Competitive Equilibrium Research Articles

Numerical analysis of the disequilibrium monetary growth model: secular stagnation, slow convergence, and cyclical fluctuations

This study presents a monetary disequilibrium growth model and conducts numerical simulations to investigate how dynamic paths are affected by the initial conditions and the parameters of expectation formation. The main results are as follows. First, dynamic properties such as stable convergence and cyclical fluctuations depend on the type of expectation formation rather than on the initial regimes. Stable convergence takes an excessively long time when expectation formation is too rational and cyclical fluctuations appear when it is too adaptive. Second, when the economy converges to the steady state (i.e., the Walrasian equilibrium), persistent Keynesian unemployment is likely to appear along the dynamic path. Third, the dynamics of inflation expectation that contain the price dynamics in the feedback loop might play an important role in convergence to the steady state.

A Note on Unemployment of Unskilled Labor due to COVID-19 led Restriction on Migration and Trade

Abstract To combat COVID-19 the entire world has resorted to global lockdown implying restriction on international labor migration and trade. This paper aims to check the effect of such restrictions on the unemployment of unskilled labor in the source country. In competitive general equilibrium framework with three goods and four factors, restriction on migration raises unemployment for given factor intensity. The results remain same even in a slightly different structure of the economy. In case of trade restriction, however, the rise or fall in unemployment depends on both the structure of the economy and the factor intensity assumption.

Directed Search and Competitive Search Equilibrium: A Guided Tour

This essay surveys the literature on directed search and competitive search equilibrium, covering theory and a variety of applications. These models share features with traditional search theory, but also differ in important ways. They share features with general equilibrium theory, but with explicit frictions. Equilibria are often efficient, mainly because markets price goods plus the time required to get them. The approach is tractable and arguably realistic. Results are presented for finite and continuum economies. Private information and sorting with heterogeneity are analyzed. While emphasizing issues and applications, we also provide several hard-to-find technical results. (JEL D50, D83)

External Habits Formation and the Environment

Abstract The present paper presents a standard overlapping generations model with external habits formation and environmental quality in the utility function. Our main objective is to study the impact of external habits on capital accumulation and environmental quality on the intertemporal competitive equilibrium. We notice that striving for status leads to environment worsening and capital increasing when the cohort size is large.

Biased preferences equilibrium

AbstractWe model economic environments in which individual choice sets are fixed and the level of a specific parameter that systematically modifies the preferences of all agents is determined endogenously to achieve equilibrium. The equilibrium concept, Biased Preferences Equilibrium, is reminiscent of competitive equilibrium: agents’ choice sets and their preferences are independent of the behaviour of other agents, the combined choices must satisfy overall feasibility constraints and the endogenous adjustment of the equilibrating preference parameter is analogous to equilibrating price adjustment. The concept is applied in a number of economic examples.

Wage Inequality and Unemployment in the Presence of Imported Intermediate Goods: A Theoretical Analysis

This article develops a static three-sector and five-factor competitive general equilibrium model of a small open economy: sector 1 is the rural agricultural sector, which produces products using informal or unorganised unskilled labour and land as inputs; sector 2 is the urban manufacturing, final-goods-producing sector that produces products with the help of unskilled labour, who get unionised wages, and capital; and sector 3 is the service sector, which uses skilled labour with formal wages, capital and sophisticated hi-technology-intensive imported intermediate goods produced abroad as inputs. We show that an exogenous increase in capital inflow or an increase in tariff on imported intermediate input reduces the skilled–unskilled wage inequality and lowers unemployment as long as the return to capital is unaltered and output adjustments absorb the entire shock of the two policies. Such capital inflow increases rural wage and reduces unemployment via the Harris Todaro mechanism but interestingly does not allow the skilled wage to increase. Thus, two critical policy targets can be accommodated at the same time. JEL Codes: F13, J31, J46

