Equilibrium Price Research Articles

Equilibrium pricing in supply chains with discrete stochastic demands: A case study in coffee supply and distribution industry

ABSTRACT This study addresses the optimization of price and production quantity using game theory in the coffee supply chain in the city of Isfahan. The presented model focuses on the competition among members of the chain in a probabilistic environment and is based on discrete selection models. This model examines the impact of inventory and routing costs on the pricing model at the same time. To effectively solve real-world problems, the method of normal distribution approximation is used instead of the binomial distribution. The results of the model indicate that the computational time of the applied approximate model does not change with increasing the number of customers, and the model can determine the optimal price and production quantity. The advantage of the proposed model over other classic models is that it considers the inventory costs that have not yet been considered in price competition models with discrete selection.

Information asymmetry, sentiment interactions, and asset price

We develop an asset pricing model with sentiment interactions between institutional and individual investors under the condition of information asymmetry. Our model considers private information and investor sentiment, two imperfections in securities markets, and integrates them into a theoretical model to investigate the role of the interaction between information asymmetry and investor sentiment in asset pricing. We show that the joint effect of private information and investor sentiment deviate the price of risky assets and efficiently explains anomalies in the stock market. Investor sentiment changes the effect of information on the equilibrium price relative to a world where all investors are completely rational. Private information changes the effect of investor sentiment on the equilibrium price in comparison with a scenario with symmetric market information. In addition, the individual investors’ learning and the disclosure of information both allow private information to be better integrated into the price and simultaneously changes the effect of investor sentiment on the equilibrium price.

Local electricity market pricing mechanisms’ impact on welfare distribution, privacy and transparency

Local energy communities and electricity markets have emerged as possibilities for interaction among prosumers. A substantial effort has been invested into creating efficient pricing mechanisms for various market arrangements, all of which take into consideration distinct characteristics of local electricity trading. However, since they are all evaluated in terms of various systems and market conditions, it is challenging to directly compare the mechanisms. In this research, three well-established pricing mechanisms from the literature are systematically compared and evaluated under identical settings on their influence on welfare distribution across various market participant groups, privacy protection, transparency and complexity level. According to the findings, the supply–demand ratio pricing system leads to the lowest costs for consumers and is also the most privacy compliant and transparent. Furthermore, prosumers obtain the highest cost-savings through the consensus alternating direction method of multipliers pricing mechanism, whereas the equilibrium pricing mechanism performs best regarding economic fairness. The aim of this article is to provide insight into the performance of different pricing mechanisms to energy regulators and local electricity market facilitators. The comparative analysis should aid in making informed decisions on the implementation of local electricity markets.

Equilibrium pricing mechanism of low-carbon supply chain considering carbon cap-and-trade policy

In the low-carbon supply chain (LSC) network, because of the different carbon emission reduction investment costs and product exhibition costs, members of the same level will show certain competitive behavior. This paper aims to realize the low-carbon development of the supply chain network based on the carbon quota trading system and the risk aversion characteristics of retailers and uses variational inequality theory to construct the network equilibrium model under the constraint of inventory capacity, and designs an improved projection contraction algorithm to solve the model. The results mean that when the retailer is risk averse, the improvement of the risk aversion coefficient (RAC) reduces the manufacturer's carbon emission rate and profit and increases the product sales price and retailer's profit. When the retailer has an inventory capacity constraint, the enhancement of the inventory capacity constraint increases the profit of the manufacturer and the retailer but reduces the emission reduction rate of the manufacturer. If the retailer has risk aversion characteristics and inventory capacity constraints, the manufacturers' profits will increase as RAC increases, while retailers' profits will decrease as RAC increases. In addition, the carbon trading mechanism can promote enterprises to invest in carbon emission reduction and raise the low-carbon level of products.

