The authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem. In addition, they develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm, the monopolist, the Bertrand oligopolist, consumer and growth theory, game theory, and general equilibrium analysis. Copyright 1994 by The Econometric Society.
BEGINNING WITH THE WORK OF A. K. SEN (1976) poverty research has made extensive use of axioms to construct and evaluate distribution-sensitive poverty measures. An index is distribution-sensitive if it satisfies Sen's (1976) weak transfer axiom; poverty decreases when income is transferred from a high income poor person to a low income poor person. A distribution-sensitive measure is appealing because it reflects the extent of deprivation among the poor and incorporates aspects of poverty that are ignored by standard measures such as the headcount ratio and poverty gap ratio. In addition to the weak transfer axiom, a number of other axioms that have considerable intuitive appeal when considered in isolation have been identified. However, several researchers (e.g., Thon (1979), Kundu and Smith (1983), and Donaldson and Weymark (1986)) have shown that in some cases it is impossible to devise a poverty index that is consistent with the joint implications of otherwise reasonable axioms. Foster (1984, p. 233) interprets the difficulties caused by the combined effects of two or more axioms . . as a warning not to measure too many aspects of poverty at the same time. As a consequence, it is now generally recognized that poverty axioms can have joint effects and it is important to explore the implications of such influences. In a comprehensive investigation of subgroup consistent poverty measures, Foster and Shorrocks (1991) examine the interaction between the scale invariance and translation invariance axioms.2 The first axiom requires a poverty index to be unaffected by the doubling of all incomes and the poverty line. The second axiom requires a poverty index to be unaffected by equal increments to each income and to the poverty line.3 Poverty indices that satisfy the first axiom are considered to be poverty while those satisfying the second are poverty indices. If a distribution-sensitive index satisfying both axioms could be found it would provide a single measure of relative and absolute poverty and have considerable intuitive appeal in poverty measurement. But, one implication of Foster and Shorrocks' (1991) work (Proposition 6) is that for the class of poverty measures they consider, a distribution-sensitive poverty index that is both relative and absolute cannot exist. This note follows Foster and Shorrocks (1991) but concentrates on the implications of the joint effects of scale and translation invariance. We drop the assumption of subgroup consistency and derive a proposition that has several important implications. First, for all poverty indices, only those relying upon simple headcounts of the poor satisfy both the scale and translation invariance axioms. This result clearly illustrates the strong restrictions imposed by combining scale and translation invariance with other standard axioms; there can be no distribution-sensitive poverty index that is relative and absolute. Second, the result provides a simple characterization of the entire class of the headcount-related poverty indices (defined below). Third, the result leads to a direct proof of the result
Strategic implications of the learning curve hypothesis are analyzed in the context of a price-setting, differentiated duopoly selling to a sequence of heterogeneous buyers with uncertain demands. A unique Markov perfect equilibrium is characterized and sufficient conditions are provided for market dominance to be self-reinforcing. Increasing market dominance implies that learning is privately disadvantageous. Finally, introducing avoidable fixed costs and possible exit into the model yields a new theory of predatory pricing based on the learning curve hypothesis. Copyright 1994 by The Econometric Society.
The objective of the Institute for Policy Reform is to enhance the foundation for broad based economic growth in developing countries.Through its research, education and training activities the Institute encourages active participation in the dialogue on policy reform, focusing on changes that stimulate and sustain economic development.At the core of these activities is the search for creative ideas that can be used to design constitutional, institutional and policy reforms.Research fellows and policy practitioners are engaged by IPR to expand the analytical core of the reform process.This includes all elements of comprehensive and customized reforms packages, recognizing cultural, political, economic and environmental elements as crucial dimensions of societies.
The Generalized Extreme Value Model was developed by McFadden for the case with discrete choice sets. The present paper extends this model to cases with both discrete and continuous choice sets and choice sets that are unobservable relative to the analyst. We also propose behavioral assumptions that justify random utility functions (processes) that have a max stable structure i.e., utility processes where the finite dimensional distributions are of the multivariate extreme value type. Finally we derive non-parametrically testable implications for the choice probabilities in the continuous case.
