On the indeterminacy of capital accumulation paths

In neoclassical optimal growth models the stability of the accumulation paths depends on the discount parameter. We prove that, for discount factors small enough, the policy function which describes an optimal path can be of any type. The result is achieved using the notion of α-concavity. We adopt a constructive approach. Given any twice differentiable map we show how to construct an optimal growth problem which produces that map as the optimal policy function. A consequence is that “chaos” can appear in these models. We also provide bounds on the values of the discount parameter for which “indeterminacy” is possible.     

Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Optimal stationary consumption with stochastic production and resources

Uncertainty about technology and resources is represented in terms of uncertainty about an (exogenous) environment whose successive states form a stationary stochastic process, with probabilities that are unaffected by economic decisions. The successive states of the economy depend both on the environment and on the decisions taken with regard to production and consumption. It is shown that, under conditions that are natural extensions of “neoclassical” conditions in the case of certainty, (1) Capital saturation is possible, i.e., an optimal stationary stochastic program exists, and (2) An optimal program can be sustained by a price system that takes the form of a stationary stochastic process of price vectors. In other words, an optimal stationary program can be sustained by a stochastic “equilibrium,” in which at each date the optimal production decisions maximize expected intertemporal profit, and the optimal aggregate consumption vector has minimum cost among all aggregate consumption vectors yielding no less (social) utility.     

The analytics of search with posted prices

Summary. This paper investigates the characteristics of the optimal posted price in the standard sequential search paradigm. Much of the intuition gleaned from the extensive sequential search literature in which the seller adopts a reservation price does not carry over to the posted price setting. For example, an increase in buyer valuations can lead to a reduction in the optimal posted price. We do, however, provide sufficient conditions on the hazard rate function h which ensure that an increase in demand induces an increase in the optimal posted price. As exhibited herein, the analysis of the posted price model depends critically upon analytical properties of h. Amongst the issues treated are the elasticity of demand, finite horizon, sale of multiple units, and competitive equilibrium. Received: October 21, 1999; revised version: March 7, 2000     

What to stabilize in the open economy*

We consider the question how “best” to maintain price‐level stability in an open economy, and evaluate three possible policy choices: (a) a constant money growth rate rule; (b) a fixed exchange rate; and (c) a policy of explicit commitment to a price‐level target. In each case we assume that policy is conducted by injecting reserves into or withdrawing reserves from the “banking system.” In evaluating the three regimes, we adopt the criterion that the “best” policy should leave the least scope for indeterminacy and “excessive” economic volatility. In a steady‐state equilibrium, the choice of regime is largely irrelevant; any steady‐state equilibrium under one regime can be duplicated by an appropriate choice of the “control” variable under any other regime. However, we show that the sets of equilibria under the three regimes are dramatically different. When all countries follow the policy of fixing a constant rate of money growth, there are no equilibria displaying endogenously arising volatility and there is no indeterminacy of equilibrium. Under a regime of fixed exchange rates, indeterminacies and endogenously arising fluctuations are impossible if and only if the country with the low “reserve‐to‐deposit” ratio is charged with maintaining the fixed rate. Finally, when one country targets the time path of its price level, under very weak conditions, there will be indeterminacy of equilibrium and endogenously arising volatility driven by expectations.     

Efficient performance in two agent bargaining

This paper concerns ex ante incentive efficient performance in the bargaining of one buyer and one seller over a single item. For any element in a specified class of distributions of the buyer's and the seller's valuations of the item, all of the (interim) individually rational and efficient allocation rules are characterized. It is also shown that the “buyer's bid” and the “seller's price” double auctions are efficient for all distributions in the specified class. These results are obtained by studying efficiency as a linear programming problem.     

Learning about the arrival of sales

We analyse optimal stopping when the economic environment changes because of learning. A primary application is optimal selling of an asset when demand is uncertain. The seller learns about the arrival rate of buyers. As time passes without a sale, the seller becomes more pessimistic about the arrival rate. When the arrival of buyers is not observed, the rate at which the seller revises her beliefs is affected by the price she sets. Learning leads to a higher posted price by the seller. When the seller does observe the arrival of buyers, she sets an even higher price.     

