Equilibrium Price Research Articles

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.

Optimality in an OLG model with nonsmooth preferences

AbstractIt is a well‐known observation that, in the overlapping generations (OLG) model with the complete market, we can judge optimality of an equilibrium allocation by examining the associated equilibrium price. Motivated by recent development in decision theory under ambiguity, this study reexamines the above observation in a stochastic OLG model with convex but not necessarily smooth preferences. It is shown that optimality of an equilibrium allocation depends on the set of possible supporting prices, not necessarily on the associated equilibrium price itself. Therefore, observations of an equilibrium price do not necessarily tell us precise information on optimality of the equilibrium allocation.

Product Quality and Consumer Search

An increase in quality shifts up the distribution of match utilities offered by firms and makes consumers pickier. The number of products that consumers inspect does not necessarily increase in quality. Higher search costs may lead to less quality investment, and the equilibrium price may decrease. If the equilibrium is inefficient, it is because of the inadequacy of quality investment. The market level of quality investment is excessive (insufficient) and consumers are too (little) picky from the point of view of welfare maximization if and only if a rise in quality results in consumers inspecting a higher (lower) number of products. (JEL D11, D21, D83, G31, L15)

Alternating-Offers Bargaining with Nash Bargaining Fairness Concerns

The Rubinstein alternating-offers bargaining game is reconsidered, where players show fairness concerns and their fairness references are characterized by the Nash bargaining solution. The objective of this paper is to explore the impact of fairness concerns in the alternating-offer bargaining game. Alternating-offer bargaining with fairness concerns is developed. We construct a subgame perfect equilibrium and show its uniqueness. Then, it is shown that players' payoffs in the subgame perfect equilibrium are positively related to their own fairness concern coefficient and bargaining power and negatively to the opponents' fairness concern coefficient. Moreover, it is shown that the limited equilibrium partition depends on the ratio of discount rates of the two players when the time lapse between two offers goes to zero. Finally, the proposed model is applied to the bilateral monopoly market of professional basketball players, and some properties of equilibrium price are shown. Our result provides the implication that players should carefully weigh their own fairness concerns, bargaining power and fairness concerns of their opponents, and then make proposals, rather than simply follow the suggestion that the proposal at the current stage is higher than that at the past stages.

Constrained-Efficient Capital Reallocation

We characterize efficiency in an equilibrium model of investment and capital reallocation with heterogeneous firms facing collateral constraints. The model features two types of pecuniary externalities: collateral externalities, because the resale price of capital affects collateral constraints, and distributive externalities, because buyers of old capital are more financially constrained than sellers, consistent with empirical evidence. We prove that the stationary equilibrium price of old capital is inefficiently high because the distributive externality exceeds the collateral externality, by a factor of two when we calibrate the model. New investment reduces the future price of old capital, providing a rationale for new-investment subsidies. (JEL D21, D24, D25, D62, E22, G31, G32)

Optimal pricing strategy for electric vehicle battery swapping: Pay-per-swap or subscription?

Electric vehicles (EVs) contribute to carbon emission reduction, but the limitations of existing charging technologies impose a bottleneck to their further diffusion. Addressing the root issues of long waiting time and range anxiety, battery swapping demonstrates great market potential. A swapping service provider may choose between two pricing strategies based on battery rental: pay-per-swap and subscription. This study establishes a game-theoretical model to portray a simplified EV replenishment market including one charging station, one swapping station, and one battery renter, and explores the optimal pricing strategy. To capture the influence of consumer preferences, the model considers high versus low opportunity cost of time. In either scenario, consumers choose between charging and swapping to maximize surplus utility. Equilibrium prices, demands, and profits under pay-per-swap and subscription strategies are obtained through backward induction. The results indicate that pricing strategy choice-making hinges on provider-side operating cost, battery depreciation and reserve size, as well as consumer-side time sensitivity and opportunity cost. Numerical and extended analyses suggest that the subscription strategy is conducive to initial market development, whereas the more consumer-friendly pay-per-swap strategy is preferred afterwards.

