Pure Exchange Economy Research Articles

Sequential trading with coarse contingencies

We consider a dynamic pure exchange economy in which agents have a coarse perception of the future, and awareness emerges gradually over time. We make the key assumption that awareness of a shock to agents' endowments emerges before the shock hits, so agents can adapt by purchasing (or selling) insurance. We provide an irrelevance theorem showing that, under suitable conditions, unawareness matters if and only if it concerns aggregate shocks. In particular, if the unforeseen endowment shocks are purely idiosyncratic, there is no loss of efficiency with respect to the economy with perfect foresight. Building on this result, we show three key implications of unforeseen aggregate shocks: the possibility of non-comonotonic consumption allocations, a systematic bias in asset prices that gives rise to opportunities for intertemporal arbitrage, and the potential of unexpected default due to the agents' inability to repay (roll over) prior debt.

Endowments, patience types, and uniqueness in two-good HARA utility economies

This paper establishes a link between endowments, patience types, and the parameters of the HARA Bernoulli utility function that ensure equilibrium uniqueness in an economy with two goods and two impatience types with additive separable preferences. We provide sufficient conditions that guarantee uniqueness of equilibrium for any possible value of γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} in the HARA utility function γ1-γb+aγx1-γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{\\gamma }{1-\\gamma }\\left( b+\\frac{a}{\\gamma }x\\right) ^{1-\\gamma }$$\\end{document}. The analysis contributes to the literature on uniqueness in pure exchange economies with two-goods and two agent types and extends the result in Loi and Matta (2022).

(No-)Betting Pareto Optima Under Rank-Dependent Utility

In a pure-exchange economy with no aggregate uncertainty, we characterize in closed form and full generality Pareto-optimal allocations between two agents who maximize (nonconcave) rank-dependent utilities (RDU). We then derive a necessary and sufficient condition for Pareto optima to be no-betting allocations (i.e., deterministic allocations or full insurance allocations). This condition depends only on the probability weighting functions of the two agents and not on their (concave) utility of wealth. Hence, with RDU preferences, it is the difference in probabilistic risk attitudes given common beliefs rather than heterogeneity or ambiguity in beliefs that is a driver of betting behavior. As by-product of our analysis, we answer the question of when sunspots matter in this economy. Funding: M. Ghossoub acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada [Grant 2018-03961].

General Equilibrium in a Heterogeneous-Agent Incomplete-Market Economy with Many Consumption Goods and a Risk-Free Bond

General equilibrium models have been extensively studied in economics, with seminal works by Arrow, Debreu, McKenzie, Gale, and Nikaido providing a proof for the existence of general equilibrium in a pure exchange economy. However, while the recently popular dynamic incomplete-markets models have attracted attention, the existence results for these models have remained limited. In “General equilibrium in a heterogeneous-agent incomplete-market economy with many consumption goods and a risk-free bond,” Light extends some general equilibrium results to a dynamic incomplete-market economy with many consumption goods and a risk-free bond. Under mild conditions, using a well-known excess demand approach, the article establishes the existence of general equilibrium, showing that the methods used to prove existence in the static pure exchange economy can be used in the much more complicated dynamic incomplete-market setting. The article also establishes uniqueness and comparative statics results for the special case where the agents’ preferences can be represented by a constant elasticity of substitution utility function with an elasticity of substitution greater than or equal to one.

Existence of an equilibrium in arrowian markets for consumption externalities

We study the existence of quasi-equilibria and equilibria for pure exchange economies with consumption externalities and Arrowian markets with personalized Lindahl prices. We provide examples showing first that quasi-equilibria and equilibria of the externality economy fail to exist under assumptions guaranteeing existence for economies without externalities. We show that the externality economy has identical equilibrium allocations of an appropriately defined constant returns to scale production economy without externalities. We exploit this equivalence to map sufficient conditions for the existence of quasi-equilibria and equilibria of the production economy into sufficient conditions of the pure exchange economy with externalities, thereby unveiling suitable irreducibility conditions and survival conditions.

Sufficient conditions for a “simple” decentralization with consumption externalities

We consider a pure exchange economy with consumption externalities in preferences. We use the notion of competitive equilibrium à la Nash. We provide the Social Redistribution assumption to restore the Second Welfare Theorem. We then introduce the differentiable characterizations of Social and Strong Redistribution. We show that all these conditions are weaker than other relevant assumptions studied in the literature. Our conditions entail interesting results on the decentralized implementation of Pareto optima, that link together the competitive supporting price and the shadow price of the utilitarian social planner. Finally, we provide a specific condition for Bergson-Samuelson utility functions, which has a nice interpretation in terms of positive or negative externalities.