How do selling mechanisms affect profits,surplus, capacity and prices with unknown demand?

I analyze a model in which a seller wishes to sell multiple homogeneous goods to a large group of buyers with unknown demand. The seller may either sell objects via a posted‐price mechanism, a discriminatory‐price auction, a uniform‐price auction, their open‐bid analogs, or a revelation mechanism in which the seller first asks all potential buyers to report their valuations and then sets a reserve price. I show that the revelation mechanism leads to the greatest profits, the auction mechanisms result in identical expected profits and the posted‐price mechanism results in the smallest profits. However, the more profitable mechanisms impose stronger informational requirements that may make these mechanisms infeasible in practice, and the posted‐price mechanism also results in the greatest total surplus. I also find the seller chooses a lower capacity and reserve price in an auction than in the posted‐price mechanism.     

Information,trade and common knowledge

In any voluntary trading process, if agents have rational expectations, then it is common knowledge among them that the equilibrium trade is feasible and individually rational. This condition is used to show that when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade. On markets, information is revealed by price changes. An equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.     

Optimal pricing of public lotteries and comparison of competing mechanisms

This article establishes optimal pricing rules for rationing indivisible units of rival and otherwise nonexcludable goods by lottery or a hybrid of a lottery and outright sale by posted price. Given the distributional objective of maximizing expected consumer surplus, the solutions to unconstrained and constrained versions of the pricing problem may be expressed in classic inverse elasticity form, with the lottery price appearing as an entry fee, user fee or a combination of the two. Numerical analysis of a rich class of private value distributions indicates that sizable gains in expected consumer surplus can be realized over competitive pricing and zero pricing.     

On relaxing the maximization postulate

We have agreed in behalf of the desirability of having a decision theory that includes nonoptimal decisions. Nonopti mal decisions are a basic cause of X-inefficiency in the production processes of firms, as well as in the economy as a whole. Therefore it is important to have a theory that allows us to examine the nature of, and use the possibility of suboptimal decision making.We suggested and examined briefly various decision procedures and behaviors which can yield suboptimal outcomes. These include faulty calculating procedures, which leave out steps from more careful calculating procedures; noncalculating responses, such as habits, conventions, rules of thumb, etc., non-responses as well as satisficing, and sacrificing types of behavior. The Yerkes-Dodson Law enables us to relate the likelihood that decisions will be optimal or suboptimal to the pressures felt by the decision maker. Up to a certain point pressure will increase the probability of optimal decisions, then will reduce it.Within the firm, in particular, there are certain behaviors which are likely to be suboptimal which are of special inter est. These are conventions, and other types of behaviors, that are constrained by peers or superiors. Conventions, in particular, are likely to prevent latent PD outcomes from occurring even though they are themselves suboptimal but Pareto superior to the PD outcome.Even though the idea of suboptimal decisions is not well accepted in economics, it is linguistically and logically consistent with the concept of maximizing behavior, and hence it is correct to allow for them in a more complete behavior postulate. The essential meanings of the words, “maximize,” “optimize,” and “choice” imqly that dissimilar options are available to the person doing the choosing. Furthermore “choice” implies that any options, optimal or suboptimal, are possible choices. Therefore, we argued that the logically correct interpretation of the maximization postulate must allow for the possibility of suboptimal choices along with optimal ones. We emphasize that we are not arguing against the possibil,ity of optimal choices being made. On the contrary, it seems likely that most decision sets will tend to be some mixture of optimal and suboptimal procedures.A major purpose of this paper has been to argue against the ideas that nonoptimal choices are unthinkable, misconceived or an unnecessary part of any decision postulate. To this end we attempted to identify several modes of argumentation in which the essential comparative meanings of “maximize,” and “choice” are commonly nullified. Such postulates were identified as, “whatever is chosen is optimal;” “preference is revealed by the choices made;” and “people maximize a function which can include the disutility of maximization.” Among the types of reasoning looked at critically were, that an apparent nonoptimal choice is really a misspecification of the objective function; and that a nonoptimal choice can be translated into an optimal one by adding another variable, or generalizing the time unit of utility. These circular reasonings amount to a denial of the comparative meaning of optimality when they are carried to the point where every assertion of nonoptimality is countered by arguments of this type. In general, we have argued that the possibility of nonoptimal choices and nonoptimal decision procedures cannot be denied.     

