substitute goods auctions and equilibrium this paper identifies two notions of substitutes for auction and equilibrium analysis weak substitutes the usual price theory notion guarantees monotonicity of t tonnement processes and convergence of clock auctions to a pseudo equilibrium but only strong substitutes which treats each unit traded as a distinct good with its own price guarantees that every pseudo equilibrium is a walrasian equilibrium that the vickrey outcome is in the core and that the law of aggregate demand is satisfied when goods are divisible weak substitutes along with concavity guarantees all of the above properties except for the law of aggregate demand

walrasian equilibrium with gross substitutes in this paper we study the problem of efficient production and allocation of indivisible objects among a set of consumers we assume that the agents preferences depend on the bundle of objects and the quantity of money they consume furthermore we assume that preferences are quasilinear in money and that agents have a large endowment of money with indivisibilities it is well known that many familiar properties of the utility functions fail to ensure existence in their striking analysis of the matching problem kelso and crawford 5 introduce the gross substitutes gs condition which ensures the non emptiness of the core we propose two new conditions and show that with quasilinearity they are equivalent article id jeth 1999 2531 available online at http www idealibrary com on

political risk national defense and the dollar the federal reserve board s trade weighted real exchange rate index is highly correlated with the u s defense budget share of gnp this paper provides evidence that the correlation is not spurious political risk associated with holding wealth in the united states varies inversely with u s military security and due to the soviet military threat to the west is a major argument in foreign asset demand functions

back to fundamentals equilibrium in abstract economies we propose a new abstract definition of equilibrium in the spirit of competitive equilibrium a profile of alternatives and a public ordering expressing prestige price or a social norm such that each agent prefers his assigned alternative to all lower ranked ones the equilibrium operates in an abstract setting built upon a concept of convexity borrowed from convex geometry we apply the concept to a variety of convex economies and relate it to pareto optimality the magic of linear equilibrium prices is put into perspective by establishing an analogy between linear functions in the standard convexity and primitive orderings in the abstract convexity jel c90 d11 in this paper we return to the fundamental concept of competitive equilibrium and extend the notion to a more abstract setting the extension is based on the idea that competitive equilibrium is a method of creating harmony in an interactive situation with a feasibility restriction and self interested agents it is built around a public ordering of the alternatives which either limits the choices available to the agents or systematically influences their preferences in the standard economic setting this ordering is given by prices that apply equally to all agents these prices determine consumers choice sets and producers preferences we propose an analogous solution concept adjusted to fit more abstract situations in which valuation using prices is replaced by valuation according to a public ordering the road to the construction of the equilibrium concept starts with a discussion of the notion of convexity in the euclidean setting the algebraic notion of convexity is central to the standard analysis of competitive equilibrium since we primarily consider settings that lack an algebraic structure we employ a more abstract form of convexity definitions of convexity involve the primitive phrase b is between the elements a 1 a l in an euclidean space this means that b is an algebraic con vex combination of a 1 a l however the phrase also has a common use in daily conversation for example one can say that game theory is between mathematics and economics and that canada is culturally between the united states the united kingdom and france to accommodate this the first step will be to borrow a formal

the law of demand and risk aversion this note proposes a necessary and sufficient condition on a utility function to guarantee that it generates a demand function satisfying the law of demand this condition can be interpreted in terms of an agent s attitude towards lotteries in commodity space as an application we show that when an agent has an expected utility function her demand for securities satisfies the law of demand if her coefficient of relative risk aversion does not vary by more than 4

a folk theorem for one shot bertrand games we show that bounded monopoly profits are essential for the uniqueness of the bertrand paradox zero profit outcome otherwise a folk theorem obtains for one shot homogeneous product bertrand games any positive but finite payoff vector can be achieved in a symmetric mixed strategy nash equilibrium

substitutes and stability for matching with contracts we consider the matching problem with contracts of hatfield and milgrom 2005 and we introduce new concepts of bilateral and unilateral substitutes we show that bilateral substitutes is a sucient condition for the existence of a stable allocation in this framework however the set of stable allocations does not form a lattice under this condition and there does not necessarily exist a doctor optimal stable allocation under a slightly stronger condition unilateral substitutes the set of stable allocations still does not necessarily form a lattice with respect to doctors preferences but there does exist a doctor optimal stable allocation and other key results such as incentive compatibility and the rural hospitals theorem are recovered

competitive equilibrium with indivisibilities abstract this paper studies an exchange economy with a finite number of agents in which each agents is initially endowed with a finite number of personalized indivisible commodities we observe that the equivalence theorem of the core and the competitive equilibrium may not hold for this economy when the coalitional form game is generated in the standard manner we provide an alternative definition of the coalitional form game to resolve this problem so that the balancedness of the new defined game provides a useful necessary and sufficient condition for the existence of competitive equilibrium for the original economy journal of economic literature classification numbers c71 d41 d51

