Equilibrium Price Research Articles

Insight into China’s economically motivated adulteration risk in online agricultural product sales

Quality uncertainty and inspectors’ imperfect testing capability leave agricultural products wide open to economically motivated adulteration (EMA), and online shopping demand for these products in China makes it even worse. We develop a game-theoretic framework to investigate online agricultural product sellers’ EMA behavior on an e-commerce platform (EP). We characterize the sellers’ equilibrium pricing and adulteration decisions and the EP’s optimal take rate decision and analyze how the sampling inspections and adulteration penalty jointly impact these decisions. Moreover, we investigate three managerial levers to deter EMA: (i) penalizing EP’s malpractice regarding food safety management, (ii) claiming a higher-than-law-requires adulteration penalty to consumers, and (iii) adopting the traceability systems to record reliable quality information. Finally, we use real-world data to calibrate our model and derive more managerial insights. We find that the quality-differentiated sellers’ adulteration decisions are symmetric and their ex-post pricing decisions lead them to evenly share the market on the EP. We show that the EP’s higher take rate can inhibit the sellers’ adulteration behavior, however, it may indulge their such behavior by intentionally decreasing this rate. Our results highlight a penalty-inspection-centered approach as essential to combat EMA, and that it can be supplemented by the three levers.

Product Sustainability and Consumer Environmental Awareness in Differentiated Markets

Sustainable management of natural stock resources can be promoted through state intervention. This study investigates optimal regulatory strategies to mitigate the negative environmental effects of human activities within a duopolistic, differentiated linear market à la Hotelling framework. The analysis is conducted from both a business and a social perspective, aiming to elucidate the role of regulatory interventions, awareness campaigns, and sustainable production characteristics in shaping firm behavior and market outcomes. Under the business perspective, a game-theoretical approach is employed, involving the regulator and two competing firms. The equilibrium in prices and production characteristics is derived, revealing how firms respond to sustainable characteristics and awareness campaigns. In the social perspective, where the regulator has complete control, optimal strategies are determined to maximize social welfare, resulting in reduced differentiation and enhanced sustainability. This study identifies the optimal level of awareness campaign and sustainable characteristic proposed by the regulator. The findings highlight the significance of coordinated regulatory policies and awareness campaigns to induce firms toward more sustainable practices, ultimately contributing to a more ecologically balanced market. The study offers insights for policymakers and practitioners seeking effective strategies to address environmental concerns in differentiated markets, thereby promoting sustainable economic growth and reducing ecological impacts.

Advertising mode of duopoly competitive enterprises based on asymmetric cost efficiency and converter preference

This study focuses on two types of online advertising: mass advertising and targeted advertising. First, models for equilibrium pricing and profit influencing decisions are constructed based on asymmetric cost efficiency and converter preference. Second, game theory is used to analyze two scenarios: competitive enterprises participating simultaneously in both mass advertising and targeted advertising, and only one enterprise participating in targeted advertising. The main research findings are as follows: 1) Between the two advertising modes, enterprises can realize Pareto optimization more easily when engaging in targeted advertising. 2) In terms of cost efficiency, enterprises with low cost efficiency are more likely to obtain more benefits by participating in targeted advertising. 3) As far as the preference of the converter is concerned, generally speaking, with the increase in converter preference, enterprises with converter advantages will obtain more (or the same) profits than others. 4) Both average price and high price strategy are more sensitive to advertising costs than the preference of the converter. The conclusions of this study provide a theoretical basis for enterprises to advertise and the corresponding best methods.

Umbrella pricing and cartel size

It is generally assumed that bigger scale and scope of private antitrust enforcement promotes effective competition. This has motivated several North American and European courts to uphold redress claims not only from clients of a detected cartel but also plaintiffs who were exposed to ‘umbrella pricing’, i.e. equilibrium price increases by non-colluding competitors. The paper shows that the presumed deterrence effects of obliging infringing firms to compensate aggrieved customers of non-infringing firms can be dominated by adverse cartel size effects: liability for umbrella damages primarily constrains small partial cartels. It thereby improves the comparative profitability and stability of large ones. More encompassing cartels can form, prices rise, and welfare falls.