Product‐line pricing with dual objective of profit and consumer surplus

In many settings, consumer surplus directly impacts a firm or organization's objective, and the profit‐only objective becomes inadequate. Our paper is the first to consider the dual objective of profit and consumer surplus in multi‐product pricing under the multinomial logit demand, where the prices are continuously set. We define a firm's marginal consumer surplus as its marginal contribution to the expected customer utility transformed into monetary unit. Although the profit is concave in the choice probability space, the marginal consumer surplus is convex, complicating the analysis. We identify the optimal monopoly pricing solution and develop solution approaches for the equilibrium solutions of both price‐competition and quantity‐competition oligopolies. In the monopolistic setting, we solve the optimal solution in a near‐closed‐form expression, and show that the firm's markup and profit decline as its emphasis for marginal consumer surplus increases and eventually drops to zero when the firm turns into a social welfare maximizer. Therefore, social welfare is maximized only when the monopolist is willing to endure zero profit. In competitive settings, if one firm's emphasis on marginal consumer surplus increases, then the improvement in marginal consumer surplus can magnify through competitive forces, reflected in reduced equilibrium prices for all firms. Moreover, we find that, while the overall marginal consumer surplus always increases with any firm's weight on marginal consumer surplus in its objective (referred to as the CS weight), a firm's marginal consumer surplus increases in its own CS weight but decreases in other firms' CS weight. Finally, we prove that, all else equal, a firm with a higher CS weight can earn a higher profit than its profit‐maximizing competitors, which is counterintuitive. In the quantity competition, a firm may even increase its absolute profit level by increasing its CS weight.

Measuring Market Efficiency Through Valuation Techniques: The Case of Visegrad Countries Stock Markets

Abstract Company valuation stands as the most controversial topic in the field of financial management. The study investigates the extent to which stock prices of the companies listed on Czech, Polish, Hungarian, and Slovak equity markets deviate from their estimated intrinsic value. DCF model was employed using Monte Carlo simulations with 500, 1000, and 10000 trials to generate estimated intrinsic value and compare them to market prices. The results of the study show that the Bratislava Stock Exchange (SAX) on average holds the lowest gap between intrinsic value per share and market prices with only 82% deviation, followed by PSE with 116% deviation, WIG20 with 207% deviation, and BUX with 246%. SAX appears with the best performance from 2009 to 2019, where the shares on average were traded with only 82% deviation from their estimated equilibrium price (intrinsic value). Findings regarding the differences between book value per share and stock prices are different, where SAX leads with 71% deviation, WIG20 with 181%, PSE with 188%, and BUX with 545%. Outcomes of the work are of interest to financial investors that seek to diversify their portfolios on the equity stocks. The study offers a new conceptual framework for testing the market efficiency of equity exchanges through company valuations techniques. From the policy perspective, institutions in charge get inform on the measures to be taken that would improve efficiency and strengthen the importance of the Visegrad equity markets.

MODIFICATIONS OF EVANS PRICE EQUILIBRIUM MODEL

The paper regards the classical Evans price equilibrium model in the free product market in the aspect of regarding the opportunities for expanding (modifying) the model given that is aimed at perfecting the accuracy of its mathematical formulating. As an accuracy criterion, we have chosen a summary quadratic deviation of the calculated indices from the given ones. One of the approaches of modifying the basic Evans model is suggesting there is a linear dependence between price function and time as well as its first and second derivatives. In this case, the model will be described through differential equation of second order with constant coefficients, revealing some oscillatory process. Besides, it is worth regarding a non-linear (polynomial) dependence between demand, supply and price. The paper proposes mathematical formulating for the modified Evans models that have been approbated for real indices of exchange rates fluctuations. It also proves that increase of the differential and/or polynomial order of the given model allows its essential accuracy perfection. Besides, the influence of arbitrary restricting circumstances of the model on its accuracyis regarded. Each expanded Evans model is accompanied by mathematically formulated price and time dependence.

The effects of information on competition on a hybrid retail platform

Many online platforms now operate in a hybrid mode, in which they act as intermediaries between manufacturers and consumers (agency mode) and resell products (reseller mode). Some hybrid platforms offer both the agency and reseller modes to a manufacturer, so that the same product can be sold through both modes simultaneously. In addition, online shopping brings uncertainty, rendering consumers dependent on information such as product descriptions when making purchase decisions. This paper aims to explore price and service level competition on a hybrid retail platform and the influence of the information displayed on the platform (collectively, “platform information”) on such competition. We establish a model to investigate the equilibrium price and service level in the agency and reseller modes. Next, we analyze how platform information influences equilibrium. We find that the service level in the reseller mode is always higher than that in the agency mode and that the platform owner’s (“e-tailer’s”) profit is higher when the information displayed in the agency mode significantly differs from the information displayed in the reseller mode. The precision of the information about quality and match has opposite effects on competition and profits. For example, an increase in the precision of the match information decreases competition and increases the profits of both the manufacturer and the e-tailer. Surprisingly, we find that both the manufacturer and the e-tailer benefit when inconsistent information is provided in the two modes (i.e., it creates a win–win situation). This paper has implications for managers seeking to understand competition between the agency mode and the reseller mode and to properly manage their platform information.

Price competition with capacity uncertainty - feasting on leftovers

There is ample empirical evidence documenting that large firms set significantly lower prices than smaller, capacity-constrained, firms. This is paradoxical in light of the standard theoretical result that large firms charge higher prices than small firms in models of price competition with capacity constraints. We argue that private information about capacity constraints can account for this puzzle. We provide concavity conditions on the demand and on the type distribution under which there exists a unique, monotone decreasing price equilibrium. Solving the model requires a novel approach of studying several different regions of pricing incentives depending on the realized capacity levels. We show that firms with intermediate capacities compete in an auction type interaction, while firms with low or high capacity levels compete less vigorously on the margin.

Multi-object auction design beyond quasi-linearity: Leading examples

In multi-object auction models with unit demand agents, two standard assumptions are the quasi-linearity of utility functions and the coincidence between price increment and valuation unit. Under these assumptions, the exact ascending auction of Demange et al. (1986), the sealed-bid Vickrey auction, as well as the approximate ascending auction of Demange et al. (1986) identify the minimum price equilibrium (MPE) while elegantly exhibiting efficiency and incentive-compatibility. We demonstrate that these auctions fail to identify the MPEs and are substantially inefficient and manipulable if these assumptions are dropped. We also discuss the implications of our negative results for multi-object auction models with multi-unit demand and matching with contracts models.

On market power and inflation

We study the connection between inflation and market power in a partial equilibrium framework with both demand and cost shocks. We derive a specific condition under which cost shocks increase market power. Conversely, when the condition is not satisfied then it is demand shocks that increase market power. Moreover, exogenous changes in the degree of competition can either shrink or amplify the effect of either type shocks on equilibrium price. Our results complement those of Menezes and Quiggin (2022) and further enrich the recurrent debate surrounding the role of market power on inflation.

Multihoming effect on the two-sided platform of second-hand cars

With the development of circular economy, second-hand cars are becoming important in the sustainable transportation. Due to the participation of many e-tailers, the platform competition of second-hand cars is increasingly strong in the two-sided market. Considering the network externality and product differentiation on the second-hand car platform, this study sets up a stylized model to analyze the multihoming effect for heterogeneous consumers and solves the equilibrium pricing strategy and quality decision in the online collecting market and reselling market. The numerical experiments examine the impact of two types of customer heterogeneity on the customer’s demand and platform’s profit. Our findings show that the customers close to each platform have the single-homing effect, otherwise they have the multihoming effect. As a result, the platform’s profit increases with the customer’s heterogeneity towards two second-hand platforms but is the same with the customer’s heterogeneity towards two online markets. Furthermore, we provide some managerial insights for all the stakeholders on the two-sided platform of second-hand cars.

The impact of product diversity and distribution networks on consumption expansion

Investigation on the influencing factors of consumption expansion is an important subject in business research. This study constructs a consumption utility function and analyzes the relationship between search cost and product heterogeneity and equilibrium price. Employing the data on 31 regions in China from 2002 to 2020, the panel data model is used to verify the results of the theoretical analysis. We draw the following conclusions. (1) Expanding the number of distribution outlets will lead to a decline in the equilibrium price, and an increase in product diversity prompts consumers to conduct more searches. (2) Expanding distribution networks can increase residents’ total consumption and consumption level. (3) An increase in product diversity can expand resident consumption. The conclusions suggest that distributors and retailers can increase the categories of their products, provide consumers with diversified decision-making space, and stimulate consumption expansion.

Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior

A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences of consumers were included in the model. Firms implement two strategies in the market: profit maximization and market share maximization. Numerical discretization of a two-dimensional area was performed for computing the equilibrium prices which allows one to consider any market area and any location of the firms. Four scenarios of oligopoly markets were developed by combining both strategies from one side and competitive behavior and a partial cartel agreement from another side. The main differences between the scenarios are outlined. Profits, market shares and equilibrium prices are presented and compared. The influence of collusion, the existence of participants with a market share maximization strategy and consumer preferences on the firm’s profits and equilibrium prices were examined. Cases whereby firms prefer to leave the cartel were investigated. Best locations for the setting of a new store for profit maximization are shown and discussed.

A Spatial Pareto Exchange Economy Problem

We use convex duality techniques to study a spatial Pareto problem with transport costs and derive a spatial second welfare theorem. The existence of an integrable equilibrium distribution of quantities is nontrivial and established under general monotonicity assumptions. Our variational approach also enables us to give a numerical algorithm à la Sinkhorn and present simulations for equilibrium prices and quantities in one-dimensional domains and a network of French cities.

