the optimal mechanism for selling to a budget constrained buyer abstract this paper finds an optimal mechanism for selling a good to a buyer who may be budget constrained we consider a seller with one unit of a good facing a buyer with a quasilinear utility function if the buyer does not face a binding budget constraint textbook monopoly pricing is optimal by contrast the possibility of a binding budget constraint can make it optimal for the seller to use nonlinear pricing to commit to a declining price sequence to require the buyer to disclose his budget or to offer financing journal of economic literature classification numbers c70 d42 d45 d89 l12

non linear pricing with budget constraint abstract this paper purports to study the non linear pricing problem when a budget constraint limits the magnitude of the monetary transfer we show that distortions even affect consumers for which the constraint does not bind

multidimensional mechanism design for auctions with externalities abstract in an auction with externalities a buyer s type is multidimensional and specifies the payoff he would get for each of the n 1 possible outcomes the seller keeps the object or buyer i i 1 n gets the object we provide a characterization of multidimensional incentive compatible mechanisms similar to that for one dimensional mechanisms although reservation utilities are endogenous and type dependent the participation constraint is binding for only one critical type a main difficulty in a multidimensional setting is the integrability condition we present a geometric characterization for discontinuous conservative vector fields in auctions where the buyers submit scalar bids and the seller transfers the object to one of the buyers for sure a second price auction maximizes revenue with two buyers this auction remains optimal even if the seller can set a reservation price journal of economic literature classification numbers c7 c72

regulation fair disclosure and the cost of adverse selection regulation fair disclosure fd imposed by the securities and exchange commission in october 2000 was designed to prohibit disclosure of material private information to selected market participants the informational advantage such select participants gain is unclear if multiple insiders receive identical information private information is immediately incorporated in price and each insider has zero expected profit if on the other hand regulation fd has curtailed the flow of information from firms private information becomes longer lived and more valuable hence market makers will demand increased compensation by widening the adverse selection component of the bid ask spread we identify the cost components of the bid ask spread for a sample of nasdaq stocks surrounding the implementation of regulation fd controlling for other factors affecting the spread we find that adverse selection costs increase approximately 36 after regulation fd we interpret our finding as regulation fd failing to achieve one of its desired objectives

selling less information for more garbling with benefits abstract the expected value of information in a standard portfolio investment problem with ex post payment can increase when the information is garbled prior to its sale distorting the information helps to resolve the incentive problem decreasing the buyer s default risk and thereby increasing the seller s expected revenues

nonuniform pricing with unobservable numbers of purchases properties are derived for the profit maximizing price schedule in a market where the firm can observe the size of any given purchase but cannot directly observe the number of purchases made by any given consumer in such a market a consumer may make multiple purchases to minimize the amount paid for a given quantity of the good it is shown that when purchase numbers are unobservable the schedule may entail quantity premia and may be strikingly different from the schedule that obtains when the numbers of purchases are observable in particular some individuals may consume more under the profit maximizing outcome than under the first best outcome

on the optimal pricing policy of a monopolist the paper presents a simple explanation of price dispersion by a monopolist assuming only that consumers arrive in a random order and are served on a first come first served basis a firm can sometimes increase its profits by charging two different prices for the same good and rationing sales at the lower price however it is never necessary to charge more than two prices and a single price is sufficient as long as either the marginal revenue curve is everywhere downward sloping or the marginal cost of production is constant

incentives for motivated agents under an administrative constraint consider an agent who has an expertise in producing a non marketable good this good is valued by a single principal and there is a verifiable measure of the agent s performance crucially the agent is intrinsically motivated due to warm glow altruism in addition the agent s budget which is controlled by the principal must not be less than the monetary performance cost faced by the agent this gives rise to a limited liability constraint it also restricts the agent s ability to under report costs in such environment we determine the link between the agent s budget and performance our results come in contrast to the received solution of the principal agent problem and to most in the literature on mission motivated organisations and public services provision

foundations of dynamic monopoly and the coase conjecture subgame perfect equilibria are characterized for a market in which the seller quotes a price each period assume zero costs positive interest rate continuum of buyers and some technical conditions if buyers valuations are positive then equilibrium is unique buyers strategies are stationary and the price sequence is determinant along the equilibrium path but possibly randomized elsewhere otherwise a continuum of stationary equilibria can exist but at most one with analytic strategies coase s conjecture is verified for stationary strategies reducing the period length drives all prices to zero or the least valuation connections to bargaining models are described journal qf economic literature classification