An incentive efficient market for mechanisms in large Akerlof economies

We study ‘Akerlof economies’, that is, economies where goods come in qualities unknown to buyers, and sellers’ quality can be ranked. Cross-subsidies at the constrained efficient allocation arise, even when there are few high-quality types in the economy. Thus, Akerlof’s markets are poorly suited to deliver constrained efficient outcomes. We then design a competitive market for mechanisms. Agents buy lottery tickets to enter mechanisms, and the price system clears the markets. Firms offer tickets to mechanisms on the basis of ‘input’ prices which, unlike in Akerlof’s competitive markets, are quality dependent. Under standard sorting conditions, we show that a ‘no-price-cut’ competitive equilibrium exists and is incentive efficient.

Randomized double auctions: gains from trade, trader roles, and price discovery

Experimental double-auction commodity markets are known to exhibit robust convergence to competitive equilibria under stable or cyclical supply and demand conditions, but little is known about their performance in truly random environments. We provide a comprehensive study of double auctions in a stochastic setting where the equilibrium prices, trading volumes and gains from trade are highly variable across periods, and with commodity traders who may buy or sell their goods depending on market conditions and their individual outcomes. We find that performance in this stochastic environment is sensitive to underlying market conditions. Efficiency is higher and convergence to the competitive equilibrium stronger when the potential gains from trade are high and when the equilibrium spans a wide range of quantities, implying a large number of marginal trades. Speculative re-trading is prevalent, especially among those who have little to gain under equilibrium pricing. Those with the largest expected gains typically earn far less than predicted, while those with little or no predicted earnings gain modestly from speculation, leading to some redistribution of gains from high to low expected earners. Excessive trading volumes are associated with negative efficiencies in markets with low gains from trade, but not in the high-gains markets, where zero-sum trading and re-trading appear to enforce efficiency and near-equilibrium pricing. Buyers earn more relative to their competitive equilibrium benchmark than sellers do. Introducing trader specialization leads to fewer trading errors and higher market efficiency, but it does not eliminate zero-sum trading and re-trading.

On equilibrium in monopolistic competition with endogenous labor

We consider a model of monopolistic competition with several heterogeneous sectors and endogenous labor supply. For low (high) values of the labor supply elasticity, we show that there is always a unique equilibrium. For medium values of the labor supply elasticity, there are either zero or two equilibria.

Competitive Equilibrium with Indivisible Goods and Generic Budgets

Competitive equilibrium from equal incomes (CEEI) is a classic solution to the problem of fair and efficient allocation of goods (Foley 1967, Varian 1974). Every agent receives an equal budget of artificial currency with which to purchase goods, and prices match demand and supply. However, a CEEI is not guaranteed to exist when the goods are indivisible even in the simple two-agent, single-item market. Yet it is easy to see that, once the two budgets are slightly perturbed (made generic), a competitive equilibrium does exist. In this paper, we aim to extend this approach beyond the single-item case and study the existence of equilibria in markets with two agents and additive preferences over multiple items. We show that, for agents with equal budgets, making the budgets generic—by adding vanishingly small random perturbations—ensures the existence of equilibrium. We further consider agents with arbitrary nonequal budgets, representing nonequal entitlements for goods. We show that competitive equilibrium guarantees a new notion of fairness among nonequal agents and that it exists in cases of interest (such as when the agents have identical preferences) if budgets are perturbed. Our results open opportunities for future research on generic equilibrium existence and fair treatment of nonequals.

Data-Driven Planning of Electric Vehicle Charging Infrastructure: A Case Study of Sydney, Australia

With the increase of vehicle travelling range and the decrease of vehicle expense, Electric Vehicles (EVs) are gaining popularity as a new transport option which offers a great opportunity for creating a smart city in terms of transportation electrification. However, the existing research of EV charger planning primarily concentrates on the optimal location seeking from a perspective of global optimization. To achieve a competitive strategy in future, a market-based mechanism is proposed for the problem of EV charger planning with a case study of Sydney where a predict-then-optimise diagram is introduced to predict the EV charging demand by a multi-relation graph convolutional network (GCN)-based encoder-decoder deep architecture and optimise the competitive resource allocation strategy for the charger planning through a Cournot competition game model. A new parallel computational algorithm is proposed to seek the Cournot competition equilibrium with the convergence analysis. Furthermore, the optimal EV charger sizing problem is considered to obtain each service provider’s EV charger number at each zone of the city. Experiments are implemented by using the Sydney public transportation dataset and the corresponding key economic indicators. The results show the effectiveness of our proposed approach which can fill the gap between data and the optimal EV charging infrastructure planning.