On-demand ride-sourcing markets with cryptocurrency-based fare-reward scheme

Cryptocurrency-based fare-reward scheme has been emerging from on-demand ride-sourcing platforms. The reward scheme provides each passenger with some units of cryptocurrency as rewards for use of ride service. The passengers can redeem the rewards for various redemption options. The redemption options offer the passengers economic benefits to offset a portion of costs of using ride services. In this way, the economic benefits serve as incentives for the passengers to repeatedly use ride services, which leads to increase in passenger demand for the platforms. From a passenger perspective, the reward scheme has a distinctive feature in that economic benefits can fluctuate according to changes in price of cryptocurrency in the future. Therefore, the passengers perceive the benefits differently based on their own risk preference and expectation of future price changes. It creates a challenge for the platforms because the optimal decisions for ride services vary by the value that the passengers place for their cryptocurrency rewards. To tackle this challenge, this paper analyzes the impacts of the reward scheme on on-demand ride-sourcing markets. The analysis is done with a mathematical model where a ride-sourcing platform makes decisions for trip fare, vehicle fleet size and cryptocurrency reward size. The reward decision is available under the assumption that the platform secures as many units of cryptocurrency as it rewards to passengers at their equilibrium price level. The model defines passengers’ perceived value of cryptocurrency rewards in terms of risk aversion level and expectation of future price growth of cryptocurrency. Afterwards, we investigate equilibrium and optimal properties of monopoly, social-optimum and second-best optimum ride-sourcing markets. Our analysis gives several key insights on the markets. First, the markets always locate at normal regime where interactions between passenger demand and vehicle supply for ride services converges to a stable equilibrium state. Second, this study shows that a ride-sourcing platform would make a decision to reward if passengers expect larger economic benefits from future redemption of cryptocurrency rewards than their current value. Third, it is shown that the quality of ride services would get worse because average pick-up time for passengers and drivers gets longer with more passenger retention. Fourth, this paper finds that the markets have more room to improve profit or social welfare as passengers expect larger speculative gains from reward redemption.

Modelling a tradable transport permit scheme using system dynamics

Introduction: In this paper we consider system dynamics (SD) modelling of tradable transport permit schemes (TTPS). TTPS are complex and uncertain, having not yet been implemented beyond experimental trials anywhere in the world, yet have for some time been suggested as an efficient and equitable policy response to reducing car-based travel and its associated externalities.Method: Although there is a large number of econometric models that explore the potential of TTPS, there have been none published (to our knowledge) that have used the SD approach. SD is an appropriate method for developing our understanding of TTPS efficiency and equity as it captures feedbacks and tracks the influence of the TTPS over a period of time. Thus, we have developed an SD model of TTPS, drawing from the literature that already exists. It is a micro-level model that considers heterogeneity within a population on a daily basis over a matter of months. We carry out sensitivity testing of price sensitivity, initial permit price, daily preference and permit allocation and develop combined scenarios of these attributes.Results: Our modelling results suggest a sensitivity of TTPS to heterogeneity across the population, which will influence the final equilibrium price. Trading encourages a redistribution of wealth across the population but may also mean that some travel needs are not met, which may require some allocation according to need or a certain portion of protected permits. The inclusion of non-car users within the allocation further encourages trading behaviours and allows for compensation for externalities of car use.Discussion: Through an analysis of outputs we are able to bring new insights into the governance frameworks required for a successful TTPS. In particular we have shown the importance of allocation considerations in the design of a TTPS when issues of fairness across the population are considered. Although there is no data of existing schemes available for us to calibrate our models, we compare the trends with data from an in-the-field TTPS experiment.

Asymmetric Information of Product Authenticity on C2C E-Commerce Platforms: How Can Inspection Services Help?

