efficient mechanisms for bilateral trading we consider bargaining problems between one buyer and one seller for a single object the seller s valuation and the buyer s valuation for the object are assumed to be independent random variables and each individual s valuation is unknown to the other we characterize the set of allocation mechanisms that are bayesian incentive compatible and individually rational and show the general impossibility of ex post efficient mechanisms without outside subsidies for a wide class of problems we show how to compute mechanisms that maximize expected total gains from trade and mechanisms that can maximize a broker s expected profit journal of economic literature classification number 026

limit theorems for markets with sequential bargaining this paper models trade as a non coopertative strategic game played at an inlinite sequence of dates a single indivisible commodity is traded buyers and sellers have transferable utility and are characterized by their reservation utilities they meet at random and bargain over the price at which a single unit of the good will be exchanged under a variety of circumstances it is shown that as the costs of search and bargaining become negligible the outcome of the game converges to the competitve flow equilibrium even when there is complete information journal of economic literature classification numbers 022 19x7

durable goods monopoly with varying demand this paper solves for the proflt maximising strategy of a durable goods monopolist when incoming demand varies over time each period additional consumers enter the market these consumers can then choose whether and when to purchase we flrst characterise the consumer s utility maximisation problem and under a monotonicity condition show the proflt maximising allocation can be solved through a myopic algorithm which has an intuitive marginal revenue interpretation consumers ability to delay creates an asymmetry in the optimal price path which exhibits fast increases and slow declines this asymmetry pushes the price level above that charged by a flrm facing the average level of demand applications of this framework include deterministic demand cycles one ofi shocks and iid demand draws the optimal policy outperforms renting and can be implemented by a time consistent best price provision

dynamic matching and bargaining games a general approach this paper presents a new characterization result for competitive allocations in quasilinear economies this result is informed by the analysis of non cooperative dynamic search and bargaining games such games provide models of decentralized markets with trading frictions a central objective of this literature is to investigate how equilibrium outcomes depend on the level of the frictions in particular does the trading outcome become walrasian when frictions become small existing specifications of such games provide divergent answers the characterization result is used to investigate what causes these differences and to generalize insights from the analysis of specific search and bargaining games

the rate of convergence to perfect competition of matching and bargaining mechanisms abstract we study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information a friction parameter is the length of the time period until the next meeting we provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in which is shown to be the fastest possible among all bargaining mechanisms the condition requires that buyers and sellers always retain some bargaining power the bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power nbp mechanisms simple random proposer take it or leave it protocols are nbp while k double auctions k da are not we find that k das have equilibria that converge to perfect competition at a linear rate converge at a slower rate or even do not converge at all

dynamic matching two sided incomplete information and participation costs existence and convergence to perfect competition consider a decentralized dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good time is discrete each period has length and each unit of time continuums of new buyers and sellers consider entry traders whose expected utility is negative choose not to enter within a period each buyer is matched anonymously with a seller and each seller is matched with zero one or more buyers every seller runs a first price auction with a reservation price and if trade occurs both the seller and the winning buyer exit the market with their realized utility traders who fail to trade continue in the market to be rematched we characterize the steady state equilibria that are perfect bayesian we show that as converges to zero equilibrium prices at which trades occur converge to the walrasian price and the realized allocations converge to the competitive allocation we also show the existence of equilibria for sufficiently small provided the discount rate is small relative to the participation