Information, market power and welfare

We study the market for a risky asset in which traders are heterogeneous both in terms of their value for the asset and the information that they have about this value. Traders behave strategically and use the equilibrium price to extract information that is relevant to them. Due to adverse selection, uninformed traders are less willing than the informed to provide liquidity. We evaluate the impact of a change in the size or composition of the investor population on price informativeness, liquidity and welfare, with applications to the rise of passive investing and the adoption of ESG standards.

A Multicommodity Spatial Price Equilibrium Model with Exchange Rates and Non-Tariff Measures for Agri-Food International Trade

A Multicommodity Spatial Price Equilibrium Model with Exchange Rates and Non-Tariff Measures for Agri-Food International Trade

Recycling channel design and coordination in a reverse supply chain with customer green preference

This study investigates the selection of recycling mode and the coordination mechanism in a reverse supply chain (RSC) that consists of one remanufacturer, one traditional recycler, and one smart recycler. We characterize the collection cost differences between traditional recycling and smart recycling, and the scrap rate of used products by smart recycling. We consider three recycling modes with recycling pricing competition, conditional on whether the remanufacturer collaborates with the traditional recycler, with the smart recycler, or with both recyclers. We show that the optimal recycling channel strategy for the remanufacturer is to enroll both the traditional recycler and the smart recycler, and the competition between these two recyclers exerts some non-trial implications on the firms’ equilibrium pricing strategy and profitability. By comparing the equilibrium outcomes with a centralized system, we further develop two coordination contracts: a two-part tariff contract and a transfer price combined with a profit-sharing contract, both of which can effectively mitigate double marginalization and improve the supply chain’s overall performance. Our findings provide useful guidance for the design of recycling channels, and for the coordination of RSC members to achieve Pareto improvement.

Heterogeneous awareness in financial markets

The overlook of some economic scenarios may result in unforeseen negative outcomes for investors. In this paper, we consider an order-driven financial market in which a fraction of the traders is only partially aware of the possible payoffs of a risky asset, but is aware of the possibility of facing unknown contingencies. Investors decide whether to acquire a costly signal about the payoff of the risky asset and whether to buy such asset given their awareness level and their perceived relations among signals, order flows, and prices. We show that as unawareness becomes more severe, the value of the signal to the partially aware traders diminishes. In turn, through its impact on the price, the reduced number of partially aware informed investors increases the incentives of the fully aware to acquire the signal. In the aggregate, the latter effect does not outweigh the former, so that the overall proportion of informed investors in the market is (weakly) decreasing in the unawareness level. As for the equilibrium price, a lower amount of informed traders makes it more difficult for market makers to distinguish between good and bad signals, and this brings the conditional expectations of the price closer to the unconditional one and reduces the price variance.

Young Duality for Variational Inequalities and Nonparametric Method of Demand Analysis in Input–Output Models with Inputs Substitution: Application for Kazakhstan Economy

The global macroeconomic shocks of the last decade entail the restructuring of national production networks and induce processes of input substitution. We suggest mathematical tools of Young duality for variational inequalities for studying these processes. Based on the tools we provide, a new mathematical model of a production network with several final consumers is created. The model is formulated as a pair of conjugated problems: a complementarity problem for optimal resource allocation with neoclassical production functions and the Young dual problem for equilibrium price indices on network products. The solution of these problems gives an equilibrium point in the space of network inter-industry flows and price indices on goods. Based on our previous results, we suggest an algorithm for model identification with an official economic statistic in the case of constant elasticity of substitution production functions. We give an explicit solution to the complementarity problems in this case and develop the algorithm of the inter-industry flows scenario projection. