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Bertrand Equilibrium with Capacity Constraints and Restricted Mobility

Econometrica 1984 52(5), 1117
This paper considers price competition among firms when there are capacity constraints and buyers have limited ability to visit firms. A natural method of allocating buyers among firms arises in the equilibrium of the buyers' search game. Sufficient conditions are given under which the buyers' equilibrium varies continuously with the prices charged by firms. Capacity constraints are used to guarantee that this ensures existence of (mixed strategy) equilibria for the pricing game played by sellers. We show that natural pure strategy equilibria arise when the game is made large in appropriate ways. SINCE BERTRAND'S CRITICISM OF COURNOT, it has been known that models where sellers compete with prices may have undesirable properties when the commodities traded are homogenous. In the simplest models with constant marginal costs, price may be driven down to the competitive level, even when there are only two firms. More problematic, if sellers are subject to capacity constraints, Nash (in prices) equilibrium may not exist at all. These problems all arise because of a discontinuity in firms' profit functions that arises when the prices of two or more firms are equal. There have been many attempts to resolve this problem. The simplest is to constrain sellers' prices to be equal, and to force them to compete in quantities. This is the basis of most of the literature on monopolistic competi

Restrictions on Price Advertising

Journal of Political Economy 1984 92(3), 472-485
In this paper the effects of advertising restrictions in an industry producing an undifferentiated product are analyzed. When the product is undifferentiated, advertising conveys information about price. The standard intuition suggests that such prohibitions will raise buyer search costs, making demand less elastic. This raises price and profits in an industry. Advertising restrictions provide an indirect means of coordinating pricing strategies in this framework. Here we consider the cost side of the same argument. The efficiency of firms in an industry is allowed to vary and information about costs is private. In this environment efficient firms are hurt by advertising restrictions, since lower advertised prices constitute their most effective competitive weapon. We show that when the number of buyers and sellers is finite, there is a nonzero probability that advertising restrictions will reduce every firm's price. This occurs when all firms are more efficient than their competitors expect them to be. Further, when the number of buyers and sellers is infinite, it is possible that average price charged in an industry can fall after a ban on advertising.

Self-Selection and Monitoring in Dynamic Incentive Problems with Incomplete Contracts

Review of Economic Studies 1993 60(1), 149
A dynamic trading problem is examined in which a monopsonistic employer tries to hire workers whose productivities and reservation wages are private information. The employer can only observe an employee's quality indirectly by monitoring a non-verifiable measure of on-the-job performance. The employer makes contract offers which employees can accept or reject. Once a contract has been accepted it is impossible for the employer to exchange messages with individual employees. On the unique stationary equilibrium path for the contracting game, the employer chooses between two mutually exclusive outcomes. In the market outcome, the employer offers long-term contracts and information is conveyed entirely through self-selection and delayed production. In the monitoring outcome, the employer offers short-term contracts, and contract renegotiation is conditioned by an employee's past performance. A simple characterization theorem is provided which illustrates the often surprising effects of improvements in information in this setting. For example, an employer who is initially offering short-term contracts to exploit performance information may stop monitoring and shift to market screening when the monitoring technology becomes more informative.

Repeated Insurance Contracts with Adverse Selection and Limited Commitment

Quarterly Journal of Economics 1989 104(2), 229
In this paper we describe the sequential equilibria of a two-period monopoly with asymmetric information and limited commitment in the market for accident insurance. The role of learning is analyzed; and the possible sequential pooling, semiseparating, and separating equilibria are described (where the probability that a buyer will make a revealing first-period contract choice is equal to zero, is positive, and is equal to one, respectively). In the absence of discounting, we show that only pooling and semiseparating equilibria exist; provide a limited characterization of when these equilibria occur; and show that accident-contingent insurance and accident underreporting occur with positive probability along the equilibrium path of the game.

Competing Premarital Investments

Journal of Political Economy 2002 110(3), 592-608 open access
This paper studies premarital parental investments in children’s wealth, where spousal wealth is a public good in marriage. By investing in their children’s wealth, parents increase the wealth of their children and the quality of the spouses that their children can marry. In large marriage markets, the hedonic return to investment internalizes all the external benefits of premarital investment in wealth so that the competitive equilibrium is efficient. Marriage market competition also increases investments in small marriage markets relative to no competition, but equilibrium investments are not efficient.