on the microeconomic foundations of linear demand for differentiated products abstract this paper provides a thorough exploration of the microeconomic foundations for the multi variate linear demand function for differentiated products which is widely used in industrial organization the setting is the standard representative consumer with a quasi linear utility function a key finding is that strict concavity of the quadratic utility function is critical for the demand system to be well defined otherwise the true demand function may be quite complex multi valued non linear and income dependent we uncover failures of duality relationships between substitute products and complementary products as well as the incompatibility between high levels of complementarity and concavity the two good case emerges as a special case with strong but non robust properties a key implication is that all conclusions derived in applied economic models via the use of linear demand that does not satisfy the law of demand ought to be regarded with some suspicion

a double track adjustment process for discrete markets with substitutes and complements we propose a new walrasian tatonnement process called a double track procedure for efficiently allocating multiple heterogeneous indivisible items in two distinct sets to many buyers who view items in the same set as substitutes but items across the two sets as complements in each round of the process a walrasian auctioneer first announces the current prices for all items buyers respond by reporting their demands at these prices and then the auctioneer adjusts simultaneously the prices of items in one set upward but those of items in the other set downward it is shown that this procedure converges globally to a walrasian equilibrium in finitely many rounds

transformations of the commodity space behavioral heterogeneity and the aggregation problem aggregation in exchange markets is studied by imposing restrictions on distributions of the households characteristics approximate bounds for market demand price elasticities that depend upon specific measures of behavioral heterogeneity are provided increasing behavioral heterogeneity makes aggregate expenditures more independent of prices this has strong consequences for the prevalence in the aggregate of the weak axiom of revealed preference of gross substitutability and on uniqueness and stability of the walrasian exchange equilibrium these strong macroeconomic regularities are obtained essentially through distributional assumptions as no rationality requirements are imposed on individual demand functions other than homogeneity and walras law journal of economic literature classification numbers d11 d41 d50 el 1992 academic press lnc there are still quite a few unpleasant gaps nowadays between macroanalysis and microanalysis of socioeconomic systems a leading instance drawn from social choice theory is arrow s celebrated impossibility theorem 1 which states that any attempt to aggregate individual preferences into a consistent social ordering or a collective choice procedure satisfying a few appealing requirements is bound to fail the impossibility arises however only if one insists that the procedure should work for every possible environment or in other words for all distributions of individual preferences a possible resolution of the problem is therefore to identify broad classes of distributions of preferences for which aggrega the bulk of the research reported in this paper was essentially done at yale university during the fall semester of 1990 i thank all my colleagues for their support and comments especially martin shubik herbert scarf and truman bewley i also had very useful conversations with jorgen weibull mike jerison andreu mas colell christian gouri6roux camille bronsard guy laroque bruno jullien and bernard caillaud i am much indebted to ai klevorick for his comments on an earlier draft but my greatest debt is to werner hildenbrand whose pioneering insights and stubborn insistance have over the years kept quite a few of us struggling beyond the fads of the moment with the aggregation problem our profession is fortunate indeed to have him around

stability and competitive equilibrium in trading networks we introduce a model in which agents in a network can trade via bilateral contracts we find that when continuous transfers are allowed and utilities are quasi linear the full substitutability of preferences is sufficient to guarantee the existence of stable outcomes for any underlying network structure furthermore the set of stable outcomes is essentially equivalent to the set of competitive equilibria and all stable outcomes are in the core and are efficient by contrast for any domain of preferences strictly larger than that of full substitutability the existence of stable outcomes and competitive equilibria cannot be guaranteed

anomalous behavior in a traveler s dilemma the notion of a nash equilibrium has joined supply and demand as one of the two or three techniques that economists instinctively try to use first in the analysis of economic interactions moreover the nash equilibrium and closely related game theoretic concepts are being widely applied in other social sciences and even in biology where evolutionary stability often selects a subset of the nash equilibria many people are uneasy about the stark predictions of the nash equilibrium in some contexts where the extreme rationality assumptions seem implausible kaushik basu s 1994 traveler s dilemma is a particularly convincing example of a case where the unrelenting logic of game theory is at odds with intuitive notions about human behavior the story associated with the dilemma is that two travelers purchase identical antiques while on a tropical vacation their luggage is lost on the return trip and the airline asks them to make independent claims for compensation in anticipation of excessive claims the airline representative announces