Matching with preferences over colleagues solves classical matching

In this note, we demonstrate that the problem of “many-to-one matching with (strict) preferences over colleagues” is actually more difficult than the classical many-to-one matching problem, “matching without preferences over colleagues.” We give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all stable matchings in the setting of “matching without preferences over colleagues,” for any set of preferences. Our construction directly extends to generalized matching settings.     

Minimum Wages and the Gender GAP in Pay: New Evidence from the United Kingdom and Ireland

Women are disproportionately in low‐paid work compared to men so, in the absence of rationing effects on their employment, they should benefit the most from minimum wage policies. This study examines the change in the gender wage gap around the introduction of minimum wages in Ireland and the United Kingdom (U.K.). Using survey data for the two countries, we develop a decomposition of the change in the gender differences in wage distributions around the date of introduction of minimum wages. We separate out “price” effects attributed to minimum wages from “employment composition” effects. A significant reduction of the gender gap at low wages is observed after the introduction of the minimum wage in Ireland, while there is hardly any change in the U.K. Counterfactual simulations show that the difference between countries may be attributed to gender differences in non‐compliance with the minimum wage legislation in the U.K.     

Choice and individual welfare

We propose an abstract method of systematically assigning a “rational” ranking to non-rationalizable choice data. Our main idea is that any method of ascribing welfare to an individual as a function of choice is subjective, and depends on the economist undertaking the analysis. We provide a simple example of the type of exercise we propose. Namely, we define an individual welfare functional as a mapping from stochastic choice functions into weak orders. A stochastic choice function (or choice distribution) gives the empirical frequency of choices for any possible opportunity set (framing factors may also be incorporated into the model). We require that for any two alternatives x and y, if our individual welfare functional recommends x over y given two distinct choice distributions, then it also recommends x over y for any mixture of the two choice distributions. Together with some mild technical requirements, such an individual welfare functional must weight every opportunity set and assign a utility to each alternative x which is the sum across all opportunity sets of the weighted probability of x being chosen from the set. It therefore requires us to have a “prior view” about how important or representative a choice of x at a given situation is.     

Planning under market socialism when iteration is incomplete

If an iterative planning procedure is cut short due to time shortage, the plan must be set subject to information gaps. But the nature of these gaps depends on which iterative procedure was used. For the case of Lange's model, Weitzman's “prices versus quantities” framework is redeveloped for the particular information gaps then found. With one good, the optimal quantity signal comes from the expected supply-demand intersection, but an optimal price signal lies between this intersection and the price from the last stage of iteration. When there are many goods, however, we cannot be so specific.     

Consumers’ preferences for a local food product: a real choice experiment

This paper analyses consumers’ preferences for a local food in Spain and assesses their willingness to pay (WTP) using a real choice experiment to mitigate possible hypothetical bias. In particular, preferences for fresh lamb meat were investigated and two attributes evaluated, “locally grown” and the type of lamb meat. Data came from an experiment conducted in Spain during 2009. An error component random Parameter model with correlated errors was used to estimate the effect of the attributes on consumers’ utility and derive their WTP. Results suggest that consumers positively value both attributes and are willing to pay a premium of 9 % price increase for the “locally grown” lamb meat (“Ojinegra from Teruel”) and 13 % price increase for the “Ternasco” lamb meat. If we assume a market where only “Ternasco” lamb meat without indication of the local origin is sold, and then a new “Ternasco” lamb is introduced in the market with the “Ojinegra from Teruel” label, this new local lamb meat would capture 18 % of the market if the package is assumed to be sold at 3.5 \(\hbox {C}\!\!\!\!\!=\) and a 10 % market share if the package is assumed to be sold at 4 \(\hbox {C}\!\!\!\!\!=\) .     

