 1, then S = ,u(I G), where G is the Gini coefficient.

Additivity and expected utility in risky multiattribute preferences

This experiment analyzed human preferences among even chance gambles for commodity bundles. The purpose of the experiment was to test several independence assumptions that distinguish between models for risky multiattribute preferences. In particular, the additivity and the expected utility part of the additive expected utility model were tested symmetrically. The degree and form of model violations were established, and the effects of instructions and of response modes were examined. All independence assumptions were violated by a bias to prefer a gamble or a commodity bundle that was previously matched against a standard. Systematic and strong violations that superseded this bias questioned the validity of the additive expected utility model. In violation of the additivity part of that model subjects consistently preferred the gamble with more balanced outcomes when comparing gambles with identical marginal probability distributions. This trend, called multiattribute risk aversion, was independent of subjects' single attribute risk attitude. Instructions and response modes had no noticeable impacts on these response patterns.

A Model of College Selection

This article presents a policy-oriented microeconomics model of college selection by undergraduates. The data base is detailed information on 1,008 college students. College choice is explained as demand for a multifaceted commodity bundle which is the institution. Demand is a function of the student's ability, family income, and the prices and aid offers of the schools in the student's opportunity set. The sample was stratified by income class to lest for the stability of coefficients across income groups. The model yields predictions concerning the effects of recent federal legislation and of the Carter educational finance initiative on college attendance. Direct student aid is found to be far less effective than price cuts in increasing the range of schools financially accessible to lower- and middle-income students.

On Revealed Preference Analysis

In this paper we shall be concerned with the theory of revealed preference understood in its original sense (Samuelson [19]), namely, as a theory of rational consumer's behaviour in competitive market situations; (see Richter [18] for the formulation and development of a general, abstract theory). As with practically all previous work in the field we will focus on the relationship between the theory of demand derived from revealed preference analysis and the one based on preference maximization; we denote the latter theory as the preference hypothesis. In 1938 Samuelson proposed as a new foundation for consumer theory the weak axiom of revealed preference (WA); the WA asserts that if a commodity bundle y is affordable, given a budget at which x is chosen (for short, if x is revealed preferred to y), then y cannot be revealed preferred to x. Although it has turned out that the demand theory implied by the WA is broader than the one generated by the preference hypothesis (Gale [6]; see also, Kihlstrom, Mas-Colell, Sonnenschein [14]) it is clear that they are conceptually close and their relationships were in need of clarification. The decisive step was given in 1951 by Houthakker [10]. He introduced the strong axiom of revealed preference (SA) and convincingly argued its equivalences with the preference hypothesis. Roughly speaking, the SA postulates the cyclical consistence of the WA. Since Houthakker's contribution the main line of research (see, for example, Uzawa [22], Stigum [21], etc.) has concentrated in finding sufficient conditions on demand functions guaranteeing that the consumer acts as a preference maximizer and his preferences are completely determined by his choice behaviour. This programme calls for both the existence of preferences underlying choice and their uniqueness in some class (usually the class defined by the property of continuity) and it is clear that, to successfully complete it, conditions on demand functions (besides, of course, the SA) will have to be imposed. So far, positive results have been obtained by combining a substantive requirement, the well definiteness of indirect demand functions, with a quite weak regularity one, the income Lipschitz property (this term will be defined later on).

Differential incidence in the presence of initial distorting taxes

This paper extends the two-sector, two-factor, general-equilibrium analysis of differential tax incidence by considering an initial situation where the government finances a fixed commodity bundle by distorting commodity and factor taxes. This alters the traditional analysis of marginal differential incidence in a fundamental way by necessitating the simultaneous determination of the change in the rental-wage ratio, the change in aggregate welfare and the change in an endogenously adjusting tax parameter. This contributes towards an integration of the study of the excess-burden effects and the distributional effects of a given tax situation.

Commodity Bundling and the Burden of Monopoly

Presents information on a study which analyzed the prevalence of commodity bundling as a marketing strategy. Cost savings in production, transactions and information associated with commodity bundling; Characteristics of commodity bundling; Problems associated with convention price discrimination that can overcome by commodity bundling; Conclusions. (Из Ebsco)