contracts versus salaries in matching workers and firms may bargain over general multidimensional contracts they may negotiate over health benefits housing retirement plans etc substitutes on the other hand is the assumption commonly placed on firms preferences to guarantee the existence of stable matchings of workers and firms in this paper i show that when firms regard contracts as substitutes bargaining over contracts can be embedded into a model of bargaining over wages the economics of the embedding is straightforward except for a small twist when a firm and a worker negotiate over a contract they may bargain over many dimensions however the pareto frontier of contracts is in a sense one dimensional what is better for the worker is worse for the firm so pareto optimal contracts may be viewed as salaries with the better contracts for the firm meaning lower salaries and the better contracts for the worker meaning higher salaries the twist is that a firm s ranking over contracts might be affected by the firm s other hires for example health plan a may be better than b for a firm if it has many employees but b beats a if it has few when contracts are substitutes it turns out that the ranking is not affected in this way hatfield and milgrom 2005 present a model of two sided worker firm matching with contracts a firm will hire a collection of workers and will negotiate a contract with each one of them the model is a generalization of kelso and crawford 1982 where each firm and each worker negotiate a wage 1 kelso and crawford show that when firms demands satisfy gross substitutes the core of the matching market is nonempty hatfield and milgrom show that when the firms preferences over contracts satisfy their notion of substitutes the core of the market is nonempty i show that hatfield and milgrom s model can be embedded into the model of kelso and crawford hatfield and milgrom s assumption of substitutability enables an embedding where firms demands for workers satisfy kelso and crawford s notion of gross substitutes as a result the nonemptiness of the core follows from the argument in kelso and crawford and their salary adjustment algorithm finds a stable matching of workers to firms and a vector of supporting salaries hatfield and milgrom s paper is an elegant analysis of two sided matching it simplifies matching models and makes their relationship to auction models more transpar ent their paper contributes much more than showing the nonemptiness of the core when firms and workers can sign general contracts and my result does not diminish

strong tiebout equilibrium under restricted preferences domain abstract we investigate the existence and give a partial characterization of a strong tiebout equilibrium which consists of an endogenously formed partition of the individuals into disjoint jurisdictions with each jurisdiction producing and financing its own public goods and moreover there exists no group of individuals who can all benefit by establishing their own community in particular no single individual finds it desirable to migrate from his equilibrium jurisdiction the existence proof makes use of the notion of consecutive games which we introduce and show that for such games there always exists a partition with a nonempty core

matching with contracts we develop a model of matching with contracts which incorporates as special cases the college admissions problem the kelso crawford labor market matching model and ascending package auctions we introduce a new law of aggregate demand for the case of discrete heterogeneous workers and show that when workers are substitutes this law is satisfied by profit maximizing firms when workers are substitutes and the law is satisfied truthful reporting is a dominant strategy for workers in a worker offering auction matching algorithm we also parameterize a large class of preferences satisfying the two conditions

competitive equilibrium in an exchange economy with indivisibilities abstract we analyze an exchange economy in which i all commodities except money are indivisible ii agents preferences can be described by a reservation value for each bundle of indivisible objects and iii all agents are price takers we obtain a necessary and sufficient condition under which market clearing prices exist implications for market mechanisms are discussed journal of economic literatureclassification numbers d51 c78

understanding preferences demand types and the existence of equilibrium with indivisibilities we propose new techniques for understanding agents valuations our classification into demand types incorporates existing definitions substitutes complements strong substitutes etc and permits new ones our unimodularity theorem generalises previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a demand type for indivisible goods contrary to popular belief equilibrium is guaranteed for more classes of purely complements than of purely substitutes preferences our intersection count theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects applications include matching and coalition formation and the product mix auction introduced by the bank of england in response to the financial crisis

iterative auction design for tree valuations we study a special class of multi item valuations tree valuations that exhibit both value complementarity and substitutability we provide a linear programming formulation of the efficient allocation problem that is of polynomial size in the number of agents and items this reveals a new class of valuations for which a walrasian equilibrium exists in the presence of value complementarities an iterative algorithm for this linear program in conjunction with an appropriate payment rule yields an iterative auction that implements the efficient outcome at an ex post perfect equilibrium this auction relies on a simple pricing rule compact demand reports and uses a novel interleaved price update structure to assign final payments to bidders that guarantee truthful bidding

a new look at the classical bertrand duopoly abstract the paper provides necessary and sufficient conditions for the uniqueness of pure strategy nash equilibrium in the standard bertrand duopoly with a homogeneous product the main condition is elementary easy to interpret and nests all known sufficient conditions in the literature

small income effects a marshallian theory of consumer surplus and downward sloping demand we formalize the marshallian idea that when the proportion of income spent on any commodity is small then the income effects are small if n is the number of goods we show under certain assumptions on preferences and prices that the order of magnitude of the norm of the income derivative of demand is 1 n as a corollary we get that for the case of a single price change the percentage error in approximating the hicksian deadweight loss by its marshallian counterpart goes to zero at least at the rate 1 n and that demand is downward sloping for n large enough

equilibria and indivisibilities gross substitutes and complements this paper examines an exchange economy with heterogeneous indivisible objects that can be substitutable or complementary we show that a competitive equilibrium exists in such economies provided that all the objects can be partitioned into two groups and from the viewpoint of each agent objects in the same group are substitutes and objects across the two groups are complements this condition generalizes the well known kelso crawford gross substitutes condition and is called gross substitutes and complements we also provide practical and typical examples from which substitutes and complements are both jointly observed