reputation and impermanent types i consider a version of the chain store game where the incumbent firm s type evolves according to a markov process with two states a tough type who always fights entry and a weak type who prefers to accommodate there exists a minimal level of persistence necessary for the incumbent to be able to sustain any reputation for being tough above that level as the number of markets t increases in equilibrium play alternates between intervals of entry by competitors and intervals of deterrence when t is infinite then regardless of the discount factor there exists a sequential equilibrium in which the incumbent s payoff is bounded below her stackelberg payoff both results are in contrast to the outcome when the incumbent s type is fixed one interpretation is that reputation is not permanent but must be renewed occasionally

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

matching with contracts comment abstract the matching with contracts model hatfield and milgrom 2005 is widely considered to be one of the most important advances of the last two decades in matching theory one of their main messages is that the set of stable allocations is non empty under a substitutes condition we show that an additional irrelevance of rejected contracts irc condition is implicitly assumed throughout their analysis and in the absence of irc several of their results including the guaranteed existence of a stable allocation fail to hold jel c78 d86

estimation of scale economies underlying growth and productivity the empirical implications of data aggregation estimation of scale economies underlying growth and productivity patterns is typically based on aggregated data raising questions about the potential for aggregation biases this paper provides empirical evidence on the existence and patterns of such biases we use a cost based model to estimate short long run and internal external scale effects for u s manufacturing data at different aggregation levels our results suggest that aggregation biases in such a model are not substantive also internal scale economies seem more appropriately represented by the aggregate data whereas more disaggregated data appears preferable for estimation of external or spillover effects that occur between industries or sectors

comparative statics in matching markets abstract this paper studies the comparative statics of adding agents to matching markets that generalize the marriage and college admissions markets of d gale and l shapley amer math monthly 69 1962 9 15 it is shown for the wide class of matching markets studied by a roth econometrica 52 1984 47 57 that adding an agent to one side of the market weakens the competitive positions of the other agents on that side and strengthens the competitive positions of the agents on the other side

on the economic interpretation and measurement of optimal capacity utilization with anticipatory expectations this study builds on recent research giving the notion of capacity utilization clearer economic foundations in this research optimal output ye is defined as the minimum point on the firm s short run average total cost curve and capacity utilization is then computed as cu y y where y is actual output here i extend these concepts to include adjustment costs due to changes in the stock of capital and nonstatic expectations of future output demand and input prices the more general notion of cu is shown to depend on the shadow values of the firm s quasi fixed inputs and is decomposed to isolate the effects of anticipatory expectations an empirical comparison is then made between traditional indices and alternative economic cu measures using annual u s manufacturing data 1954 1980 the calculated indices exhibit plausible patterns which can be interpreted as the effects of nonstatic expectations and adjustment costs

on stable and strategy proof rules in matching markets with contracts abstract this paper studies stable and one sided strategy proof rules in many to one matching markets with contracts not assuming any kind of substitutes condition or the law of aggregate demand we obtain the following results first the number of stable and strategy proof rules is at most one second the doctor optimal stable rule whenever it exists is the unique candidate for a stable and strategy proof rule third a stable and strategy proof rule whenever it exists is second best optimal for doctor welfare in that no individually rational and strategy proof rule can dominate it this last result is further generalized to non wasteful and strategy proof rules due to the weak assumptions our analysis covers a broad range of markets including cases where a unique stable and strategy proof rule is not equal to the one induced by the cumulative offer process or the deferred acceptance algorithm

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

on the correspondence of contracts to salaries in many to many matching abstract in this note i extend the work of echenique 2012 to show that a model of many to many matching with contracts may be embedded into a model of many to many matching with wage bargaining whenever 1 all agents preferences are substitutable and 2 the matching with contracts model is unitary in the sense that every contractual relationship between a given firm worker pair is specified in a single contract conversely i show that unitarity is essentially necessary for the embedding result

reputation and entry deterrence under short run ownership of a firm abstract this paper discusses the role of the changing ownership of a long run firm facing a sequence of potential entrants to its market when there is uncertainty about the firm s type about its cost of taking an aggressive action that is observed only by the current owner it is shown that there exists an equilibrium in which each generation of owners takes the same aggressive action to deter entry regardless of the type under a natural refinement of equilibrium beliefs the path induced by this pooling equilibrium is shown to be unique the results sharply contrast with the case of long run ownership where for the same discount factor the firm s owner separates his actions depending on the type of the firm so that the high coat firm allows entry every period while the low cost firm plays aggressively every period consequently the value of the high cost firm is shown to be strictly higher under short run ownership than under long run ownership journal of economic literature classification numbers c72 l13

