Intergenerational consumption rules: An axiomatization of utilitarianism and egalitarianism

This paper considers choice rules that prescribe intergenerational consumption programs in an infinite horizon setting. An axiomatization is provided for utilitarian and egalitarian rules on a specific and concrete class of choice sets. The axiomatization provides new perpective on the relationship between the utilitarian and egalitarian rules and points out some trade-offs between norms that are inherent in the choice of a consumption rule. Finally, the analysis is extended to provide an axiomatization of the egalitarian rule for a broad class of choice sets.     

A concern about low relative income, and the alignment of utilitarianism with egalitarianism

A utilitarian social planner who maximizes social welfare assigns the available income to those who are most efficient in converting income into utility. However, when individuals are concerned about their income falling behind the incomes of others, the optimal income distribution under utilitarianism is equality of incomes.     

Factor substitution,ex ante and ex post

The amount of labor used per unit of capital stock (or investment) can be varied by any one of four quite different mechanisms. Two of these – changes in crew size and in capital utilization – are variable even ex post. These mechanisms are systemmatically related and all induce factor substitution in the same (neoclassical) direction with a change in relative factor prices. The conditions necessary to support the view that ‘factor prices don't matter’ are shown to be terribly stringent.     

On the efficiency of ex ante and ex post pricing institutions

Summary This paper compares the performance of three pricing institutions in a decentralized matching model in which random matching occurs. In the first, sellers make public ex ante commitments to trade at pre-specified prices before matching occurs. In the second, the buyer and seller engage in an alternating offer bargaining game once a match has occurred. In the final pricing institution, one party is chosen at random to make a take it or leave it price offer. The steady state equilibrium with ex ante pricing pareto dominates the steady state equilibrium with ex post take it or leave it offers, which in turn pareto dominates the steady state equilibrium with alternating offers. As the discount factor goes to one, the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level. The ex post pricing institutions generate participation rates that are bounded away from efficient levels. The surplus loss associated with switching from ex ante pricing to take it or leave it offers is small when the discount factor is close to one. Contrary to many models of decentralized trade, ex post pricing institutions encourage too much search by buyers.The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. The research for this paper was completed while the author was visiting the University of California at San Diego. The author thanks Douglas Gale for comments.     

Discrepancies between ex ante and ex post efficiency under identical subjective probabilities

Summary. Starr (1973) showed that, if people have different subjective probabilities, ex ante and ex post efficiency conflict. Conversely, under the simple preferences that he considered, the discrepancy between ex ante and ex post efficiency disappears when subjective probabilities are identical. Here I consider identical subjective probabilities, but more general preferences. First, risk attraction is admitted. Second, I dispense with the double requirement (dubbed IZU) of additive separability and state-independence of the utility of zero-date consumption, an unrealistic requirement when modeling the investment in durable goods. I find that, under IZU, and as long as ex post preferences satisfy the natural assumption of quasiconcavity (and satisfy some technical qualifications), an ex ante efficient allocation is indeed ex post efficient, but the converse is not necessarily true under risk attraction. If, on the other hand, IZU is violated, then one can have ex ante efficient allocations that are not ex post efficient, and vice-versa, even under risk aversion. Received: June 25, 1999; revised version: March 2001     

The public management of risk: Separating ex ante and ex post monitors

When a firm undertakes risky activities, the conflict between social and private incentives to implement safety care requires public intervention which can take the form of both monetary incentives and also ex ante or ex post monitoring, i.e., before or after an accident occurs. We delineate the optimal scope of monitoring depending on whether public monitors are benevolent or corruptible. We show that separating the ex ante and the ex post monitors increases the likelihood of ex post investigation, helps prevent capture and improves welfare.     

Sequential communication with ex post participation constraints

This paper examines an informed principal-agent game with ex post participation constraints for the agent. It shows that the players do not lose by communicating in turn among themselves rather than simultaneously if and only if the principal communicates first. It then considers every Bayesian incentive compatible allocation rules that assign non-negative payoffs for one player in a bilateral asymmetric information framework. It provides necessary and sufficient conditions for sequential communication to be as efficient as simultaneous communication in implementing these allocation rules when the player with unbounded payoffs moves first.     

The role of ex ante and ex post decisions in the valuation of life

This paper examines the use of ex ante and ex post criteria in the evaluation of projects involving the risk of death. One issue concerns the appropriate welfare function, and it is argued that this should reflect both ex post and ex ante considerations, but not in the form of restrictions on the welfare function. The second issue concerns the form of compensation. The argument in favour of ex post compensation as a means of reducing the cost of risk-bearing needs to be modified when risks involve more than a single dimension as they do in projects involving the risk of death.     

Ex ante and ex post long-run average cost functions

The traditional, neoclassical derivation of the long-run average cost(LAC) function is based on minimizing the cost of a given output. However, there are a number of reasons why the theoretical concept of this ex ante LAC function is likely to differ significantly from ex post cost-output observations when output is stochastic. In agriculture, the farmer's decision making criterion is assumed to be one of minimizing the cost of producing some planned output level. Average cost is then a function, inter alia, of planned output rather than realized output. It is argued that there is no operational significance in the cost-realized output relationship; in practice, the farmer's concern is with the cost-planned output relationship. This paper proposes a two-stage procedure to estimate the latter relationship. Cross-section data on UK dairy farms for 1980/1 are used to show significant differences in the ex ante and ex post relationships.     