The Impact of Internal Auditor Compensation and Role on External Auditors' Planning Judgments and Decisions*

Contemporary Accounting Research 2001 18(2), 257-281
This paper reports the results of an experiment that investigates how external audit planning is affected when internal auditors have incentives and the opportunity to bias their evaluations. Specifically, we draw on attribution theory to examine how internal auditor eligibility for incentive compensation and participation in consulting (i.e., two factors that provide incentives to bias audit evaluations) affect external audit planning. In addition, we examine the effects of incentive compensation and a consulting role across two routine internal audit tasks — an objective tests of controls task and a subjective inventory valuation task — to evaluate whether their effects are contingent upon task subjectivity (i.e., opportunity to bias audit evaluations). Seventy‐six external auditors from four Big 5 public accounting firms participated in an experiment that manipulated internal auditor compensation (fixed salary versus incentive compensation), the type of work that the internal auditors routinely perform (primarily auditing versus primarily consulting), and audit task subjectivity (objective tests of controls versus subjective inventory valuation). Our results suggest that the nature of internal auditors' compensation and work affect audit planning recommendations differently. The opportunity to receive incentive compensation results in less reliance on internal auditors' work and greater budgeted audit hours, but only for the subjective task. Although a consulting role decreases perceived internal auditor objectivity, it has a limited effect on planning recommendations. Specifically, consulting has no effect on reliance, and leads to greater budgeted audit hours only when incentive compensation is available. We discuss potential explanations for the results as well as implications for audit research, practice, and regulation.

The Impact of Internal Auditor Compensation and Role on External Auditors' Planning Judgments and Decisions

Contemporary Accounting Research 2001 18(2), 257-281
This paper reports the results of an experiment that investigates how external audit planning is affected when internal auditors have incentives and the opportunity to bias their evaluations. Specifically, we draw on attribution theory to examine how internal auditor eligibility for incentive compensation and participation in consulting (i.e., two factors that provide incentives to bias audit evaluations) affect external audit planning. In addition, we examine the effects of incentive compensation and a consulting role across two routine internal audit tasks — an objective tests of controls task and a subjective inventory valuation task — to evaluate whether their effects are contingent upon task subjectivity (i.e., opportunity to bias audit evaluations). Seventy-six external auditors from four Big 5 public accounting firms participated in an experiment that manipulated internal auditor compensation (fixed salary versus incentive compensation), the type of work that the internal auditors routinely perform (primarily auditing versus primarily consulting), and audit task subjectivity (objective tests of controls versus subjective inventory valuation). Our results suggest that the nature of internal auditors' compensation and work affect audit planning recommendations differently. The opportunity to receive incentive compensation results in less reliance on internal auditors' work and greater budgeted audit hours, but only for the subjective task. Although a consulting role decreases perceived internal auditor objectivity, it has a limited effect on planning recommendations. Specifically, consulting has no effect on reliance, and leads to greater budgeted audit hours only when incentive compensation is available. We discuss potential explanations for the results as well as implications for audit research, practice, and regulation.

The Audit Risk Model, Business Risk and Audit-Planning Decisions

The Accounting Review 1999 74(3), 281-298
This study identifies conditions under which the audit risk model does, and does not, describe audit-planning (investment and pricing) decisions. In an experiment, audit partners and managers examined one of two cases where a material misstatement—error or irregularity—was discovered. The auditors assessed the elements of the audit risk model, assessed business risk and provided recommendations for the audit investment and fee. When the likelihood of an error was high, the audit risk model dominated business risk in the explanation of the audit investment, and the fee did not contain a risk premium. When the likelihood of an irregularity was high, business risk dominated the audit risk model in the explanation of the audit investment, and the fee contained a risk premium. These results suggest that the ability of the audit risk model to describe auditor behavior and the inclination of auditors to charge a risk premium depend upon the nature of the risks present in the audit. In the presence of errors, the audit risk model adequately described audit-planning decisions; in the presence of irregularities it did not.

Definable and Contractible Contracts

Econometrica 2012 80(1), 363-411
This paper analyzes Bayesian normal form games in which players write contracts that condition their actions on the contracts of other players. These contracts are required to be representable in a formal language. This is accomplished by constructing contracts which are definable functions of the Godel code of every other player's contract. We provide a complete characterization of the set of allocations supportable as pure-strategy Bayesian equilibria of this contracting game. When information is complete, this characterization provides a folk theorem. In general, the set of supportable allocations is smaller than the set supportable by a centralized mechanism designer.

Growing Like India—the Unequal Effects of Service‐Led Growth

Econometrica 2023 91(4), 1457-1494 open access
Structural transformation in most currently developing countries takes the form of a rapid rise in services but limited industrialization. In this paper, we propose a new methodology to structurally estimate productivity growth in service industries that circumvents the notorious difficulties in measuring quality improvements. In our theory, the expansion of the service sector is both a consequence—due to income effects—and a cause—due to productivity growth—of the development process. We estimate the model using Indian household data. We find that productivity growth in nontradable consumer services such as retail, restaurants, or residential real estate was an important driver of structural transformation and rising living standards between 1987 and 2011. However, the welfare gains were heavily skewed toward high‐income urban dwellers.