stability in large matching markets with complementarities labor markets can often be viewed as many to one matching markets it is well known that if complementarities are present in such markets a stable matching may not exist we study large random matching markets with couples we introduce a new matching algorithm and show that if the number of couples grows slower than the size of the market a stable matching will be found with high probability if however the number of couples grows at a linear rate with constant probability not depending on the market size no stable matching exists our results explain data from the market for psychology interns

environmental regulations and productivity growth the case of fossil fueled electric power generation this paper measures and analyzes the effect of sulfur dioxide emission restrictions on the rate of productivity growth in the electric power industry over the 1973 79 business cycle a firm specific measure of regulatory intensity is developed which depends on the severity of the emission standard the extent of enforcement and the unconstrained emission rate relevant to each utility the results indicate that emission regulations result in significantly higher generating costs primarily from the increased use of low sulfur fuels the average rate of productivity growth was reduced by 0 59 percentage points per year for constrained utilities

contracts versus salaries in matching a general result abstract it is shown that a matching market with contracts can be embedded into a matching market with salaries under weaker conditions than substitutability of contracts in particular the result applies to the recently studied problem of cadet to branch matching as an application of the embedding result a new class of mechanisms for matching markets with contracts is defined that generalize the firm proposing deferred acceptance algorithm to the case where contracts are unilateral substitutes for firms

sequential rules for house allocation with price restrictions this paper considers a housing market with price restrictions on such markets the existence of a unique minimum rationing equilibrium price vector has been established for each preference profile on a general preference domain that contains almost all preference profiles this vector can be used as a key ingredient in a direct and strategy proof allocation mechanism the main contribution of this paper is to provide two price sequences one with increasing prices and one with decreasing prices that both terminate to a minimal rationing equilibrium price vector in a finite number of steps these sequences are demonstrated to play key roles in an english auction and a dutch auction respectively for the considered housing market with price restrictions less

union behavior industry rents and optimal policies abstract this paper examines the welfare gains from strategic industrial policy in the u s steel industry focusing on the role of capacity utilization and the potential gains from capturing labor rents with underutilized capacity strategic policies to capture labor rents lead to an endogenous response that diminishes their importance on the other hand reducing domestic labor market distortions results in welfare gains nearly as large as those from the optimal subsidy this suggests that the focus on labor rents as the subject of industrial policy is overstated at least in manufacturing industries such as integrated steel

efficiency in new zealand sheep and beef farming the impacts of regulatory reform in this study we consider the impacts of dramatic regulatory reform during the 1980s on the efficiency of farms in new zealand using unbalanced panel data a translog distance function representing the multiple output and input technology and incorporating nonneutral regulatory impacts is used for the analysis determinants of technical inefficiency including a regulatory variable a time term and a debt equity ratio are also incorporated in a one step model estimated by maximum likelihood stochastic production frontier methods we find evidence of regulatory induced changes in output composition toward beef and deer and away from wool and especially lamb but little associated technical inefficiency these patterns motivated investment in complementary capital land and beef deer livestock inputs firms that were more flexible in their adaptation toward these new mixes adjusted to regulatory changes with less upheaval so any existing inefficiency appears linked to debt equity levels

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

competitive equilibria in two sided matching markets with general utility functions we present an exact characterization of utilities in competitive equilibria of two sided matching markets in which the utility of each agent depends on the choice of partner and the terms of the partnership potentially including monetary transfer examples of such markets include sellers and buyers or jobs and workers demange and gale showed that the set of competitive equilibria in this type of market forms a complete lattice with each extreme point of the lattice representing an equilibrium with the highest utilities for the agents on one side and the lowest utilities for the agents on the opposite side our characterization is based on establishing a connection between the competitive equilibria of a market and the competitive equilibria of certain strict subsets of that market each obtained by removing exactly one agent this characterization captures the effect of competition when agents are added to the market or removed from the market it gives a precise procedure for constructing competitive eq