Unite and Conquer: A Multiplicative Inequality for Choice Probabilities

Two probabilistic theories of choice behavior (the model of independent random utility and the model of elimination by aspects) imply a testable property, the multiplicative inequality, according to which the probability of selecting an alternative x from an offered set A u B is at least as large as the product of the probabilities of selecting x from A and from B. WHEN FACED WITH a choice among complex alternatives (e.g., commodity bundles, investment plans, job offers) people often exhibit inconsistency. That is, they do not always select the same alternative under seemingly identical conditions. In order to accommodate this fact and obtain an adequate conception of choice behavior, psychologists and economists (e.g., Thurstone [18 and 19], GeorgescuRoegen [8], Luce [12], and Marschak [14]) developed models of choice in which the traditional concept of preference is replaced by the notion of choice probability. These models were investigated by many authors (e.g., Davidson and Marschak [5], Debreu [6], Chipman [4], Luce and Suppes [13], and Tversky [20]) from both mathematical and experimental standpoints, and they have also been applied to various aspects of economic theory such as equilibrium analysis (Hildenbrand [10] and Bhattacharya and Majumdar [2]) and consumer behavior (GeorgescuRoegen [9], Quandt [17], Mossin [16], and McFadden and Richter [15]). Two general forms of probabilistic choice models, called random utility and constant utility, were investigated (see Luce and Suppes [13]). In the random utility form, the subjective values undergo random fluctuations, and the alternative with the highest momentary value is selected. In the constant utility form, choice probability is expressed as a function of some (constant) scale values. Thus, the two forms differ regarding the locus of the random element in the choice process. The random utility form attributes uncertainty to the determination of subjective value, whereas the constant utility form attributes uncertainty to the application of the decision rule. (Some choice models, however, can be expressed in either form.) This paper investigates one prominent example of each form: the independent random utility model and the model of elimination by aspects. It shows that both models satisfy two testable properties which provide (fairly tight) upper and lower bounds for all choice probabilities. To formulate the results, we introduce the following definitions:

THE MULTI‐EQUATION UTILITY FUNCTION, INFORMATION, AND THE OPTIMAL COMMODITY BUNDLE

THE MULTI‐EQUATION UTILITY FUNCTION, INFORMATION, AND THE OPTIMAL COMMODITY BUNDLE

An equilibrium existence theorem for a general model without ordered preferences

In a recent paper the second author has shown that some of the usual hypotheses on consumers’ preferences are not needed for the proof of existence of a Walrasian General Equilibrium [Mas-Cole11 (1974)]. Specifically, it is not necessary that preferences come from a preference ordering. The only order property required is irreflexivity (meaning that a given commodity bundle is not preferred to itself). The properties of non-satiation, continuity and convexity of preferred sets turn out to be sufficient to obtain the existence result. The main purpose of the present note is to give a second proof of this fact which seems simpler than that of Mas-Cole11 (1974), and no more lengthy or complicated than the known equilibrium existence proofs which use ordered preferences. In two additional respects the model studied here generalizes the usual equilibrium model. The standard Walras, Arrow-Debreu theory treats what might be called the laissez-faire model in which each agent’s income is whatever he gets from selling goods plus his share of the profits of any firm in which he may own stock. In the present model the income of a consumer may be any continuous function of the prices, so the laissez-faire income function is included, but so also would any rule for assigning income to consumers (e.g., according to his ability or his need or the color of his eyes). Another way of saying this is that the model includes the possibility of arbitrary lump sum transfers of income among consumers, as might be achieved, for example, by a program of income taxes and subsidies. This substantial economic generalization requires no change whatever in the mathematical argument. The second generalization concerns production. The only requirement on our production set, besides the usual closure, convexity, and free disposal, is that it intersect the positive orthant in a boundedset.This means that the usual assumption

A New Approach to the Uniqueness of Equilibrium

A problem of major concern to economists is that of knowing whether certain phenomena are likely or not. For example, the econometrician would doubtless be happy if it were true that Cobb-Douglas production functions are very likely in the sense that any production function could be closely approximated by a function of the Cobb-Douglas type. Such results would provide excellent protection against those critics who claim that such functions are only special cases . The lack of these results is due largely to the idea of being likely having been used in too general and intuitive a way. In showing here that economies with a unique equilibrium are likely we will incidentally show that if being likely is interpreted carefully, within the context of a particular problem, then a surprising number of apparently improbable phenomena may in fact rigorously, be shown to be likely. We will now examine the fundamental problem of establishing whether uniqueness of equilibrium is likely (see Arrow and Hahn [1, Chap. 9]). The standard way to demonstrate the likeliness of some property is to show that it holds generically, i.e. on an open dense set with respect to some meaningful topology. We show that for a carefully chosen topology on the space of all economies, which we call the y topology just such a statement is true for the uniqueness of equilibrium.3 A suggestion that such a statement might be true can be inferred from Dierker's result [4] that the number of equilibrium prices is generically odd. He also gives an indication of the significance of establishing the uniqueness of equilibrium. Following Debreu [3] we define an economy with a commodity space R' as a tuple (f1, *--, fm1~l ..., COm). Here m denotes the number of consumers involved, fi (resp. woi E R') denotes the C' demand function 4 (resp. the strictly positive resources) of the ith consumer. An equilibrium for this economy is a tuple (p, x1, ..., x.) of prices p E R', zPh = 1, and commodity bundles xi e R' , such that lixi = Sioi and xi = fi(p, p cioi) for each consumer i. In the following all topological notions are with respect to the y topology. The definition of this topology, however, is somewhat technical, so it is relegated to the appendix, as one of the proofs of the theorems. We now state our main result.

