Competitive Equilibrium Research Articles

Constrained Trading Networks

Trades based on bilateral (indivisible) contracts can be represented by a network. Vertices correspond to agents, whereas arcs represent the nonprice elements of a bilateral contract. Given prices for each arc, agents choose the incident arcs that maximize their utility. We enlarge the model to allow for polymatroidal constraints on the set of contracts that may be traded, which can be interpreted as modeling limited one-for-one substitution. We show that, for two-sided markets, there exists a competitive equilibrium; however, for multisided markets, this may not be possible. Funding: This work was supported by the Defense Advanced Research Projects Agency [Grant HR001118S0045].

Competition in Pricing Algorithms

We document new facts about pricing technology using high-frequency data, and we examine the implications for competition. Some online retailers employ technology that allows for more frequent price changes and automated responses to price changes by rivals. Motivated by these facts, we consider a model in which firms can differ in pricing frequency and choose pricing algorithms that are a function of rivals’ prices. In competitive (Markov perfect) equilibrium, the introduction of simple pricing algorithms can increase price levels, generate price dispersion, and exacerbate the price effects of mergers. (JEL D21, D22, D43, G34, L13, L81)

Partial secrecy in vertical contracting

This paper introduces a notion of partial secrecy in bilateral contracting games between one upstream firm and several competing downstream firms. The supplier’s offer quantities are subject to trembles, and each downstream firm observes a noisy signal about the offer received by its competitor before deciding whether to accept its offer. A downstream firm’s belief about its competitor’s quantity is determined endogenously as a weighted average of the competitor’s expected equilibrium quantity and the signal about the actual quantity that the competitor was offered. The degree of contract secrecy is captured by the weight that this belief puts on the competitor’s expected equilibrium quantity. We find that a higher degree of secrecy implies a more competitive equilibrium outcome, both in a game with simultaneous offers and in a dynamic game with alternating offers similar to the one in Do and Miklós-Thal (2022, “Opportunism in Vertical Contracting: A Dynamic Perspective,” CEPR Discussion Paper No. DP16951).

Production in Urban Environments

Abstract We analyze an urban economy with free entry of firms in which prices differ across locations. We show that in a competitive equilibrium, land rent is determined such that firms produce at constant returns to scale point—at minimum average costs. (JEL codes: R32 and R38)

Competition and Misconduct

ABSTRACTMisconduct is widespread. Practices such as misselling, pump and dump, and money laundering cause harm while raising profits. This paper presents a mechanism that can determine what sorts of misconduct can be sustained in competitive equilibrium in concentrated markets, oligopoly settings, and markets with many small competing firms. The model studied allows general demand and distinguishes types of ethical dilemma using current psychological understanding. The paper shows, for example, that markets with many small competing firms are not vulnerable to misconduct if firms respond to entry with niche strategies or if the ethical dilemma draws an emotional response.

Human capital and pensions with endogenous fertility and retirement

AbstractWe study an OLG model with child policies and a PAYG pension with endogenous retirement and fertility. The result of the planned economy is compared to the decentralized competitive equilibrium deriving optimal policies. We show that in the presence of a PAYG pension system, the optimal policy mix includes an education subsidy and a subsidy for the supply of labor in old age. Fertility should be taxed or incentivized depending on whether there is full or partial retirement, and on the parameters. We focus on the parameter reflecting the deterioration of human capital and show that a child tax may be required.

Stablecoins: Legal restrictions theory and monetary policy

This paper studies the effect of introducing stablecoins on monetary policy implementation. In the model, decentralized issuers can provide the monies by holding reserves and government bonds, but it is costly to monitor their collateral. The competitive equilibrium is suboptimal because the individual issuers cannot internalize the effect of issuing money on aggregate liquidity. In a channel system, the open-market operations are ineffective because the issuers can rewind it until there is no profit. However, the monetary policy is effective in a floor system and welfare can improve as the demand for money can be adjusted by the interest on reserves.

A spatial theory of urban segregation

AbstractWe provide a competitive equilibrium theory of urban segregation in a linear city. Households demand consumption and housing along the city and are exposed to neighborhood externalities. We show that equilibria that are robust to small coalitional deviations are segregated. Our results explain urban segregation in a standard neoclassical framework and shed new light on the difficulties faced by authorities to integrate cities.