Problem definition: We consider a customer-to-customer (C2C) platform that provides an inspection service. Uncertain about product authenticity, a seller sells a product through the platform. Before purchasing, a buyer obtains a signal of the product authenticity from the product’s price set by the seller. The platform’s inspection service can detect a counterfeit with a probability. If the product passes the inspection, the platform sends it to the buyer and charges the seller a commission fee. Otherwise, the platform returns it to the seller and charges the seller a penalty fee. Methodology/results: We develop a two-stage game-theoretical model. In the first stage, the platform designs a contract specifying the commission and penalty fees. In the second stage, the seller signals the product authenticity by setting a price and the buyer decides whether to purchase it. This results in a contract design problem that governs a signaling game. We find that the effect of inspection is beyond merely detecting counterfeits. The inspection, even an imperfect one, changes the signaling game’s structure and incentivizes the seller whose product is likely authentic to sell through the platform. This can only be achieved by carefully choosing the commission and penalty fees. Moreover, a larger platform’s expected profit does not imply a larger commission fee or price in equilibrium. Under some mild conditions, the optimal commission increases but the optimal penalty decreases as the platform’s inspection capability improves. Managerial implications: The inspection service is not widely available among leading C2C platforms as it is considered imperfect and costly. Our study suggests that its benefit may be underestimated in practice. Moreover, the inspection can eliminate the seller’s information rent and generate more revenue for the platform. This paper provides guidance on how to set commission and penalty fees when the inspection service is provided. Funding: L. Li is supported by the National Natural Science Foundation of China [Grant 72071198] and the Hong Kong Polytechnic University Distinguished Postdoctoral Fellowship Scheme [Grant 1-YWC7]. X. Fang and Y. F. Lim are grateful for the support from the Lee Kong Chian School of Business, Singapore Management University [Maritime and Port Authority Research Fellowship and Retail Centre of Excellence Research Grant]. Y. F. Lim is supported by the Association of South-East Asian Nations Business Research Initiative Grant [Grant G17C20421], the Research Grants Council of Hong Kong [Grants 15501920 and 15501221], and the Key Program of National Natural Science Foundation of China [Grant 71931009]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.1186 .

Mekanisme Pasar untuk Mencapai Keseimbangan Pasar Dalam Sistem Ekonomi Islam

A country's economic activity is very dependent on the role of the market, even though injustice and fraud often occur in its trading activities, especially in determining the price offered. Therefore a rule is needed regarding market price determination, where the rule is known as a market mechanism, namely price setting based on demand and supply. The market is where the process of demand and supply occurs until the equilibrium price is reached. This research is a literature research or library reasearch that examines information through books, documents, articles, and other literature media that can be used as a source in preparing a study. This study aims to determine the role of market mechanisms to create market balance in the view of Islamic economics. The results showed that Islam puts the market in an important position in the economy of the market mechanism in accordance with sharia does not promote government intervention in normal market conditions. However, when the market is distorted, it takes the role of the government in overcoming problems to realize the benefits of the people

Economic Feasibility of Management of Fertilization in the Soybean-Corn System Cultivated in Succession

Fertilization management is one of the agricultural practices that demand high investment. Thus, the objective was to evaluate the economic viability of using combinations of fertilizers applied to soybean and corn cultivated in succession in Goiás Savanna soil. The experiment was carried out in the field, in randomized blocks. The fertilization management consisted of the combination of monoammonium phosphate fertilizers; urea; 08:40:00 +9.3%S and 3.2% Ca; simple superphosphate; potassium chloride; elemental sulfur; polyhalite (37% K2O + 9.2% S, 5.8% Ca and 1.7% Mg) and polyhalite S (14% K2O + 19.2% S, 12% Ca and 3.6% Mg) which were applied in soybean sowing and evaluated the residual effect on corn. The economic assessment took into account crop productivity and fertilizer prices in the 2018/2019 agricultural year. For each treatment, the operating cost (COi) and profitability indicators were calculated: gross revenue (GRi); net revenue (NRi); profitability index (PITi); equilibrium production (Yei) and equilibrium price (Pei). Crop productivity was not influenced by fertilizer management, showing that economic indicators can help producers choose the management with the best return and that adjusts to the financial situation of the rural company. Thus, it is concluded that the management of MAP + KCl fertilization was economically outstanding in soybean cultivation and the MAP/S + KCl applied to soybeans, associated with nitrogen fertilization in corn coverage was the most viable for off-season corn. The economic indicators showed that the MAP+KCl fertilization performed on soybean, associated with urea in corn coverage, is the most viable management system for the soybean-corn production system cultivated in succession.