Online promotion format selection for a supply chain with environment responsibility in an uncertain market

Corporate environmental responsibility has received considerable attention. In our study, we consider a supply chain in which a manufacturer invests in green technology to decrease the carbon footprint. The main issue addressed here is how the manufacturer selects the optimal online selling format between agency selling and reselling to ensure profitability with a lower carbon footprint. In an uncertain market with considering different pricing sequences in dual-channel promotion,we explore six scenarios. The results show that the different pricing sequences will not affect the equilibrium green degree and pricing strategies under agency selling, whereas it may result in an improved greenness in reselling format. Furthermore, under the interaction of uncertain demand, pricing sequence and green technology investment, we reveal the agent selling format is not always superior to the reselling format with a double-marginalization effect, which contrary to the general intuition. Specifically, in an optimistic market, the manufacturer is more profitable in reselling format when the promotion price set in online channel prior to traditional channel, and in a pessimistic market, the opposite pricing sequence formulated will bring a considerable benefit to the manufacturer.

Resource efficiency and pricing policy of industries the sustainable development context

In the article, the authors analyzed the theoretical foundations of sustainable economic growth based on the research of modern foreign and domestic scientists. It is proved that the economy of the linear type has exhausted itself due to the effect of scale. That is why, today, one of the foreground of research areas among leading domestic and foreign scientists is the concept of sustainable development which should be based on cyclical or circular economy principles. One of the directions of development is working out methods of products price formation taking into account resource-efficient strategies. The article presents price equilibrium scenarios developed by the authors, which were implemented in the oil and gas industry based on business activities for 2015-2020. These scenarios were developed by the authors using Leontiev’s cross-industry model, which explores how do these changes can impact the performance of resource use, based on changes in direct cost ratios, value added ratios and intermediate consumption ratios.

Inbound container storage pricing considering price-dependent container storage time and congestion in container terminals

ABSTRACT Congestion at ports and railheads is attracting more and more attention from both the government and industry. In this paper, we intend to improve container terminal operation efficiency from the perspective of inbound container storage pricing. We study a two-stage pricing game model for a profit-maximising shipping company and a container terminal operator. Two types of objective functions are investigated for the container terminal operator: profit maximisation and cost minimisation. Price-dependent container storage time is considered. After theoretical analysis, the pricing equilibria is derived. Through numerical studies, we find that the cost-minimising objective is recommended for the terminal operator to relieve the stress of yard congestion. Container terminal operators have an incentive to raise storage prices to cope with congestion in terminal yards.

Equilibrium Bitcoin Pricing

ABSTRACTWe offer a general equilibrium analysis of cryptocurrency pricing. The fundamental value of the cryptocurrency is its stream of net transactional benefits, which depend on its future prices. This implies that, in addition to fundamentals, equilibrium prices reflect sunspots. This in turn implies multiple equilibria and extrinsic volatility, that is, cryptocurrency prices fluctuate even when fundamentals are constant. To match our model to the data, we construct indices measuring the net transactional benefits of Bitcoin. In our calibration, part of the variations in Bitcoin returns reflects changes in net transactional benefits, but a larger share reflects extrinsic volatility.

Food Donations, Retail Operations, and Retail Pricing

Problem definition: For grocery retailers, managing perishable food that is nearing expiry is a major challenge. Donating food to food banks is socially responsible, as it improves local communities and reduces waste generation. It also diverts food to a secondary, quality-differentiated market. Academic/practical relevance: In this paper, we quantify the economic impacts of this secondary market for food by examining donation and pricing behaviors for competing retailers. Methodology: We use a structural model of price-discriminating oligopoly retailers to study the effect of food donations on store and category-level demand and equilibrium prices. Empirically, we estimate the food donation effect using a unique data set of food donations and sales for several categories of perishable foods across two major retail chains that compete in the same market. Results: The competitive effects of food donations follow from the price-discrimination logic. First, food donations create a direct demand effect. Donations raise the average quality of products on display, shifting demand curves inward and rotating them clockwise (e.g., more inelastic). Second, food donations create a market enhancement effect, softening price competition and raising equilibrium prices among competing retailers. Managerial implications: Food donations increase food prices and store profits, tying the socially responsible option to an economic benefit. This study contributes a new type of reuse operation to the literature on closed-loop supply chains.Funding: Funding from the Agriculture and Food Research Initiative (National Institute for Food and Agriculture, U.S. Department of Agriculture) [Grant 2020-67021-31377] is acknowledged.Supplemental Material: The online supplement is available at https://doi.org/10.1287/msom.2022.1185 .