Pricing in non-convex electricity markets with flexible trade-off of pricing properties

For the pricing in the non-convex electricity markets, the various pricing properties including supporting a competitive equilibrium, non-discrimination, cost recovery of participants, and revenue adequacy of the market operator can hardly be simultaneously fulfilled. Current pricing methods cannot balance these properties because there lacks a computationally tractable pricing model that explicitly formulates these properties as objective functions or constraints. In this paper, we propose a pricing optimization model taking prices as decision variables and taking important pricing properties as objective functions or constraints. Based on duality theory, the Karush-Kuhn-Tucker conditions of the self-dispatch problem processed by convex relaxation are extended to construct the constraints related to supporting a competitive equilibrium. Taking advantage of the modeling flexibility, the constraints for non-discrimination, cost recovery, and revenue adequacy are established. The delicately designed pricing optimization model is a linear programming problem with an acceptable computational burden. It applies to the market clearing problem with non-convexity, time-coupling and network transmission characteristics. To be specific, the application of the proposed pricing method for the unit commitment problem is provided. The reasonability, scalability, and tractability of the proposed approach are illustrated in systems with over 2000 buses. Numerical experiments show that the proposed method shows better performance compared with other representative pricing methods.

Social transition, economic development and gender-based wage disparity in a developing economy.

A four-sector competitive general equilibrium model has been developed with both male and female labour in presence of capital market distortion to analyse the effect of social transition on female labour force participation and gender-based wage inequality. The analysis finds that although gender wage inequality worsens in the existing structure, the consequence on female participation in the workforce depends on the stage of social transition. While it falls in the early stages, it begins to rise once a certain critical level of transition is crossed. Finally, we have advocated in favour of a policy that can effectively speed up the process of social transition thereby gender empowerment.

How does market competition affect supplier-induced demand? An experimental study.

This study investigated the impact of competition on supplier-induced demand in medical markets theoretically and experimentally. We employed the framework of credence goods to describe the information asymmetry between physicians and patients, and theoretically derives predictions of physicians' behaviors in monopolistic and competitive markets. Then we conducted behavioral experiments to empirically test the hypotheses. The theoretical analysis revealed that an honest equilibrium would not exist in a monopolistic market, whereas price competition could induce physicians to reveal their types of treatment cost and provide honest treatments; thus, a competitive equilibrium is superior to that of a monopolistic market. The experimental results only partially supported the theoretical predictions, which showed that the cure rate of patients in a competitive environment was higher than that in a monopolistic market, although supplier-induced demand occurred more frequently. In the experiment, the main channel through which competition improved market efficiency was increased patient consultations through low pricing, as opposed to the theory, which stated that competition would lead to physicians' honest treatment of patients through fair prices. We discovered that the divergence between the theory and the experiment stemmed from the theory's reliance on the assumption that humans are rational and self-interested, which means that they are not as price-sensitive as predicted by theory.

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.

COMPETITIVE MARKET BEHAVIOR: CONVERGENCE AND ASYMMETRY IN THE EXPERIMENTAL DOUBLE AUCTION

AbstractWe conducted a large number of controlled continuous double auction experiments to reproduce and stress‐test the phenomenon of convergence to competitive equilibrium under private information with decentralized trading feedback. Our main finding is that across a total of 104 markets (involving over 1,700 subjects), convergence occurs after a handful of trading periods. Initially, however, there is an inherent asymmetry that favors buyers, typically resulting in prices below equilibrium levels. Analysis of over 80,000 observations of individual bids and asks helps identify empirical ingredients contributing to the observed phenomena including higher levels of aggressiveness initially among buyers than sellers.

Implicit Tax, Tax Incidence, and Pretax Returns

ABSTRACTWe investigate the relation between tax rates and pretax returns by showing how implicit tax, tax incidence, and tax capitalization change in response to a tax rate change. We examine these issues in the context of both financial assets and real investments made by corporations in a competitive equilibrium in which all investments earn the same after-tax rate of return. Results show that the pretax return increases in the statutory tax rate due to an explicit tax rate effect and decreases due to a cost of capital effect; the net effect is ambiguous. In contrast, the implicit tax rate is weakly increasing in the statutory tax rate. We also relate our findings to the empirical literature on the effects of taxes on pretax returns.JEL Classifications: H22; H25.