multidimensional incentive compatibility and mechanism design abstract incentive compatibility conditions are characterized in general for problems in which several goods are to be allocated and agents types are multidimensional two questions of monopoly pricing under multidimensional uncertainty are then analyzed first we find the optimal nonlinear pricing scheme when the monopolist knows only the distribution of an arbitrarily parameterized family of demand curves and second we solve for the optimal bundling policy for a multiproduct monopolist

screening when some agents are nonstrategic does a monopoly need to exclude we characterize the optimal screening mechanism for a monopolist facing consumers with privately known demands some of whom have limited abilities to misrepresent their preferences we show that consumers with better abilities to misrepresent information benefit from the presence of consumers who lack such abilities whenever the fraction of the latter group is positive there is no exclusion the firm supplies a positive quantity of the good to all consumers whose valuations exceed marginal cost of production our analysis is motivated by the evidence indicating that some individuals have limited ability to misrepresent themselves and imitate others

nonlinear pricing in village economies this paper examines the prices of basic staples in rural mexico we document that nonlinear pricing in the form of quantity discounts is common that quantity discounts are sizable for basic staples and that the well known conditional cash transfer program progresa has significantly increased quantity discounts although the program as documented in previous studies has not affected unit prices on average to account for these patterns we propose a model of price discrimination that nests those of maskin and riley 1984 and jullien 2000 in which consumers differ in their tastes and because of subsistence constraints in their ability to pay for a good we show that under mild conditions a model in which consumers face heterogeneous subsistence or budget constraints is equivalent to one in which consumers have access to heterogeneous outside options we rely on known results to characterize the equilibrium price schedule which is nonlinear in quantity we analyze the effect of nonlinear pricing on market participation as well as the impact of a market wide transfer analogous to the progresa one when consumers are differentially constrained we show that the model is structurally identified from data on prices and quantities from a single market under common assumptions we estimate the model using data on three commonly consumed commodities from municipalities and localities in mexico interestingly we find that relative to linear pricing nonlinear pricing is beneficial to a large number of households including those consuming small quantities mostly because of the higher degree of market participation that nonlinear pricing induces we also show that the progresa transfer has affected the slopes of the price schedules of the three commodities we study which have become steeper as consistent with our model leading to an increase in the intensity of price discrimination finally we find that a reduced form of our model in which the size of quantity discounts depends on the hazard rate of the distribution of quantities purchased in a village accounts for the shift in price schedules induced by the program

search money and inflation under private information abstract i study monetary exchange and inflation when buyers have private information about their willingness to pay for certain goods introducing imperfect information in the lagos wright a unified framework for monetary theory and policy analysis j polit economy 113 3 2005 463 484 economy shows that the existence of monetary equilibrium is a more robust feature of the environment in general my model has a monetary steady state in which only a proportion of the agents hold money agents who do not hold money cannot participate in trade in the decentralized market the proportion of agents holding money is endogenous and depends negatively on the level of expected inflation as in lagos and wright s model in equilibrium there is a positive welfare cost of expected inflation but the origins of this cost are very different

optimal selling strategies when to haggle when to hold firm a seller encountering risk neutral buyers one at a time should if commitments are feasible quote a single take it or leave it price to each this strategy is superior to any other for finite or infinite buyer populations whether there is learning or the distribution of buyer prices is known at the outset with one object for sale or many although haggling may offer advantages in terms of price discrimination these gains are more than offset by the losses it generates by encouraging buyers to refuse purchases at high prices

monopoly with incomplete information recent theoretical research on principal agent relationships has emphasized incentive problems that arise when the parties involved are constrained by either asymmetric information or their inability to monitor each other s actions here we concentrate on the former constraint and consider the case of a single principal the monopolist the main contribution is to show that under a separability assumption strong conclusions can be drawn about the nature of optimal incentive schemes although the primary focus is on optimal quantity discounts in a monopolized market the results also shed light on related topics such as optimal income taxation and commodity bundling

optimal auctions with financially constrained buyers abstract we study the sale of an indivisible good to liquidity constrained buyers they cannot pay more than their budget regardless of their valuation both valuation and budget are private information we derive the symmetric revenue maximizing and constrained efficient auctions in this setting we show an implementation via a modified all pay auction the highest bidder need not win the good outright or stated differently the auction has pooling despite the usual regularity conditions subsidizing low budget buyers cannot increase revenue from a technical standpoint we contribute to auction design with multidimensional private information by working directly with reduced form allocation rules

earnings predictability information asymmetry and market liquidity we investigate the relation between earnings predictability information asymmetry and the behavior of the adverse selection cost component of the bid ask spread around quarterly earnings announcements for nasdaq firms while we find an increase in the adverse selection component of the bid ask spread on the day of and the day prior to quarterly earnings announcements for firms with less predictable earnings we find no evidence of such changes for firms with more predictable earnings during a non announcement period we find that firms with relatively less predictable earnings have consistently higher total bid ask spreads than firms with more predictable earnings this finding suggests that firms with relatively less predictable earnings have a higher cost of equity capital than comparable firms with more predictable earning streams ceteris paribus hence earnings predictability may be a legitimate concern of managers who wish to minimize their cost of equity capital at least as it pertains to bid ask spreads

modeling the bid ask spread measuring the inventory holding premium the need to understand and measure the determinants of market maker bid ask spreads is crucial in evaluating the merits of competing market structures and the fairness of market maker rents this study develops a simple parsimonious model for the market maker s spread that accounts for the effects of price discreteness induced by minimum tick size order processing costs inventory holding costs adverse selection and competition the inventory holding and adverse selection cost components of spread are modeled as an option with a stochastic time to expiration this inventory holding premium embedded in the spread represents compensation for the price risk borne by the market maker while the security is held in inventory the premium is partitioned in such a way that the inventory holding and adverse selection cost components as well as the probability of an informed trade are identified the model is tested empirically using nasdaq stocks in three distinct minimum tick size regimes and is shown to perform well both in an absolute sense and relative to competing specifications

optimal auctions with endogenous budgets we study the benchmark independent private value auction setting when bidders have endogenously determined budgets before bidding a bidder decides how much money she will borrow bidders incur a cost to borrowing we show that bidders are indifferent between participating in a first price second price and all pay auction the all pay auction gives higher revenue than the first price auction which gives higher revenue than the second price auction in addition when the distribution of values satisfies the monotone hazard rate condition the revenue maximizing auction is implemented by an all pay auction with a suitably chosen reserve price

who is afraid of reg fd the behavior and performance of sell side analysts following the sec s fair disclosure rules we examine regulation fd s impact on the accuracy and dispersion of sell side analysts earnings forecasts using a large sample of quarterly forecasts made over a nearly 10 year period surrounding fd s adoption we uncover two main sets of findings first individual and consensus forecasts become less accurate post fd particularly for early forecasts and for smaller companies second forecast dispersion increases post fd this effect is stronger for early forecasts and has increased with the passage of time these results which are quite robust to alternative empirical methodologies suggest that there has been a reduction in both selective guidance and forecast quality post fd

robust monopoly pricing we consider a robust version of the classic problem of optimal monopoly pricing with incomplete information in the robust version the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution we characterize the pricing policies under two distinct decision criteria with multiple priors i maximin utility and ii minimax regret the equilibrium price under either criterion is lower then in the absence of uncertainty the concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty

efficient and competitive rationing abstract the contracts that interest us here are called priority service contracts the salient feature of such contracts is that they specify each customer s priority in obtaining service that is they specify the tank order in which a customer is served out of the available supply until all customers are served or supply is exhausted such contracts essentially establish queues for customers in section 1 the author provides some background about priority service section 2 formulates a basic model and offer several illustrations also describes two main examples that motivate the theoretical development section 3 derives some key results that show how the prices of priority service contracts are designed to induce customers to self select efficient service orders in section 4 the author discusses various ways that state enterprises can organize markets that implement priority service efficiently in section 5 we study the operation of competitive markets for priority service section 6 concludes with some summary remarks two themes are emphasized one is that a state enterprise can promote substantial efficiency gains by substituting priority service for absent spot markets the other is that oligopolistic firms may have insufficient incentives to offer efficient product diversity consequently allocative efficiency depends on entry of numerous firms even so dispersal of supplies among many firms can prevent productive efficiency when there are advantages from pooling supplies

pre announcement and event period private information abstract pre announcement information is private information gathered in anticipation of a public disclosure event period information is private information useful in conjunction with the announcement itself typically rational models of trade are based exclusively on one type of information such models are less descriptive of real market settings and misspecified empirically therefore we introduce a model of rational trade with both features and discuss its implications

socially optimal procurement with tight budgets and rationing abstract we investigate the behaviour of a social planner that secures the supply of a good e g an environmental benefit through contracting with private agents while the social planner seeks to maximise net social benefits she is also controlled with a fixed budget private agents are profit maximising and hold private information concerning their variable costs of production they also have known fixed costs of contracting we find that budget constraints and fixed costs change the optimal contract design in more than one way the social planner minimises costs rations high cost contracts to reduce fixed costs and information rents and distorts contracts for all agent types including low cost agents we find that rationing improves social welfare also even though social costs including tax distortion are explicitly taken into consideration they do not affect the design of optimal contracts when budgets are tight in those cases the budget constraint dominates the solution