equilibrium in a market with sequential bargaining this paper considers a market where pairs of agents who are interested in carrying out a transaction are brought together by a stochastic process and upon meeting initiate a bargaining process over the terms of the transaction the basic bargaining problem is treated with the strategic approach the paper derives the steady state equilibrium agreements analyzes their dependence on market conditions such as the relative numbers of agents of different types and discusses their relations with the competitive equilibrium outcome and other results in the search equilibrium literature this paper considers a market that operates in the following way pairs of agents who have mutual interest in carrying out a transaction are brought together by a stochastic process when two agents meet they initiate a bargaining process over the terms of the transaction if two agents reach an agreement a transaction takes place and they leave the market of course the bargaining positions and hence the agreement reached in any particular meeting will be affected by the conditions prevailing in the market these will include the chances that each of the negotiating parties have of meeting other partners in the event that the agreement in the current negotiations is delayed also the expected length of time required to achieve an alternative transaction and the expected behavior of alternative partners the study of such a market mechanism is of interest for two reasons firstly it captures some realistic aspects of the trade in certain specific markets e g asset markets such as housing and some labor markets secondly it contributes to an understanding of the micro mechanisms of price formation and their role in shaping market outcomes in both cases the features studied are largely neglected in the traditional market equilibrium analyses the related literature includes the articles by diamond 4 5 diamond and maskin 6 mortensen 8 9 and zusman and bell 13 these articles consider markets of the type described above in which transactions are concluded at pairwise meetings of agents the major difference between our work and these articles is in the approach to the basic bargaining problem in the cited articles it is assumed that a meeting is concluded with an instantaneous agreement which divides the associated surplus in an arbitrary predetermined way when the surplus is assumed to be divided equally the division rule is in fact nash s axiomatic bargaining solution in contrast the present paper treats the basic bargaining problem with the strategic approach see rubinstein 19 which constitutes an attempt to look into the bargaining black box this approach explicitly models the time dimension of the bargaining process describes in detail the bargaining procedure and justifies the agreement as a perfect equilibrium in

chicken and egg competition among intermediation service providers we analyze a model of imperfect price competition between intermediation service providers we insist on features that are relevant for informational intermediation via the internet the presence of indirect network externalities the possibility of using the nonexclusive services of several intermediaries and the widespread practice of price discrimination based on users identity and on usage efficient market structures emerge in equilibrium as well as some specific form of inefficient structures intermediaries have incentives to propose non exclusive services as this moderates competition and allows them to exert market power we analyze in detail the pricing and business strategies followed by intermediation services providers copyright 2003 by the rand corporation

indivisible labor lotteries and equilibrium abstract this paper considers an economy where labor is indivisible and agents are identical although the discontinuity in labor supply at the individual level disappears as a result of aggregation it is shown that indivisible labor has strong consequences for the aggregate bahavior of the economy it is also shown that optimal allocations involve lotteries over employment and consumption

will there be a dollar crisis almost everyone believes that the us current account deficit must eventually end and that this end will involve dollar depreciation however many believe that this depreciation will take place gradually this paper shows that any process of gradual dollar decline fast enough to prevent the accumulation of implausible levels of us external debt would impose capital losses on investors much larger than they currently expect as a result there will at some point have to be a wile e coyote moment a point at which expectations are revised and the dollar drops sharply it is much less clear however whether this crisis will produce macroeconomic problems paul krugman

for profit search platforms we consider optimal pricing by a profit maximizing platform running a dynamic search and matching market buyers and sellers enter in cohorts over time meet and bargain under private information the optimal centralized mechanism which involves posting a bid ask spread can be decentralized through participation fees charged by the intermediary to both sides the sum of buyers and sellers fees equals the sum of inverse hazard rates of the marginal types and their ratio equals the ratio of buyers and sellers bargaining weights we also show that a monopolistic intermediary in a search market may be welfare enhancing

indivisible labor and the business cycle abstract a growth model with shocks to technology is studied labor is indivisible so all variability in hours worked is due to fluctuations in the number employed we find that unlike previous equilibrium models of the business cycle this economy displays large fluctuations in hours worked and relatively small fluctuations in productivity this finding is independent of individuals willingness to substitute leisure across time this and other findings are the result of studying and comparing summary statistics describing this economy an economy with divisible labor and post war u s time series

a search model of rental markets who should pay the commission abstract we develop a dynamic search equilibrium model of rental markets with brokerage fees an endogenous mass of landlords and tenants is active in the search market while the mass of entering tenants is exogenous the mass of entering landlords is endogenously determined by the rate at which apartments become vacant brokerage fees paid by tenants are used as a device to screen short term and long term tenants we analyze a policy that requires fees to be paid by landlords such a policy decreases efficiency by preventing efficient screening but also increases turnover and hence efficiency in the search market we further provide empirically testable implications of our theory