Factor Misallocation and Optimization in China’s Manufacturing Industry

Factor allocation has an important impact on production efficiency, and this study discusses factor misallocation and proposes an optimized method that could improve efficiency and reduce factor inputs. Under a multi-industry competitive equilibrium model, by introducing distortion tax that represents frictions on factor inputs (capital, labor, energy, and other intermediate consumption), we define factor price distortion indexes to measure factor misallocation and set the standardized comprehensive distortion index at the optimal value of one to obtain optimized allocation of each factor. Using actual and optimized inputs, we compute input-oriented efficiencies separately by employing a slack-based measurement data envelopment analysis (SBM-DEA). The superiority of the new allocation method is tested by comparing changes in efficiency and input redundancy before and after optimization. An empirical test based on China’s manufacturing sector during 1999–2016 shows that, under the optimized reallocation, on average, efficiency is improved by 43.40%, capital, labor, energy, and other intermediate consumption are reduced by 18.06%, 16.34%, 30.91%, and 31.24%, respectively, and the total carbon emission is reduced by 55.22% from 2000 to 2016. Our results imply that factor misallocation causes losses in efficiency and excessive input of factors, and factor allocation needs to be further optimized for sustainable development.

Preface

Preface

From Debt to Green Growth: A Policy Proposal

Concurrent and overlapping crises, such as the COVID-19 pandemic and increases in energy and food costs, are particularly affecting developing and poor countries, in addition to the continuous and growing negative impacts from climate change. In this paper, we develop a policy proposal and show through a model how an implicit debt servicing standstill for a country with large external debt can be combined with a policy for promoting power generation from renewable energy sources, with positive effects for economic growth and for ensuring debt sustainability. Through a typical decentralized competitive general equilibrium endogenous growth model, we show the long term effects of partially redirecting debt payments to green energy infrastructure to facilitate economic growth and achieve a sustained debt-to-output level. The results indicate that a higher percentage of external public debt increases public capital accumulation, resulting in a higher long-run growth rate, albeit with a slower transition to a steady state. Equivalent results are found regarding the level of financial aid provided for public productive capital.

The Weak Hybrid Equilibria of an Exchange Economy with a Continuum of Agents and Externalities

Abstract Inspired by Zhao, J. 1996. “The Hybrid Equilibria and Core Selection in Exchange Economies with Externalities.” Journal of Mathematical Economics 26 (4): 387–407, Askoura, Y. 2011. “The Weak-Core of a Game in Normal Form with a Continuum of Players.” Journal of Mathematical Economics 47: 43–7, Askoura, Y. 2017. “On the Core of Normal Form Games with a Continuum of Players.” Mathematical Social Sciences 89: 32–42, Yang, Z. 2020. “The Weak α-core of Exchange Economies with a Continuum of Players and Pseudo-utilities.” Journal of Mathematical Economies 91: 43–50 and Yang, Z., and X. Zhang. 2021. “A Weak α-core Existence Theorem of Games with Nonordered Preferences and a Continuum of Agents.” Journal of Mathematical Economics 94: 102464, we establish an exchange economy with externalities and a continuum of agents. We define the weak hybrid equilibrium in this model and prove the existence theorem under the regular conditions. Furthermore, we analyze the relation between the set of hybrid equilibria and the set of competitive equilibria in an exchange economy without externalities and with a continuum of agents.

Protecting nature's most effective carbon sink: an important role for fungi in peatlands.

This article is a Commentary on Shao et al. (2023), 238: 80–95.

Price Competition in a Vertizontally Differentiated Duopoly

This paper develops a price competition duopoly model in which products are both horizontally and vertically differentiated. Firms each offer a standard and a premium product to buyers—some of whom are brand loyal. We establish the existence of a unique and symmetric competitive pricing equilibrium. Equilibrium prices are increasing in the degree of horizontal differentiation and the number of brand-loyal customers. The equilibrium price of the standard (premium) good is decreasing (increasing) in the quality difference and profits can increase in costs when this difference is large enough. If the pricing decision is taken at the product (division) level, then there is again a unique (and symmetric) competitive pricing equilibrium. Equilibrium prices and profits are lower than in the centralized case and demand for the standard product is higher when the quality difference is sufficiently large. Welfare is unambiguously lower with decentralized pricing.