A real effect across time: disclosure quality, cost of capital and profitability

PurposeIn the presence of “real effects” of disclosure in a production economy, this research aims to investigate the link between disclosure and cost of capital relating to different time periods: namely the post-disclosure cost of capital (the cost of capital subsequent to disclosure), the pre-disclosure cost of capital (the cost of capital for the period leading up to disclosure) and the overall cost of capital (the cost of capital across both periods). The author also extends the analysis to whether and how in the presence of a real effect of disclosure, investors' ex ante welfare might be affected.Design/methodology/approachThis research is conducted via stylized models.FindingsThe author demonstrates that, first, in contrast to findings in a pure-exchange economy, in a production-based economy where disclosure affects firms' investment decisions, both the overall cost of capital and the investors' ex ante welfare can be affected by disclosure quality. As disclosure quality improves, the post-disclosure cost of capital may either increase or decrease, as may the pre-disclosure cost of capital. The change in the post-disclosure cost of capital is not fully offset by the change in the pre-disclosure cost of capital, and therefore the overall cost of capital can either increase or decrease. Second, a firm's profitability of existing and new production are critical factors in determining whether cost of capital increases or decreases with disclosure quality. The author characterizes conditions under which higher disclosure quality increases or decreases the disclosing firm's cost of capital over different time periods. Third, when disclosure affects interrelated firms' production decisions, the disclosing firm's overall cost of capital changes with disclosure quality, even when the marginal (unconditional) distribution of the disclosing firm's cash flow is not affected by the disclosure.Originality/valueThis research contributes to a largely unexplored but important area: the real effect of disclosure on the cost of capital.

Two characterizations of cost share equilibria

We consider pure exchange economies with a finite number of private goods and the choice of non-Samuelsonian public goods. For this type of economies, [5] proposed the notion of cost share equilibrium with individual payments for public goods varying according to individual benefits. This situation arises naturally when a level of provision is interpreted as a whole configuration of public policies or when cost share functions are interpreted as voluntary contributions rather than predetermined tax systems (see [31]). We establish the equivalence of cost share equilibria with cooperative and non-cooperative game-theoretic solutions: 1. we characterize cost share equilibria as those allocations which cannot be improved upon by society; 2. we characterize cost share equilibria as the Nash equilibria of a game with two players. The cooperative solutions analyzed in the paper are defined via a contribution scheme which captures the fraction of the total cost of collective goods that each coalition of agents is expected to cover.

Filling the gap and moving forward: a review of analytical and empirical studies of disclosure and cost of capital

PurposeThe author in this paper identifies the gap between analytical and empirical studies regarding the relation between disclosure and cost of capital. Distinct from prior reviews, this paper focuses on the various assumptions of theoretical models and the insights and key results derived from those assumptions. The author also reviews how these theoretical papers are “applied” in empirical studies.Design/methodology/approachThe author systematically analyzes both theoretical and empirical papers that investigate disclosure and cost of capital between 2000 and 2020.FindingsThe author shows (1) that there is ample room for theorists to move from the pure exchange economy to the production-based economy setting to investigate the real effect of disclosure on the cost of capital; (2) structural estimation, although still nascent, is a promising direction to build the bridge between analytical and empirical studies in disclosure and cost of capital, and (3) besides ordinary least squares (OLS) regressions, researchers are encouraged to think outside the box regarding how to investigate the interplay between disclosure and cost of capital via a Deep Neural Network design.Originality/valueThe author provides a unique perspective and synthesized knowledge in the relations of disclosure and cost of capital.

Truthfulness of a Network Resource-Sharing Protocol

We consider a sharing economy over a network in which each vertex agent allocates resources to its neighbors in response to their contributions. General equilibrium theory can be applied here to solve the problem of deciding how to fairly and efficiently allocate resources among agents as resource sharing over the network can be modeled as a pure exchange economy. It is known that proportional sharing dynamics converges to a market equilibrium solution. We are particularly interested in proportional sharing dynamics as a mechanism for network resource sharing. Our focus is on the key issue in internet market design: whether an agent may manipulate its report of its own private information to gain more resources under this mechanism. This work establishes the first mathematical proof that such a practical distributed network resource-sharing protocol is truthful against the manipulative strategies of feasible weight misreporting and edge deletion applied both individually and together. Funding: This work was supported by the National Nature Science Foundation of China [Grants 11871366, 62172012]; Beijing Outstanding Young Scientist Program [Grant BJJWZYJH012019100020098]; the Fundamental Research Funds for the Central Universities; the Research Funds of Renmin University of China [Grant 297522503709]; and the Intelligent Social Governance Platform, Major Innovation & Planning Interdisciplinary Platform for the “Double-First Class” Initiative, Renmin University of China.

General Equilibrium with Price Adjustments—A Dynamic Programming Approach

This research article develops a dynamic framework for the Walrasian pure exchange economy and thus extends the static Walrasian general equilibrium theory into a dynamic one with price adjustments. An evolution equation for the price vector is derived from dynamic programming considerations. The economy tries to move from disequilibrium to general equilibrium by minimizing certain cost functional. The cost functional measures transactions costs and the total expenditure of agents when they optimize individually. Price determination is directly related to a gradient search. The general equilibrium is shown to be stable in the sense of Lyapunov if price adjustments can be large, when needed. The conditional stability could be one reason for volatility clustering in financial time series.