Artificial intelligence adoption in a competitive market

AbstractEconomists have often viewed the adoption of artificial intelligence (AI) as a standard process innovation where we expect that efficiency will drive adoption in competitive markets. This paper models AI based on recent advances in machine learning that allow firms to engage in better prediction. Focusing on prediction of demand, it is demonstrated that AI adoption is a complement to variable inputs whose levels are altered directly by predictions and whose use is economized by them (that is, labour). It is shown that in a competitive market, this increases the short‐run elasticity of supply and may or may not increase average equilibrium prices. Generically, there are externalities in adoption, with this reducing the profits of non‐adoptees when variable inputs are important, and increasing them otherwise. Thus AI does not operate as a standard process innovation, and its adoption may confer positive externalities on non‐adopting firms. In the long run, AI adoption is shown to lower prices generally and raise consumer surplus in competitive markets.

A new approach to the uniqueness of equilibrium with CRRA preferences

This paper investigates the uniqueness of equilibrium in the economy where agents have preferences with possibly distinct levels of relative risk aversion. Equilibrium prices exist in a price range determined by micro and macroeconomic information. Macroeconomic information is inferred from two representative-agent economies, which provide lower and upper bounds on aggregate demand, respectively. Analysis of the first and second-order price effects shows that individual demand has a unique inflection point at which the income effect maximally dominates the substitution effect. In contrast, aggregate demand may have multiple inflection points, which creates multiple equilibria. Sufficient conditions for the uniqueness of equilibrium are characterized by the local behavior of individual demand at the inflection point. They require that aggregate demand must have no more than two inflection points in the equilibrium price range. The result of this paper sheds light on the Sonnenschein-Mantel-Debreu theory that has negative implications for the uniqueness of equilibrium.

The underlying coherent behavior in intraday dynamic market equilibrium

PurposeThis paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.Design/methodology/approachThe authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.FindingsThe authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).Research limitations/implicationsThe authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.Practical implicationsThe authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.Social implicationsUnderstanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.Originality/valueIt uncovers subjects' intelligent interactively trading behaviors.

Optimal reduction and equilibrium carbon allowance price for the thermal power industry under China’s peak carbon emissions target

As the largest source of carbon emissions in China, the thermal power industry is the only emission-controlled industry in the first national carbon market compliance cycle. Its conversion to clean-energy generation technologies is also an important means of reducing CO2 emissions and achieving the carbon peak and carbon neutral commitments. This study used fractional Brownian motion to describe the energy-switching cost and constructed a stochastic optimization model on carbon allowance (CA) trading volume and emission-reduction strategy during compliance period with the Hurst exponent and volatility coefficient in the model estimated. We defined the optimal compliance cost of thermal power enterprises as the form of the unique solution of the Hamilton–Jacobi–Bellman equation by combining the dynamic optimization principle and the fractional Itô’s formula. In this manner, we obtained the models for optimal emission reduction and equilibrium CA price. Our numerical analysis revealed that, within a compliance period of 2021–2030, the optimal reductions and desired equilibrium prices of CAs changed concurrently, with an increasing trend annually in different peak-year scenarios. Furthermore, sensitivity analysis revealed that the energy price indirectly affected the equilibrium CA price by influencing the Hurst exponent, the depreciation rate positively impacted the CA price, and increasing the initial CA reduced the optimal reduction and the CA price. Our findings can be used to develop optimal emission-reduction strategies for thermal power enterprises and carbon pricing in the carbon market.