Emigration, Tax on Remittances and Export Quality

We examine the implications of the emigration of unskilled workers for the quality of a skill-based good exported by a small open economy. This issue is relevant in the context of quality constraints faced by the developing countries like China and India in promoting their exports, on the one hand, and the significantly large emigrations of workers, particularly unskilled workers, which lower their productive capacities, on the other hand. We show that even though unskilled workers are not directly used in the production of quality-differentiated export goods, their emigration would lower export quality when quality upgradation requires more intensive use of skilled workers relative to capital. This result follows from the complementarity between skilled and unskilled wages in a competitive general equilibrium model. A quality-content production subsidy in such a case can mitigate the adverse effects of emigration. The significantly large remittances received from unskilled emigrants create scope for taxing such remittances to finance the subsidy. JEL Classification: F16, F20, F22, F24

Incentive-based coordination mechanism for distributed operation of integrated electricity and heat systems

Pipeline energy storage in district heating networks (DHNs) has shown to be capable of improving energy efficiency in an integrated electricity and heat system (IEHS). However, most electric power networks (EPNs) and DHNs are managed by different entities, while the incentives inducing such flexibilities from DHNs have been seldom discussed. This paper fills the research gap by investigating price incentives offered by EPNs to encourage DHN operators to fully utilize pipeline energy storage. Individual interests of EPNs and DHNs are addressed via a bi-level model, where the EPN operator determines the best price incentive based on optimal power flow (OPF) in the upper-level, while the lower-level problem describes the optimal response of the DHN operator based on optimal thermal flow (OTF). To preserve the privacy of DHNs in distributed operation, a reduced and accurate OTF model is then proposed where internal states are eliminated and system parameters are not exposed, which also relieves model complexity. Finally, a price-quantity decomposition method along with warm-start strategies are proposed to solve the reduced bi-level model, and the solution obtained is interpreted as the equilibrium of Stackelberg competition between EPNs and DHNs. Case studies of two IEHSs validate that the proposed decomposition method can efficiently reach Stackelberg equilibrium in a distributed setting, while the introduced incentive-based coordination mechanism can effectively improve social welfare by lowering total costs in both EPNs and DHNs.

Optimal fiscal policies and market structures with monopolistic competition

This paper develops a unified imperfectly competitive macroeconomic model, and uses it to analyze optimal fiscal policies in the presence of market imperfections. The salient feature of the model is that it is able to deal with three distinct types of market structure, including constant monopoly firms, endogenous monopoly firms and endogenous overhead costs. Several findings emerge from the analysis. First, the extent of production externalities will vary under the three distinct market structures, and in turn lead the government to implement different labor and capital tax policies to correct the different extents of the distortions. Second, the optimal ratio of government expenditure is determined solely by the extent of productive government spending if the number of firms is constant, while the optimal ratio is related to the internal increasing returns to scale and production specialization if the number of firms is determined endogenously. Finally, free entry in the competitive equilibrium may result in over entry or under entry, depending upon the relative degree between monopoly power and production specialization.