budget constraints and demand reduction in simultaneous ascending bid auctions the possibility even if arbitrarily small of binding budget constraints in simultaneous ascending bid auctions induces strategic demand reduction and generates significant inefficiencies under mild conditions on the distributions of the bidders values unconstrained bidders behave as if they were liquidity constrained even as the probability that bidders are budget constrained goes to zero

assigning resources to budget constrained agents this article studies different methods of assigning a good to budget constrained agents schemes that assign the good randomly and allow resale may outperform the competitive market in terms of utilitarian efficiency the socially optimal mechanism involves random assignment at a discount an in kind subsidy and a cash incentive to discourage low valuation individuals from claiming the good copyright oxford university press

multiproduct nonlinear pricing typically work on mechanism design has assumed that all private information can be captured in a single scalar variable this paper explores one way in which this assumption can be relaxed in the context of the multiproduct nonlinear pricing problem it is shown that the firm will choose to exclude some low value consumers from all markets a class of cases that allow explicit solution is derived by making use of a multivariate form of integration by parts in such cases the optimal tariff is cost based

motivating wealth constrained actors we examine how owners of productive resources e g public enterprises or financial capital optimally allocate their resources among wealth constrained operators of unknown ability optimal allocations exhibit 1 shared enterprise profit the resource owner always shares the operator s profit 2 dispersed enterprise ownership resources are widely distributed among operators of varying ability 3 limited benefits of competition the owner may not benefit from increased competition for the resource and sometimes 4 diluted incentives for the most capable more capable operators receive smaller shares of the returns they generate implications for privatizations and venture capital arrangements are explored

auctions vs fixed pricing competing for budget constrained buyers abstract we investigate price mechanism selection in a setting where sellers compete for budget constrained buyers by adopting either fixed pricing or auctions first or second price we show that first and second price auctions are payoff equivalent when some bidders are financially constrained so sellers are indifferent to adopt either format we characterize possible equilibria and show that if the budget is high then sellers compete via fixed pricing if it is low then they compete via auctions and if it is moderate then they mix so both mechanisms coexist the budget constraint becomes less binding if sellers use entry fees interestingly an improvement of the budget e g letting customers pay in installments may lead to fewer trades and a loss of efficiency

regulation competition and liberalization in many countries throughout the world regulators are struggling to determine whether and how to introduce competition into regulated industries this essay examines the complexities involved in the liberalization process while stressing the importance of case specific analyses this essay distinguishes liberalization policies that generally are procompetitive from corresponding anticompetitive liberalization policies

efficient assignment mechanisms for liquidity constrained agents we study alternative methods of assigning scarce resources to individuals who may be liquidity constrained selling the resources via auctions is increasingly popular but that method may produce an inefficient allocation when agents are liquidity constrained a simple non market scheme such as random assignment does better if resale is allowed since individuals with a high valuation but low liquidity are more likely to be assigned initially and recipients with low valuations will resell to those with high valuations similarly a need based assignment scheme favoring those with low liquidity enhances welfare lotteries with entry fees could also be desirable the optimal mechanism displays features of the non market schemes such as in kind and cash subsidies

long lived private information and imperfect competition we develop a multi period auction model in which multiple privately informed agents strategically exploit their long lived information we show that such traders compete aggressively and cause most of their common private information to be revealed very rapidly in the limit as the interval between auctions approaches zero market depth becomes infinite and all private information is revealed immediately these results are in contrast to those of kyle 1985 in which the monopolistic informed trader causes his information to be incorporated into prices gradually and when the interval between auctions is vanishingly small market depth is constant over time fama 1970 defines a strong form efficient market as one in which security prices fully reflect all available information including both publicly and privately held information in a pioneering and influential article kyle 1985 develops a model in which a single privately informed trader with long lived information optimally exploits his monopoly power over time kyle s 1985 main results are i the informed trader trades in a gradual manner so that his information is incorporated into prices at a slow almost linear rate and ii when auctions are held continuously the depth of the market is constant over time however kyle s 1985 assumption of a single informed trader is strong in the sense that in actual financial markets it is reasonable to expect that at least a few players will have access to private information and will trade in the knowledge that they will face competition with other informed agents in the market 1 we develop a multi period auction model in which multiple strategic informed traders optimally exploit their long lived informational advantage we thus explore the restrictiveness of kyle s assumption of a single informed trader and also examine

