Yuk-fai Fong

The Identification of Unobservable Independent and Spousal Leisure

This paper is based on the idea that for each partner in a marriage, there are two distinct types of leisure. One type is each person’s independent (or private) leisure, and the other type is spousal leisure, whose importance has long been emphasized in the literature of psychology. While each type of leisure is unobservable (only total leisure is observed), it is shown that the recent collective models of the intrahousehold allocation initiated by Chiappori can be extended to identify each type of leisure up to an additive constant. In particular, the effects of each member’s wage, household unearned income, and extrahousehold environmental parameters on the independent and spousal leisure and on the sharing rule are fully identified. The observational requirement here is the same as in other studies, namely, the observation of individual labor supply, individual wages, household unearned income, one assignable good, and consumption expenditure at the household level.

Product Quality, Reputation, and Market Structure

In a repeated game in which firms simultaneously choose price and product quality, but quality is observed only after consumption takes place, equilibria exhibiting high quality may exist in oligopoly markets even when the low‐quality one is a unique equilibrium outcome in monopoly and competitive markets. Oligopolists can sustain high quality through the threat of both a loss of reputation and a breakdown in tacit collusion. While we abstract from other reasons that market structure might affect product quality, we show that the inverted‐U shaped relationship between feasible quality and market structure is robust to several generalizations of the model.

Relational Contracts, Limited Liability, and Employment Dynamics

This paper studies a relational contracting model in which the agent is protected by a limited liability constraint. The agents effort is his private information and affects output stochastically. We characterize the optimal relational contract and compare the dynamics of the relationship with that under the optimal long-term contract. Under the optimal relational contract, the relationship is less likely to survive, and the surviving relationship is less efficient. In addition, relationships always converge to a steady state under the optimal long-term contract, but they can cycle among different phases under the optimal relational contract.

Long‐Lived Consumers, Intertemporal Bundling and Collusion

In a repeated price game with long but finitely-lived consumers, the use of staggered long-term contracts enables firms to earn positive profits for a wider range of discount factors and market structures. Intertemporal bundling reduces the gains from business- stealing while leaving the cost of the resulting price war unchanged. Though less empirically relevant, we also show that in a repeated price game with infinitely-lived, and arbitrarily-small, consumers, firms can use menus of single-period and infinite- length contracts to earn strictly positive profits for any discount factor and any market structure.

Loyalty Rewards Facilitate Tacit Collusion

Using a dynamic overlapping-generations model, we show that loyalty rewards robustly facilitate tacit collusion. We compare the sustainability of tacit collusion when uniform prices are used, when loyal customers are rewarded without using commitment, and when loyalty rewards are implemented by committing to offering customers either lower fixed repeat-purchase prices or fixed repeat-purchase discounts. We find that, relative to uniform prices, rewarding loyalty without using commitment on the equilibrium path makes tacit collusion easier to sustain, because a deviating firm is unable to steal one period of industry profit before losing all future profits. When loyalty rewards are offered by firms committing to repeat-purchase prices, collusion is even easier to sustain, since a deviating firm cannot renege on its discounted price for repeat-purchase customers. When firms commit to repeat-purchase discounts, they also commit to lowering the price for their repeat-purchase customers if they undercut the regular price, rendering tacit collusion to be even more readily sustainable. Our results hold whether products are homogeneous or horizontally differentiated as in a Hotelling model.

Signaling by an Expert

In this paper, we allow an expert with moral hazard to have private information on what would happen to his client both with his service and without his service. The contingent component in the contract this expert offers helps overcome his moral hazard, but also serves as a signal of his private information. We distinguish two concepts: the value of the service and the service outcome. Focusing on Intuitive-Criterion-satisfying equilibria, we show that the expert’s incentive to signal through the contract influences the contract very differently depending on whether a good service outcome is associated with a high service value or a low service value. In the former case, the contingent fee in any pooling equilibrium is positive and a high-value expert offers a more contingent contract than a low-value expert in any separating equilibrium. In the latter case, under some conditions there exists a pooling equilibrium with both types of experts offering a non-contingent contract and for all separating equilibria a high-value expert offers a less contingent contract than a low-value expert.

When Does Aftermarket Monopolization Soften Foremarket Competition

This paper investigates firms’ abilities to tacitly collude when these firms each monopolize a proprietary aftermarket. When firms’ aftermarkets are isolated from foremarket competition, they cannot tacitly collude more easily than single product firms do. However, when their aftermarket power is contested by foremarket competition as equipment owners view new equipment as a substitute for their incumbent firm’s aftermarket product, the monopoly profit is sustainable among al arger number offirms. More strikingly, as long as existing customers have a shorter market life expectancy than incoming customers, for any discount factor, supranormal profits are sustainable among arbitrarily many firms each selling ex ante identical products. These results suggest the importance of distinguishing between two types of aftermarket power which are often considered to be qualitatively the same. Conditions under which introduction of aftermarket competition hinders firms’ ability to tacitly collude are characterized.

Bidding in a possibly common-value auction

We analyze a second-price auction with two bidders in which only one of the bidders is informed as to whether the object is valued commonly. We show that any equilibrium strategy of the bidder who is uninformed must be part of an equilibrium when both bidders instead know that the auction is not common value, regardless of the way in which the values are different. We derive sufficient conditions for equilibrium existence.