Hierarchic competitive equilibria

Without an interiority or strong survival assumption, an equilibrium may not exist in the standard Arrow–Debreu model. We propose a generalized concept of competitive equilibrium, called hierarchic equilibrium. Instead of using standard prices we use hierarchic prices. Existence will be shown without a strong survival assumption and without a non-satiation condition on the preferences. Under standard assumptions this reduces to the Walras equilibrium. Hierarchic equilibria are weakly Pareto optimal and any Pareto optimum can be decentralized without a border condition. We prove the existence of a Pareto optimal hierarchic equilibrium under additional assumptions. Later, we establish a core equivalence result.     

Consistent collusion-proofness and correlation in exchange economies

We present a feasible strategic market mechanism with finitely many agents whose Nash, semi-strong Nash and coalition-proof Nash equilibria fully implement the Walrasian equilibria. We define a strategic equilibrium concept, called correlated semi-strong equilibrium, and show that the Walrasian equilibria can be implemented by these equilibria, and also by the coalition-proof correlated equilibria of our mechanism. We show that these two concepts, suitably modified with transfers, fully implement the Pareto optimal allocations.     

Pareto efficiency in the jungle

We revisit the jungle economy of Piccione and Rubinstein (Econ J 117(July):883–896, 2007) in which the allocation of resources is driven by coercion. In this economy the unique equilibrium satisfies lexicographic maximization. We show that relaxing the assumptions on consumption sets and preferences slightly, allocations other than lexicographic maximizers can be jungle equilibria. We attribute this result to single unilateral taking where a stronger agent takes goods from only one weaker agent. Once multiple unilateral takings are introduced, we show that jungle equilibria coincide with lexicographic maximization under weak assumptions. However, we also present examples of equilibria that are Pareto inefficient, where voluntary gift giving by stronger agents is needed to achieve Pareto efficiency and even voluntary trade has a role in the jungle.     

Optimality in a financial economy with outside money and restricted participation

We analyze an economy with inside financial assets and outside money. Households have differing restricted access on both types of assets and, according to a well-known approach, they use money to pay taxes. Since competitive equilibria are generically inefficient, we perform a Pareto improvability analysis through a monetary intervention. It results that, if the government modifies the amount of money endowments for just one consumer in period one, then Pareto improvements upon the market equilibrium are possible.     

Inconsequential arbitrage

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, prove that inconsequential arbitrage is sufficient for existence of equilibrium. Moreover, with a slightly stronger condition of nonsatiation than that required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that inconsequential arbitrage, the existence of a Pareto optimal allocation, and compactness of the set of utility possibilities are equivalent. Thus, when all equilibria are Pareto optimal — for example, when local nonsatiation holds — inconsequential arbitrage is necessary and sufficient for existence of an equilibrium. By further strengthening our nonsatiation condition, we obtain a second welfare theorem for exchange economies allowing short sales.Finally, we compare inconsequential arbitrage to the conditions limiting arbitrage of Hart [Hart, O.D., 1974. J. Econ. Theory 9, 293–311], Werner [Werner, J., 1987. Econometrica 55, abs1403–1418], Dana et al. [Dana, R.A., Le Van, C., Magnien, F., 1999. J. Econ. Theory 87, 169–193] and Allouch [Allouch, N., 1999. Equilibrium and no market arbitrage. CERMSEM, Universite de Paris I]. For example, we show that the condition of Hart (translated to a general equilibrium setting) and the condition of werner are equivalent. We then show that the Hart/Werner conditions imply inconsequential arbitrage. To highlight the extent to which we extend Hart and Werner, we construct an example of an exchange economy in which inconsequential arbitrage holds (and is necessary and sufficient for existence), while the Hart/Werner conditions do not hold.     

Spatial competition under uniform delivered pricing

A Hotelling-type model of spatial competition is considered, in which two firms compete in uniform delivered prices. First, it is shown that there exists no uniform delivered price–location equilibrium when the product sold by the firms is perfectly homogeneous andwhen consumers buy from the firm quoting the lower delivered price. Second, when the product is heterogeneous and when preferences are identically, independently Weibull-distributed with standard deviation μ, we prove that there exists a single uniform delivered price–location equilibrium iff μ≧1/8 times the transportation rate times the size of the market. In equilibrium, firms are located at the center of the market and charge the same uniform delivered price, which equals their average transportation cost, plus a mark-up of 2μ. Finally, we discuss how our result extends to the case of n firms and proceed to a comparison of equilibria under uniform mill and delivered pricing.     