On a System of Inequalities in Demand Analysis: An Extension of the Classical Method

AN EXPENDITURE CORRESPONDENCE being defined as a correspondence between budget constraints and admitted commodity bundles, a demand system, or its associated expenditure system, appears as one special case, and another case is that of a finite correspondence. A theorem will be proved on the existence of a positive solution for a certain system of homogeneous linear inequalities. Such a system can be associated with any finite expenditure correspondence, together with a number e between 0 and 1 interpreted as a level of cost-efficiency. The existence of a solution is equivalent to the admissibility of the hypothesis that the consumer, whose behavior is represented by the correspondence, (i) has a definite structure of wants, represented by an order in the commodity space, and (ii) programs at a level of cost-efficiency e. Any solution permits the immediate construction of a semi-increasing polyhedral concave utility function which realizes the hypothesis. The method for this construction is shown. When e = 1 the utility function fits the data exactly, in the usual sense that its maximum under any budget constraint is at the corresponding commodity point, and when e < 1 it can be considered to fit it approximately, to an extent indicated by e. A formula is given for the critical cost-efficiency, defined as the upper limit of possible e. Standard demand analysis which involves a strict maximum under the budget constraint, expressed also by the revealed preference idea, is put in perspective with this approach.

The Core of an N Person Game

THE PROBLEMS of distribution in an economic system may be analysed either by means of the behavioral assumptions of a competitive model or by the more flexible techniques of n person game theory. In the competitive model, consumers are assumed to respond to a set of prices by maximizing utility subject to a budget constraint and producers by maximizing profit. Consistent production decisions and an allocation of commodities are obtained by the determination of a set of prices at which all markets are in equilibrium. The analysis of these problems by means of n person game theory requires us to specify the production and distribution activities that are available to an arbitrary coalition of economic agents. It is frequently sufficient to summarize the detailed strategic possibilities open to a coalition by the set of possible utility vectors that can be achieved by the coalition. For example, in a pure exchange economy each coalition will have associated with it the collection of all utility vectors that can be obtained by arbitrary redistributions of the resources of that coalition. The core of an n person game is a generalization of Edgeworth's contract curve. A vector of utility levels is suggested which is feasible for all of the players acting collectively, and an arbitrary coalition is examined to see whether it can provide higher utility levels for all of its members. If this is possible, the utility vector which was originally suggested is said to be blocked by the coalition. The core of the n person game consists of those utility vectors which are feasible for the entire group of players and which can be blocked by no coalition. As we have seen during the last several years, there is an intimate connection between these two methods of analysis. If the conventional assumptions of the competitive model are made, such as convexity of preferences and convexity and constant returns to scale for the production set, then there will be a price system at which all markets are in equilibrium and a resulting assignment of commodity bundles to consumers. The utility vector associated with this competitive equilibrium may be shown to be in the core. Even further, if the number of consumers tends

Measuring equal increments of utility for money without measuring utility itself

Let (A, P) denote the commodity bundle consisting of $A and some other commodity P. With P and Q fixed, then for any A determine that B for which S is indifferent between (A,P) and (B,Q). If utility is additive over the components, each money difference induces the same utility difference. Two choices for P and Q, all jazz records of equal monetary value, and two levels for A, 53¢ and $5.03, were studied. One S did not maintain consistent indifference points, two exhibited constant marginal utility, and two exhibited diminishing marginal utility.

Existence of Competitive Equilibria in Markets with a Continuum of Traders

Abstract : It is well known, and easy to establish, that there exist markets that do not have competitive equilibria, provided the traders do not have convex preferences--that is, that the set of commodity bundles preferred or indifferent to a given bundle is not always convex. It is proved, nevertheless, that in a market consisting of a continuum of traders, each one individually insignificant, there is always a competitive equilibrium, even when the preferences are not convex. (Author)