Henry Sidgwick,moral order,and utilitarianism

Abstract

Henry Sidgwick is today remembered as a later nineteenth-century moral philosopher who struggled with his Christian faith, having difficulty reconciling this with an emergent modern and secular philosophy. In this paper, it is suggested that the only accurate part of this statement relates to the century in which Henry Sidgwick lived. It is argued that modern readers lack sensitivity to questions of faith and religiosity that were commonplace in the later nineteenth century, and that to have doubts in an Anglican faith did not necessarily imply any weakening of Christian faith. Furthermore, a misreading of Sidgwick as a moral philosopher in the modern sense neglects Sidgwick's central role in a Moral Sciences Tripos that included logic and political economy. Only after Marshall extracted political economy and political science from the Moral Sciences Tripos in 1903 did that Tripos become the foundation for a new Philosophy Tripos, and it is an error to read that later configuration back into the Tripos that Sidgwick led from 1883 to 1900.     

Invention under uncertainty and the threat of ex post entry

This article proposes a theoretical framework for studying the invention of new products when demand is uncertain. In this framework, under general conditions, the threat of ex post entry by a competitor can deter invention ex ante. Asymmetric market power in the ex post market exacerbates the problem. The implications of these general results are examined in a series of examples that represent important markets in the computer industry. The first is a model that shows how an operating system monopolist, by its mere presence, can deter the invention of complements, to its own detriment as well as that of society. The implications of policies such as patent protection, price regulation, and mandatory divestiture are considered. Three additional examples consider the ability of a monopolist in one market to commit to bundling an unrelated product, a pair of horizontally differentiated firms that can add a new feature to their products, and a platform leader that can be challenged in its base market by the supplier of a complementary product.     

Risk aversion and incentive compatibility with ex post information asymmetry

Summary. The paper extends Diamond's (1984) analysis of financial contracting with information asymmetry ex post and endogenous “bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literature, in which debt contracts are optimal for risk averse as well as risk neutral borrowers. Received: December 7, 1998; revised version: June 9, 1999     

Optimal algorithms and lower partial moment: ex post results

Portofolio management in the finance literature has typically used optimization algorithms to determine security allocations within a portfolio in order to obtain the best trade-off between risk and return. These algorithms, despite some improvements, are restrictive in terms of an investor's risk aversion (utility function). Since individual investors have different levels of risk aversion, this paper proposes two portfolio-optimization algorithms that can be tailored to the specific level of risk aversion of the individual investor and performs ex postevaluation tests of the algorithm performance.     

On efficient partnership dissolution under ex post individual rationality

This paper studies ex post individually rational, efficient partnership dissolution in a setting with interdependent valuations. We derive a sufficient condition that ensures the existence of an efficient dissolution mechanism that satisfies Bayesian incentive compatibility, ex post budget balancedness, and ex post individual rationality. For equal-share partnerships, we show that our sufficient condition is satisfied for any symmetric type distribution whenever the interdependence in valuations is non-positive. This result improves former existence results, demonstrating that the stronger requirement of ex post individual rationality does not always rule out efficiency. We also show that if we allow for two-stage revelation mechanisms, in which agents report their realized payoffs from the allocation, as well as imposing penalties off the equilibrium path, efficient dissolution is always possible even when the interdependence is positive. We further discuss the possibility of efficient dissolution with ex post quitting rights.     

Payoff equivalence between Bayesian and ex post individually rational dominant strategy mechanisms

Summary. An efficient, interim individually rational, ex post budget balanced Bayesian mechanism is shown to be payoff equivalent to an ex post individually rational and ex ante budget balanced dominant strategy mechanism. This result simplifies the search for mechanisms that implement efficient allocation rules by pointing to a class of Groves mechanisms. It eliminates the strict requirement of common knowledge of priors and can be applied to many problems of incomplete information. Received: October 22 1996; revised version: November 25, 1997     

Equivalence scales,horizontal equity and optimal taxation under utilitarianism

This paper analyzes the question of how differences in family size should be treated by the income tax system in order to achieve horizontal equity. Family size is incorporated into the demand system by the procedure of demographic scaling. Horizontal equity is defined as ‘equal treatment of equals’. It is shown that when lump-sum taxes are not available and the government has to rely on income taxation, then the only way to entail equal utilities for household of different size is to equate the labor supplies and the per-standard-adult consumptions of these households.     

Revealed favorability,indirect utility,and direct utility

This paper studies the axiomatic foundations of the indirect utility function, based upon a revealed preference approach. A chain of comparisons of budgets is regarded as giving a relation on the price-income space (a revealed favorability relation) rather than a relation on the commodity space (a revealed preference relation). The weak and strong axioms of revealed favorability are introduced by analogy with the weak and strong axioms of revealed preference, and the relationship between the former two axioms is investigated. The indirect and direct utility functions are then derived on the basis of the strong axiom of revealed favorability. Neither the continuity property of the demand function nor the convex property of its range is required for the approach taken in the paper.