variety growth and world welfare economists since john richard hicks have known that one of the principal means if not the principal means through which countries benefit from international trade is by the expansion of varieties the seminal work of paul r krugman 1979 brought the study of varieties into sharp focus by presenting a simple generalequilibrium model in which countries gain from trade through the import of new varieties since then economists have been hampered in their ability to quantify the impact of new varieties on national welfare by the econometric and data hurdles that need to be surmounted in this paper we document some stylized facts about the growth in global varieties which suggest that there may have been substantial welfare gains through the import of new varieties moreover we calculate the impact of increased variety on import prices and find that conventional measures of import price inflation may be dramatically biased upward classical international trade theory postulates that the elimination of trade barriers improves welfare by reducing the wedge between domestic and import prices as well as the ensuing deadweight loss an entirely different reason for the gains from trade arises from models of monopolistic competition if consumers value variety and countries cannot produce all varieties due to a fixed cost in the production of each variety countries stand to gain from trade because it expands the set of available varieties in these models the gains hinge crucially on a number of parameters and variables the first is the elasticity of substitution among varieties if varieties are highly substitutable as might be true for varieties of gasoline then increasing the number of varieties is unlikely to have much of an effect on prices and welfare second quality variation across varieties may matter presumably most americans care more about having access to french red wine than to japanese red wine finally import quantities matter as ceteris paribus one cares more about variety growth in big sectors than in small sectors in broda and weinstein 2004 we carefully estimate the impact of increased variety in the united states over the period from 1972 to 2001 using the most disaggregated import data available we document that the number of varieties imported by the united states defined as the number of import categories multiplied by the average number of source countries for each category quadrupled about half of this increase was due to increases in the number of categories and half due to a doubling of the number of countries from which the united states imported each good measuring the impact of this increase on u s import prices and welfare is a complex process that we will only discuss briefly here essentially we used robert c feenstra s 1994 methodology to estimate 30 000 elasticities and then construct an aggregate price index that is robust to common changes in quality variation the arbitrary splitting of categories the introduction of new goods and a host of other data problems after reconstructing the u s import price index we found that the price of u s imports has been falling at a rate 1 2 percent per year faster than one would have thought without taking new varieties into account to get some sense of the enormity of this bias consider that the impact of quality adjustments on the consumer price index is estimated to be 0 6 percent per year using this adjusted import price index we estimate the impact of new imported varieties on broda research department federal reserve bank of new york 33 liberty street new york ny 10045 weinstein economics department columbia university 420 w 118th street new york ny 10027 and nber we thank joshua greenfield for excellent research assistance we thank robert feenstra and peter klenow for excellent comments 1 the extension of trade does not primarily imply more goods the variety of goods available is also increased with all the widening of life that that entails there can be little doubt that the main advantage that will accrue to those with whom our merchants are trading is a gain of precisely this kind this is a gain which quantitative economic history which works with index numbers of real income is ill fitted to measure or even to describe hicks 1969 p 56

optimal pricing mechanisms with unknown demand the standard profit maximizing multi unit auction intersects the submitted demand curve with a preset reservation supply curve which is determined using the distribution from which the buyers valuations are drawn however when this distribution is unknown a preset supply curve cannot maximize monopoly profits the optimal pricing mechanism in this situation sets a price to each buyer on the basis of the demand distribution inferred statistically from other buyers bids the resulting profit converges to the optimal monopoly profit with known demand as the number of buyers goes to infinity and convergence can be substantially faster than with sequential price experimentation

convergence to perfect competition of a dynamic matching and bargaining market with two sided incomplete information and exogenous exit rate abstract consider a decentralized dynamic market with an infinite horizon and incomplete information in which buyers and sellers values for the traded good are private and independently drawn time is discrete each period has length and each unit of time a large number of new buyers and sellers enter the market within a period each buyer is matched with a seller and each seller is matched with zero one or more buyers every seller runs a first price auction with a reservation price and if trade occurs the seller and winning buyer exit with their realized utility traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate we show that in all steady state perfect bayesian equilibria as approaches zero equilibrium prices converge to the walrasian price and realized allocations converge to the competitive allocation

differences in income elasticities and trends in real exchange rates abstract one might expect that differences in income elasticities in trade and or differences in growth rates among countries would give rise to strong secular trends in real exchange rates for example fast growing countries might need steady depreciation to get the world to accept their growing exports in fact however income elasticities are systematically related to growth rates by the 45 degree rule under which fast growing countries appear to face high income elasticities of demand for their exports while having low income elasticities of import demand the net effect of this relationship between elasticities and growth rates is that secular trends in real exchange rates are much smaller than one might otherwise have expected relative ppp holds fairly well this paper documents the existence of a 45 degree rule and suggests an explanation in terms of increasing returns and product differentiation