The proportional ordinal Shapley solution for pure exchange economies

We define the proportional ordinal Shapley (the POSh) solution, an ordinal concept for pure exchange economies in the spirit of the Shapley value. Our construction is inspired by Hart and Mas-Colell's (1989) characterization of the Shapley value with the aid of a potential function. The POSh exists and is unique and essentially single-valued for a fairly general class of economies. It satisfies individual rationality, anonymity, and properties similar to the null-player and null-player out properties in transferable utility games. The POSh is immune to agents' manipulation of their initial endowments: It is not D-manipulable and does not suffer from the transfer paradox. Moreover, we characterize the POSh through a Harsanyi's (1959) system of dividends and, when agents' preferences are homothetic, through a weighted balanced contributions property à la Myerson (1980).

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

AbstractDebreu and Scarf (1963), Hildenbrand (1974), Aumann (1964), Dierker (1975), Bewley (1973), and others have shown that the core of an exchange economy with infinitely many or finitely many traders converges. However, an exchange economy does not always consist of infinitely many or finitely many traders. This note provides proof of the core convergence theorem on an exchange economy with limited traders by a bargaining game methodology. The main contribution of this note is to innovate the equilibrium solution to the bargaining game in the exchange economy. In this note, the concept of common payoff is introduced; in the bargaining game of a coalition on its common payoff, all coalition members will get the same distribution, thus the distribution scheme of the cooperation surplus of the exchange economy is determined.This note shows that the bargaining game among the traders on the distribution of the cooperation surplus will make the pure exchange economy with limited traders converge to the Walrasian equilibrium, all the allocations other than the Walrasian equilibrium will be eliminated from the core of this economy.

Remarks on criticality and crisis in pure exchange economies

Remarks on criticality and crisis in pure exchange economies

Fixed price equilibria on peer‐to‐peer platforms: Lessons from time‐based currencies

There are many online platforms for peer-to-peer exchange that introduce a platform-specific currency and fix prices to some extent. We model such platforms as pure exchange economies and characterize all fixed price equilibria. We demonstrate the inherent inefficiency following from the combination of fixed prices and voluntary trade and show that simple additional Pareto improving trades exist. While our theoretical analysis predicts that fixed prices lead to less trade than competitive prices, we also discuss some potential advantages of price restrictions, in particular, with respect to simplicity and fairness considerations. Strikingly, it is not those agents with the most attractive goods who have the highest willingness to participate in a fixed price platform. In an empirical illustration, we explore how these theoretical insights unfold in reality by describing patterns of several platforms covering around 100k transactions. This work is informative for the market design of peer-to-peer platforms and for markets with price restrictions more generally.

Transfer paradox in a general equilibrium economy: An experimental investigation

The transfer paradox, whereby a transfer of resources that influences the equilibrium price benefits the donor while harming the recipient, is a classic paradox in general equilibrium theory. This paper pursues an experimental investigation of the transfer paradox using a three-agent pure exchange economy that is predicted to have such a paradox. The results indicate that an endowment adjustment among agents influences the market price, and consequently the donors benefit from the transfer, consistent with the competitive equilibrium theory. When given an option to make a transfer, half of donor agents voluntarily decide to adjust the endowment distribution.

Constructing pure-exchange economies with many equilibria

Constructing pure-exchange economies with many equilibria

Dropping rational expectations

We consider a two-period pure-exchange economy, where uncertainty prevails and agents, possibly asymmetrically informed, exchange commodities and securities of all kinds. Consumers’ characteristics, anticipations, beliefs and actions are all private and typically not known nor assessed by the other agents. This setting drops rational expectations along the ‘common knowledge of rationality and market clearing’ (CKRMC) assumptions, and, in particular, it drops the Radner (1979) price model and price inference assumptions. Unaware agents are shown to face an incompressible uncertainty over future states and prices, represented by a so-called ”minimum uncertainty set”. A sequential equilibrium obtains when agents expect the ‘true’ price as a possible outcome on every spot market, and elect optimal market-clearing strategies. This so-called ”correct foresight equilibrium” (CFE) is shown to exist whenever agents’ anticipation sets include the minimum uncertainty set. When the CKRMC assumptions are restored, the CFE is shown to lead to an overarching concept of rational expectations equilibrium, which generalizes the classical concepts.

Gainers and losers from market integration

We compare integration of economic, matching and networking markets. There can be losers from integration in all three cases, but their relative numbers depend on the type of market. There can be many losers from integration of pure exchange economies. There are relatively few losers from integration of networking markets. In the matching case, the relative numbers tend to lie between those of the other two cases. In particular, in the grand economy of matching markets, there are weakly more non-losers than losers, and with strict preferences there are weakly more gainers than losers.

Minimal entropy and uniqueness of price equilibria in a pure exchange economy

We introduce uncertainty into a pure exchange economy and establish a connection between Shannon’s differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and, under certain conditions, for an arbitrary number of consumers and two goods.