monopoly price dispersion under demand uncertainty when a monopolist sets its price before its demand is known then it may set more than one price and limit the availability of its output at lower prices this article adds demand uncertainty and price rigidities to the standard model of monopoly pricing when there are two states of demand and the ex post monopoly price is greater when demand is high then the monopolist s optimal ex ante pricing strategy is to set two prices and limit purchases at the lower price

repeated auctions with budgets in ad exchanges approximations and design ad exchanges are emerging internet markets where advertisers may purchase display ad placements in real time and based on specific viewer information directly from publishers via a simple auction mechanism advertisers join these markets with a prespecified budget and participate in multiple second price auctions over the length of a campaign this paper studies the competitive landscape that arises in ad exchanges and the implications for publishers decisions the presence of budgets introduces dynamic interactions among advertisers that need to be taken into account when attempting to characterize the bidding landscape or the impact of changes in the auction design to this end we introduce the notion of a fluid mean field equilibrium fmfe that is behaviorally appealing and computationally tractable and in some important cases it yields a closed form characterization we establish that an fmfe approximates well the rational behavior of advertisers in these markets we then show how this framework may be used to provide sharp prescriptions for key auction design decisions that publishers face in these markets in particular we show that ignoring budgets a common practice in this literature can result in significant profit losses for the publisher when setting the reserve price this paper was accepted by dimitris bertsimas optimization

the dynamics of bidding markets with financial constraints we develop a model of bidding markets with financial constraints a la che and gale 15 in which two firms choose their budgets optimally and we extend it to a dynamic setting over an infinite horizon we provide three main results for the case in which the exogenous cash flow is not too large and the opportunity cost of budgets is positive but arbitrarily low first firms keep small budgets and markups are high most of the time second the dispersion of markups and money left on the table across procurement auctions hinges on differences both endogenous and exogenous in the availability of financial resources rather than on significant private information third we explain why the empirical analysis of the size of markups based on the standard auction model may have a bias downwards or upwards positively correlated with the availability of financial resources a numerical example illustrates that our model is able to generate a rich set of values for markups bid dispersion and concentration

product line rivalry with brand differentiation competition with product rivalry is examined in a model where products are differentiated by both quality and brand name with no commitment firms produce a full product line when firms can commit to restrict their product offerings firms specialize if the degree of brand specific differentiation is small and they produce a full product line if brand specific differentiation is large relative to intrafirm differentiation firms may crowd a product space when all competitors would be better off with specialization brand proliferation is a credible entry deterring strategy if the degree of brand specific differentiation is not too large copyright 1993 by blackwell publishing ltd

strategic ex ante contracts rent extraction and opportunity costs this article cosiders the possibility that a seller can contract with one uninformed buyer prior to an auction involving two potential buyers the seller s optimal strategic ex ante contract more accurately reflects joint opportunity costs of the seller and the contracted buyer and therefore extracts more rent from the entrant moreover this ex ante contract mitigates the seller s ex post rent seeking vis a vis the contracted buyer accordingly it may create more social welfare than the absence of ex ante contracts depending upon the contracted buyer s financial constraint and the distributions of trade surplus implementation of the optimal strategic ex ante contract and policy implications are discussed

high bids and broke winners abstract this paper analyzes auctions where budget constrained bidders have options to declare bankruptcy it predicts a bidding equilibrium that changes discontinuously in a borrowing rate available to bidders when the borrowing rate is above a threshold high budget bidders win and the likelihood of bankruptcy is low when the borrowing rate is below the threshold the winner is the most budget constrained bidder and is most likely to declare bankruptcy this result explains the high bids and broke winners anomaly in the c block fcc spectrum auction based on its equilibrium analysis the paper proves that a seller can profit from offering to finance the highest bidder at a below market interest rate even with default risk journal of economic literature classification numbers d44 d45 d82 g33 l96

money and price posting under private information abstract we study price posting with undirected search in a search theoretic monetary model with divisible money and divisible goods ex ante homogeneous buyers experience match specific preference shocks in bilateral trades the shocks follow a continuous uniform distribution and the realizations of the shocks are private information we show that there exists a unique monetary equilibrium for generic values of the inflation rate in equilibrium each seller posts a continuous pricing schedule that exhibits quantity discounts buyers may spend nothing a fraction or all of their money holdings depending on their preference shock realizations inflation reduces the extent of non linear pricing the model captures the hot potato effect of inflation along both the extensive margin as an increase in the trading probability and the intensive margin as higher fractions of money being spent