intertemporal substitution in labor supply evidence from micro data the sensitivity of the supply of labor to intertemporal variation in the wage is an important issue in macroeconomics the analysis of social security and pensions and the study of life cycle patterns of work this paper explores two approaches to the measurement of intertemporal substitution that have appeared in the literature the first approach is to use consumption to control for wealth and unobserved expectations about future wages in the labor supply equation the second approach is to estimate a first difference equation for hours in which labor supply from the previous period serves as a control for wealth and wage expectations the results indicate that intertemporal substitution elasticity for married men is positive but small

varieties and the transfer problem abstract we revisit the classic transfer problem accounting for two channels of adjustment increased trade in existing goods and services the intensive margin and net creation and destruction of product varieties the extensive margin over the medium term the latter reduces the scope for real exchange rate and terms of trade variability in response to cross border flows we embed our transfer analysis in popular models of current account adjustment where initial imbalances are driven by domestic demand for or foreign supply of net saving possibly associated with over optimistic expectations simulation exercises based on 2006 data suggest that a transfer of the size of the pre crisis u s current account deficit may require only moderate trend depreciation in real terms and that the aggregate welfare impact of the transfer is disconnected from the size of the relative price correction

transfers returns to scale tied aid and monopolistic competition we examine transfers and tied aid in a model with increasing returns to scale and monopolistic competition transfers give rise to an additional love of variety welfare effect and affect the utility possibility locus generic tied aid may exacerbate or reverse these results the popularity of aid tied to specific manufactured goods can be explained through rent seeking behavior since such aid gives rise to profits in the donor country these profits in turn largely repatriate the transfer such that donors can appear to be more generous than they really are

dynamic markets with competitive bidding the model features a dynamic market in steady state in which prices are determined in first price auctions it combines competition over time familiar from the pairwise meeting models with instantaneous bidding competition it inquires how different properties of the model determine the relative importance of these two aspects of the competition and in particular how the non market clearing price result of the matching and bargaining models is affected by the

a note on the seller s optimal mechanism in bilateral trade with two sided incomplete information it is shown with an example that in bilateral trade problems with two sided incomplete information some seller types may obtain higher expected payos in mechanisms other than the one where they make a take it or leave it oer contrary to popular belief if one looks at the mechanism selection problem of the informed seller then the op timality of a take it or leave it oer for the seller is restored journal of economic literature classi cation numbers c72 c78 d82

two sided markets a progress report the paper provides a road map to the burgeoning literature on two sided markets and presents new results it identifies two sided markets with markets in which the structure and not only the level of prices charged by platforms matters the failure of the coase theorem is necessary but not sufficient for two sidedness the paper builds a model integrating usage and membership externalities that unifies two hitherto disparate strands of the literature emphasizing either form of externality and obtains new results on the mix of membership and usage charges when price setting or bargaining determine payments between end users

competitive pricing and efficiency in search equilibrium we consolidate and generalize some results on price determination and efficiency in search equilibrium extending models by rubinstein and wolinsky and by gale heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition when the discount rate r and search costs converge to 0 we show that prices in all exchanges are the same and equal the competitive market clearing price given positive search costs efficiency obtains iff bargaining satisfies hosios condition and r 0 when prices are set by third party market makers however we show that search equilibrium is necessarily efficient

bilateral matching and bargaining with private information we study equilibria of a dynamic matching and bargaining game dmbg with two sided private information bilateral bargaining the model is a private information replica of mortensen and wright 2002 there are two kinds of frictions time

market share pioneering advantage a theoretical approach in this paper we present an industry in which a pioneer has entered accumulated capital in the form of goodwill and in his monopoly period has also reduced his cost of production as a result of some form of learning by doing at some later date a newcomer enters his production cost is higher than that of the monopolist at that date however due to diffusion of information the costs of the two firms equate at some future date once the new firm enters the market a duopolistic game begins in which the firms choose prices and investment rates analyzing this game we discover the conditions under which the final market shares no longer depend on the order of entry the initial cost advantage the length of the monopoly period or the length of time it took the newcomer to overcome the pioneer s cost advantage we analyze the speed and pattern of convergence to the final market shares and the capital path of the pioneer in his monopoly period depending on his beliefs concerning the possibility of entry