Optimal sale across venues and auctions with a buy-now option

We characterize the optimal selling mechanism for a seller who faces demand demarcated by a high and a low end and who can access an (online) auction site (by paying an access cost) in addition to using his own store that can be used as a posted price selling venue. We first solve for the optimal mechanism of a direct revelation game in which there is no venue-restriction constraint. We find that the direct optimal mechanism must necessarily incorporate a certain kind of pooling. We then show that even with the venue constraint, the seller can use a two stage indirect mechanism that implements the allocation rule from the optimal direct mechanism, and uses the venues in an optimal fashion. The first stage of the indirect mechanism is a posted price at the store. If the object is not sold, we move to stage two, which involves an auction at the auction site. A feature of this auction is a buy-now option which is essential for implementing the pooling feature of the optimal direct mechanism. We also show that the buy-now option in the optimal mechanism is of a “temporary” variety, and that a “permanent” buy-now option, in contrast, cannot implement the optimal mechanism. Auctions with a temporary buy-now option are in widespread use on eBay. We thank the Associate Editor, George Deltas, for his insightful comments. We also thank seminar participants at the University of Basel and the SAET conference 2007.     

Optimal collusion-resistant mechanisms with verification

We present the first general positive result on the construction of collusion-resistant mechanisms, that is, mechanisms that guarantee dominant strategies even when agents can form arbitrary coalitions and exchange compensations (sometimes referred to as transferable utilities or side payments). This is a much stronger solution concept as compared to truthful or even group strategyproof mechanisms, and only impossibility results were known for this type of mechanisms in the “classical” model.We describe collusion-resistant mechanisms with verification that return optimal solutions for a wide class of mechanism design problems (which includes utilitarian ones as a special case). Note that every collusion-resistant mechanism without verification must have an unbounded approximation factor and, in general, optimal solutions cannot be obtained even if we content ourselves with truthful (“non-collusion-resistant”) mechanisms. All these results apply to problems that have been extensively studied in the algorithmic mechanism design literature like, for instance, task scheduling and inter-domain routing.     

DIRECTED SEARCH,COORDINATION FAILURE,AND SELLER PROFITS: AN EXPERIMENTAL COMPARISON OF POSTED PRICING WITH SINGLE AND MULTIPLE PRICES

We experimentally examine posted pricing and directed search. In one treatment, capacity‐constrained sellers post fixed prices, which buyers observe before choosing whom to visit. In the other, firms post both “single‐buyer” (applied when one buyer visits) and “multibuyer” (when multiple buyers visit) prices. We find, based on a 2 × 2 (two buyers and two sellers) market and a follow‐up experiment with 3 and 2 × 3 markets, that multibuyer prices can be lower than single‐buyer prices or prices in the one‐price treatment. Also, allowing the multibuyer price does not affect seller profits and increases market frictions.     

Toward a “constitution” for behavioral policy-making

Behavioral policy interventions aimed at redirecting individuals’ behavior toward optimal choices are characterized by an important issue which is often overlooked: the lack of an instrument to define what “optimal” means. If agents are subject to behavioral biases leading them to make “wrong” choices, the policy-maker can no longer rely on the revealed preferences approach (e.g., what people choose is what people prefer) for defining a welfare criterion. In this article, we reiterate the argument put forward by some scholars that choosing a suitable welfare criterion once the link between observed choices and individuals’ preferences is broken becomes a problematic task. We review the state of the art in the literature and the possible approaches proposed to overcome the problem, concluding that a solution has not yet been reached. Moreover, we argue that the lack of an established welfare criterion characterizing behavioral policy-making could pave the way to government wanting to restrict individual freedom. In the absence of any legislative constraint for the executive, stating that what individuals choose is not what they prefer in principle justifies any freedom-reducing government intervention, since choices can be arbitrarily labeled “sub-optimal” or “welfare-reducing.” To avoid this risk without turning down the potential of behavioral policy-making, we propose that an independent committee establishes ex ante procedural rules and domains where behavioral policy-making can be implemented. The article suggests some possible examples of normative provisions characterizing this constitution-type document, such as the selective identification of the only sectors where behavioral policies could be effectively applied, the periodic evaluation of policy effects, and the use of sunset clauses.