Revisiting Cournot and Neoclassical Economics

This study highlights the deep influence that Cournot’s economic thought had on subsequent neoclassical and mainstream economics. Cournot’s idea for price stability and perfect competition through an infinite number of firms, each of inappreciable production that cannot affect the price, has been fully adopted by subsequent neoclassical theorists and embodied in today’s mainstream economics. But, in the passage of this idea from Cournot to neoclassical economics, there was a misinterpretation of this price stability condition that led neoclassical economics to the notion of price taking and horizontal demand curve for the individual firm, while Cournot himself considered this individual demand curve to be sloping. This misconception led neoclassical and mainstream economics to erroneous models and outcomes. The most serious implication is that the equilibrium price in perfect competition is not at the minimum average cost, as neoclassical economics argues, but at a higher cost, which, in turn, has further implications for social welfare.

Pricing decision of dual-channel supply chain with members risk-aversion under the participation of e-commerce platform

In this paper, it considers a two-stage dual-channel supply chain model composed of a risk aversion manufacturer, a risk aversion retailer and a risk-neutral e-commerce platform. Under the condition of information symmetry, it is supposed that the manufacturer is financially constrained. Besides, the analysis is based on Stackelberg game theory. The equilibrium price without capital constraint is compared with the equilibrium price in three cases of e-commerce platform financing, bank loan financing and prepayment financing. Then the effects of risk aversion coefficients of the manufacturer and the retailer on equilibrium prices are compared in four cases. The influence of different financing rates on wholesale price, direct selling price and retail price is analyzed simultaneously.

Особенности рыночных структур с позиции регулярно-динамической теории

The article focuses on the application of the regular-dynamic method in the theory of industry markets. It introduces the Hamilton function and key parameters of portal connections that describe market barrier properties and formulates the fundamental equations of market dynamics. The solutions of these equations determine crucial characteristics of commodity-money exchange at each market link and establish relationships that describe typical regimes of local equilibrium market interaction, including perfect and monopolistic competition, pure monopolies and monopsonies, as well as oligopolies and oligopsonies. The study reveals that the interaction among agents in a perfectly competitive market is influenced by weakly disturbed portal connections, which prevent firms from reaching a profitable level of exchange with an equilibrium price solely determined by technological parameters within the firms. In the case of a monopolistically competitive market, the price demonstrates an inversely proportional dependence on the volume of supply, which is characteristic of small businesses offering differentiated goods based on quality. It is observed that the equilibrium price in monopoly markets exhibits monotonic growth as the production activity of interacting firms increases. This price increase is attributed to an elevation in the seller’s barrier and a reduction in the depth of buyers’ market pits in the case of pure monopoly, while the reverse occurs in pure monopsony with an increase in the depth of the buyer’s pit and a decrease in sellers’ barriers. The article investigates the relationship between the equilibrium price and the parameters of technological processes, as well as the barrier properties of firms acting as sellers and buyers in oligopoly and oligopsony markets. Furthermore, the study highlights that the structure and effectiveness of oligo markets significantly depend on the relative positioning of technological frequencies between market leaders and outsiders. The article proposes an analytical description of the “race for the leader” effect. Lastly, for all the analyzed modes of market interactions, the stability of the processes governing equilibrium price formation is substantiated.

Reducing the dynamic model of the software development market to a block problem of convex programming

The authors propose to reduce a discrete dynamic model of the software development market to a block problem of convex programming, which can be solved by successive approximations based on contraction mapping, in case of abandoning the integer elements of the destination matrix. However, there are also peculiarities: equilibrium prices can be calculated directly and therefore a variational formulation of the internal problem of determining equilibrium prices based on Debreu's theorem is not required. The functions of phase coordinates’ change can be taken as convex, for example, the norm of the difference squared, and do not take into account the fixed costs for each control switch, which is excluded from the equations of system’s dynamics. The resulting block problem of convex programming allows decomposition by freezing the connection variables with neighboring blocks at the level of the previous iteration. It is shown that the operator on the right side of the resulting recurrent equation is compressive under fairly general conditions. This allows the authors to prove successive approximations for solving the resulting problem, based on the principle of contraction mapping. The authors give the model example of its use in the dynamic expansion of the transport problem according to the value.

Price Equilibrium with Selling Constraints

Price Equilibrium with Selling Constraints