unilateral substitutability implies substitutable completability in many to one matching with contracts abstract we prove that the unilateral substitutability property introduced in hatfield and kojima 2010 implies the substitutable completability property from hatfield and kominers 2014 this paper provides a novel linkage between these two sufficient conditions for the existence of a stable matching in many to one matching markets with contracts a substitutable completion of a preference is a substitutable preference created by adding some sets of contracts to the original preference order we provide an algorithm which when operated on the unilaterally substitutable preferences produces such a substitutable completion thus it provides a constructive proof of the connection between the two properties

some further properties of the cumulative offer process we investigate extension resource monotonicity and respecting improvements properties of the cumulative offer process cop extension monotonicity says that no doctor is to be better off whenever others start preferring more contracts to being unmatched resource monotonicity on the other hand requires that no doctor becomes worse off whenever hospitals start hiring more doctors the cop becomes extension and resource monotonic whenever contracts are unilateral substitutes us satisfying an irrelevance of rejected contracts condition irc this result implies that the cop is population monotonic under us and the irc we then turn to the respecting improvements property which states that no doctor should be harmed if some of his contracts become more popular with an additional law of aggregate demand condition we show that the cop respects improvements

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

matching with branch of choice contracts at the united states military academy branch selection is a key decision in a cadet s military career cadets at usma can increase their branch priorities at a fraction of slots by extending their service agreement this real life matching problem lls an important gap in market design literature although priorities fail a key substitutes condition the agent optimal stable mechanism is well dened and in contrast to the current usma mechanism it is fair stable and strategy proof adoption of this mechanism benets cadets and the army this new

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

subequilibrium in the north american steel industries a study of short run biases from regulation and utilisation fluctuations the purpose of this paper has been to develop a short run framework for assessment of various biases including technical output or scale utilization and regulatory biases to address questions about the impacts of exogenous shocks on firm behavior this framework was then used to assess issues about the effects of regulation utilization output demand fluctuations and technical change on the structure of the steel industry the theoretical development as well as the application to the u s and canadian steel industries indicate the wide ranging applications of such a framework copyright 1988 by royal economic society

how to control controlled school choice we characterize choice rules for schools that regard students as substitutes while expressing preferences for a diverse student body the stable or fair assignment of students to schools requires the latter to regard the former as substitutes such a requirement is in conflict with the reality of schools preferences for diversity we show that the conflict can be useful in the sense that certain unique rules emerge from imposing both considerations we also provide welfare comparisons for students when different choice rules are employed

relaxing the substitutes condition in matching markets with contracts in the many to one matching model with contracts i provide new necessary and new sufficient conditions for the existence of a stable allocation these new conditions exploit the fact that one side of the market has strict preferences over individual contracts

strategic wholesale pricing in a supply chain with a potential entrant this paper develops an adverse selection model for a two stage supply chain with one supplier one retailer and a potential outside entrant supplier who makes a partially substitutable product the work is different from most research on entry deterrence that only considers a single stage model our main interest is to investigate how the incumbent supplier can strategically maximize her profit by a wholesale pricing policy when facing the potential entrant we focus on a model where the entrant supplier will sell her product through the same incumbent retailer we derive the optimal decisions for each player and study the comparative statics of the equilibrium to investigate how the supply chain structure may affect the deterrence strategy of the incumbent supplier we also consider three alternative models with different channel structures when both suppliers sell their products directly when the entrant has another independent retailer and when the entrant sells her product directly through the comparison we find that the existence of the common downstream retailer often enhances the deterring motivation of the incumbent supplier

cumulative offer process is order independent this note shows that in the matching with contracts model the outcome of the cumulative offer process is order independent if every hospital has a choice function that satisfies the bilateral substitutability condition and the irrelevance of rejected contracts condition

bidding for army career specialties improving the rotc branching mechanism motivated by the low retention rates of us military academy and reserve officer training corps graduates the army recently introduced incentives programs in which cadets could bid 3 years of additional service obligation to obtain higher priority for their desired branches the full potential of this incentives program is not utilized because of the rotc s deficient matching mechanism i propose a design that eliminates these shortcomings and mitigates several policy problems the army has identified in contrast to the rotc mechanism my design utilizes market principles more extensively and it is a hybrid between a market mechanism and a priority based allocation mechanism