Trading equilibrium in a public good economy with smooth preferences and a mixed measure space of consumers

Lindahl and Nash equilibria are often used in the theory of public good. Shitovitz and Spiegel (1998) present an example of 2-person economy with one private good and one pure public good, where the core efficient Lindahl allocation does not Pareto dominate the (inefficient) Nash allocation. In this paper we introduce the new concept of Trading equilibrium for a general public good economy with smooth preferences and a mixed measure space of consumers. We obtain that this economy admits a unique Trading equilibrium. Moreover, the Trading equilibrium induces a core allocation that strictly Pareto dominates the Nash allocation.     

Pareto improving interventions in a general equilibrium model with private provision of public goods

Most of the literature on government intervention in models of voluntary public goods supply focuses on interventions that increase the total level of a public good, which is considered to be typically underprovided. However, an intervention that is successful in increasing the public good level need not benefit everyone. In this paper we take a direct approach to welfare properties of voluntary provision equilibria in a full blown general equilibrium model with public goods and study interventions that have the goal of Pareto improving on the voluntary provision outcome. Towards this end, we study a model with many private goods and non-linear production technology for the public good, and hence allow for relative price effects to serve as a powerful channel of intervention. In this setup we show that Pareto improving interventions generally do exist. In particular, direct government provision financed by “small” , or “local” , lump-sum taxes can be used generically to Pareto improve upon the voluntary provision outcome.     

Factor market effects upon product market equilibrium

Conventional duopoly models typically assume agents possess specific conjectures concerning other agents’ behavior. In this paper equilibrium conjectures are endogenous and are a result of a joint factor market and product market equilibrium. Factor markets affect product markets since potential managers or owners of firms engage in product market competition and compete for corporate control in labor or capital markets. The resulting factor and product market joint equilibrium (FPE) endogenizes conjectures and can thus potentially endogenize market structure. This approach provides economic rationales for both Stackelberg and consistent conjectural equilibria. Copyright © 1999 John Wiley & Sons, Ltd.     

Better Late than Early: Vertical Differentiation in the Adoption of a New Technology

After the initial breakthrough in the research phase of R&D, a new product undergoes a process of change, improvement, and adaptation to market conditions. We model the strategic behavior of firms in this development phase. We emphasize that a key dimension to this competition is the innovation that leads to product differentiation and quality improvement. In a duopoly model with a single adoption choice, we derive endogenously the level and diversity of product innovations. We demonstrate the existence of equilibria in which one firm enters early with a low-quality product while the other continues to develop the technology and eventually markets a high-quality good. In such an equilibrium, no monopoly rent is dissipated and the later innovator makes more profits. Incumbent firms may well be the early innovators, contrary to the predictions of the "incumbency inertia" hypothesis.     

Constrained inefficiency in GEI: A geometric argument

In this paper we use global analysis to study the welfare properties of general equilibrium economies with incomplete markets (GEI). Our main result is to show that constrained Pareto optimal equilibria are contained in a submanifold of the equilibrium set. This result is explicitly derived for economies with real assets and fixed aggregate resources, of which real numéraire assets are a special case. As a by product of our analysis, we propose an original global parametrization of the equilibrium set that generalizes to incomplete markets the classical one, first, proposed by Lange [Lange, O., 1942. The foundations of welfare economics. Econometrica 10, 215–228].     

Tiebout's tale in spatial economies: Entrepreneurship, self-selection, and efficiency

This paper establishes the existence and efficiency of equilibrium in a local public goods economy with spatial structures by formalizing Hamilton's [Hamilton, B.W., 1975. Zoning and property taxation in a system of local governments Urban Studies 12, 205–211] elaboration of Tiebout's [Tiebout, C., 1956. A pure theory of local public expenditures. Journal of Political Economy 64, 416–424] tale. We use a well-known equilibrium concept from Rothschild and Stiglitz [Rothschild, M., Stiglitz, J.E., 1976. Equilibrium in competitive insurance markets: an essay on the economics of imperfect information. Quarterly Journal of Economics 40, 629–649] in a market with asymmetric information, and show that Hamilton's zoning policy plays an essential role in proving the existence and efficiency of equilibrium. We use an idealized large economy following Ellickson, Grodal, Scotchmer and Zame [Ellickson, B., Grodal, B., Scotchmer, S., Zame, W.R., 1999. Clubs and the market, Econometrica 67, 1185–1217] and Allouch, Conley and Wooders [Allouch, N., Conley, J.P., Wooders, M.H., The Tiebout Hypothesis: On the Existence of Pareto Efficient Competitive Equilibria, (2004), mimeograph]. Our theorem is directly applicable to the existence and efficiency of a discrete spatial approximation of mono- or multi-centric city equilibria in an urban economy with commuting time costs, even if we allow the existence of multiple qualities of (collective) residences, when externalities due to traffic congestion are not present.     