THE CENTRAL PURPOSE OF THIS PAPER is to develop a model of insider trading (i.e., trading based on private information) in the context of an imperfectly competitive multi-security market with risk-neutral agents. Imperfect competition allows us to consider strategic behavior, and a multi-security market lets us study the effect of a correlated environment on equilibrium. We employ the informational assumption that market makers can observe all order flows, and so portfolio diversification arises in this model for strategic reasons. Given correlated fundamentals, market makers can potentially learn about every security from each order flow. This causes even a risk neutral trader who does not face short-selling restrictions to refrain from determining the demand for each security independently. This contrasts with traditional multi-asset models, which focus on the incentive to reduce portfolio variance, or the effect of short-selling restrictions or budget constraints. Under imperfect competition, correlation has two effects. One, ceteris paribus, it allows the uninformed to learn from additional variables since each order flow could potentially have information about all payoffs. On the other hand, it creates an incentive for informed traders to restrict what others can learn from public information. Thus, our analysis can be viewed as an application to the multi-security, heterogeneous-information model in Admati (1985) of the imperfectly competitive equilibrium concept which Kyle (1985) first applied to the single-security, homogeneous-information model of Grossman and Stiglitz (1980). Our principal results include an explicit characterization of a linear equilibrium as a function of three general covariance matrices associated with payoffs, noise trading, and errors in private signals. Under general covariance structures, we show that there always exists an equilibrium in which the relationship between the vector of prices and the vector of order flows is governed by a symmetric positive definite matrix. The plan of the paper is as follows. In Section 2, we introduce our model. We derive the equilibrium in Section 3, and Section 4 comments on the properties of the equilibrium. The proofs of the results are in the Appendix.
This paper presents conditions under which a person's beliefs about the occurrence of uncertain events are quantified by a capacity measure, i.e., a nonadditive probability. Additivity of probability is violated in a large number of applications where probabilities are vague or ambiguous due to lack of information.The key feature of the theory presented in this paper is a separation of the derivation of capacities for events from a specific choice model. This is akin to eliciting a probability distribution for a random variable without committing to a specific decision model. Conditions are given under which Choquet expected utility, the Machina-Schmeidler probabilistically sophisticated model, and subjective expected utility can be derived as special cases of our general model.
IT IS OFrEN THE CASE that an individual's decision is at least partly based on information received from another. And when the agents' payoffs depend on both the former's decision and on the latter's information, there is an incentive for the individual to attempt to bias the decision maker's decision in his or her favor by strategically manipulating the information transmitted. In a seminal paper, Crawford and Sobel (1982) (hereafter, C/S) study such strategic information transmission in the context of an abstract sender/receiver game. Variants of the Crawford and Sobel model have been applied widely, and as the application varies so often does the interpretation of type. In some cases, type refers to a preference parameter given by Nature-as, for example, in bargaining theory (e.g., Farrell and Gibbons (1989), Matthews (1989)), whereas in other settings-for instance, legislative decision making or expert testimony -type refers to more or less technical information concerning how decisions map into final consequences and, as such, is acquired information (e.g., Gilligan and Krehbiel (1987), Milgrom and Roberts (1986)). When the information has to be acquired, it is natural to suppose the acquisition is costly; for otherwise, there is no reason why such information is asymmetrically distributed. So long as the receiver can observe surely-or, at least, accurately infer-whether the sender is informed, and so long as messages are cheap-talk, there is no issue here for strategic information transmission (save whether to become at all). However, there are many circumstances when it is inappropri- ate to assume the receiver has such knowledge. One possibility is that a receiver may know that a sender has some relevant informa- tion, but be uncertain of the quality of this information. A second, perhaps more important, possibility is that a receiver is unable to tell whether a (potential) sender is uninformed. Inter alia, this problem constitutes the rationale for of the law being inadmissible as a legal defense (were it admissible, then informed miscreants would mimic uninformed transgressors); leads voters to be skeptical of politicians claiming ignorance of illegal arms deals; and makes the SEC sensitive to problems in distinguishing insider trading from legitimate good judgement. So there is an intrinsic asymmetry in that it is generally possible for, say, senders to verify possession of at least some information, but it is typically prohibitively difficult to verify any lack of knowledge