Decomposition Algorithms for Some Deterministic and Two-Stage Stochastic Single-Leader Multi-Follower Games

We consider a certain class of hierarchical decision problems that can be viewed as single-leader multi-follower games, and be represented by a virtual market coordinator trying to set a price system for traded goods, according to some criterion that balances supply and demand. The objective function of the market coordinator involves the decisions of many agents, which are taken independently by solving convex optimization problems that depend on the price configuration and on realizations of future states of the economy. One traditional way of solving this problem is via a mixed complementarity formulation. However, this approach can become impractical when the numbers of agents and/or scenarios become large. This work concerns agent-wise and scenario-wise decomposition algorithms to solve the equilibrium problems in question, assuming that the solutions of the agents’ problems are unique, which is natural in many applications (when solutions are not unique, the approximating problems are still well-defined, but the convergence properties of the algorithm are not established). The algorithm is based on a previous work of the authors, where a suitable regularization of solution mappings of fully parameterized convex problems is developed. Here, we show one specific strategy to manage the regularization parameter, extend some theoretical results to the current setting, and prove that the smooth approximations of the market coordinator’s problem converge epigraphically to the original problem. Numerical experiments and some comparisons with the complementarity solver PATH are shown for the two-stage stochastic Walrasian equilibrium problem.

Competitive Equilibrium and Trading Networks: A Network Flow Approach

This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In “Competitive Equilibrium and Trading Networks: A Network Flow Approach,” Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability.

Nash Equilibrium to Competitive Equilibrium Mechanisms Design: Subsidization and Punishment

Due to the small number of participants in realistic cases, the Nash equilibrium generated by an oligopolistic market is more appropriate for depicting the actual energy market than the competitive equilibrium generated by a competitive market. However, the market efficiency decreases when the Nash equilibrium is used rather than the competitive equilibrium because of the strategic behaviors of the participants. In this paper, we propose two new mechanisms (subsidization and punishment) for each generator, both of which drive the Nash equilibrium to the competitive equilibrium in heterogeneous oligopolistic energy markets with a uniform pricing mechanism. Under the two proposed mechanisms, the equivalence of the Nash equilibrium and the competitive equilibrium is strictly proven. Furthermore, we apply a distributed algorithm to numerically confirm that both mechanisms perfectly eliminate the market efficiency loss. Finally, these two mechanisms are applied to the energy market under three different stages of development. Simulation results illustrate that the additional costs caused by the mechanisms converge to a low value and that the subsidization mechanism slightly outperforms the punishment mechanism.

General equilibrium of Bertrand game: A spatial computational approach

<abstract> In this paper, the competitive equilibrium of the Bertrand game is discussed with bounded rationality and the utility function. When the parameters changing and the number of firms increasing, the competitive equilibrium valve of Bertrand duopoly game is gradually being blurred. When the number of competitors is more than four, it is very difficult to derive the value of the equilibrium points. How to find the general competitive equilibrium points for Bertrand game, which is studied from spatial agglomeration with mean value theorem. A Bertrand duopoly game is proposed based on a demand function. Celestial bodies motion as method is introduced to handle the number and stability of competitive equilibrium points, and the stable points is symmetry. The results are supported by numerical computation and simulations. </abstract>

On the Foundations of Competitive Search Equilibrium with and Without Market Makers

The literature offers two foundations for competitive search equilibrium, a Nash approach and a market-maker approach. When each buyer visits only one seller (or each worker makes only one job application), the two approaches are equivalent. However, when each buyer visits multiple sellers, this equivalence can break down. Our paper analyzes competitive search equilibrium with simultaneous search using the two approaches. We consider four cases defined by (i) the surplus structure (are the goods substitutes or complements?) and (ii) the mechanism space (do sellers post fees or prices?). With fees, the two approaches yield the same constrained efficient equilibrium. With prices, the equilibrium allocation is the same using both approaches if the goods are complements, but is not constrained efficient. In the case in which only prices are posted and the goods are substitutes, the equilibrium allocations from the two approaches are different.

Market Pricing for Matroid Rank Valuations

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 15 December 2020Accepted: 25 August 2021Published online: 08 November 2021Keywordspricing scheme, Walrasian equilibrium, gross substitutes valuation, matroid rank functionAMS Subject Headings90C27, 91B52Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and Applied MathematicsCODEN: sjdmec