Real indeterminacy of equilibria and manipulability

In this paper, we analyze the indeterminacy of equilibria in financial markets and propose a selection mechanism. We suggest that there is one equilibrium that prevails over the others, as a result of the market power of the agents that some states of nature become monopolists of certain commodities. Given a financial assets model, we define a price game and show the existence of mixed strategies equilibria. Then we purify these equilibria by considering a price game with incomplete information.     

Stability and efficiency from a Neo-Keynesian viewpoint

This paper raises once more the Keynesian challenge of the classical doctrine that an unguided market economy has a natural tendency towards optimal employment of resources. By means of a simple macromodel, we show that if quantity expectations are incorporated into the Walrasian model, then it is no longer generally true that the ‘invisible hand’ leads the economy to Walrasian equilibrium. Instead, it may lead the economy to a kind of Keynesian equilibrium in which the firms' sales expectations constitute a binding constraint on production. Moreover, while Pareto optimum is unstable and hence unattainable in our model, a ‘second-best’ optimum among stable equilibria exists and requires a public sector. Accordingly, a trade-off between efficiency and other policy aims occurs only at tax rates above the positive tax rate in optimum     

Market selection with an endogenous state

This paper explores market selection in general equilibrium when the state of the economy is endogenous. Analysis of consumer survival in this case requires solution of the model’s dynamics, for which evolutionary game theory can be useful; for instance, if the state and beliefs are Markovian and utility logarithmic, then the dynamics of consumption shares are described by the replicator dynamics. This is illustrated in a simple exchange economy, and in a standard monetary economy with multiple long-run equilibria where a plausible form of inflation targeting serves to destabilize a liquidity trap in favor of the target equilibrium.     

Efficiency loss in a Cournot oligopoly with convex market demand

We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature.     

Housing markets with indivisibilities

A model of a rental housing market in which houses are treated as indivisible commodities is presented. A recursive equation that determines a competitive equilibrium is provided, and it is argued that this competitive equilibrium is representative of the set of all competitive equilibria. Using this representative equilibrium, several propositions on comparative statics are considered that have to do with how the competitive rents change when certain parameters of the model change.     

Inefficiency of equilibria with incomplete markets

As is well known, equilibria with incomplete markets are generically Pareto inefficient. In this paper, we demonstrate the leading role of a budget constraint in the occurrence of Pareto inefficiency of equilibria with incomplete markets. Specifically, on the basis of the classical two-period one-good pure exchange model we prove that so long as a budget constraint is met for all agents, equilibria with incomplete markets are generically Pareto inefficient in initial endowments and utility functions regardless of the optimization behavior of each agent. All we require of utility functions is a very weak hypothesis called current monotonicity. A simple unified method applicable to both a real asset case and a nominal asset case is presented, so that our claim is proved in both cases.     

Cost sharing: efficiency and implementation

We study environments where a production process is jointly shared by a finite group of agents. The social decision involves the determination of input contribution and output distribution. We define a competitive solution when there is decreasing-returns-to-scale which leads to a Pareto optimal outcome. Since there is a finite number of agents, the competitive solution is prone to manipulation. We construct a mechanism for which the set of Nash equilibria coincides with the set of competitive solution outcomes. We define a marginal-cost-pricing equilibrium (MCPE) solution for environments with increasing returns to scale. These solutions are Pareto optimal under certain conditions. We construct another mechanism that realizes the MCPE.     

Competing Platforms

Why do competing platforms or networks exist? This paper focuses on instances where the value of a platform depends on the adoption decisions of a small number of firms, and analyzes the strategic competition among platforms to get this oligopolistic side on‐board. I study a bilateral contracting game among platforms and firms that allows for general externalities across both contracting and noncontracting partners, and examine when a market will sustain a single or multiple platforms. When firms can join only one platform, I provide conditions under which market‐tipping and/or market‐splitting equilibria may exist. In particular, even without coordination failure, congestion effects, or firm multihoming, multiple platforms can co‐exist in equilibrium despite being inefficient from the perspective of the contracting parties. Expanding the contracting space to include contingent contracts may exacerbate this inefficiency.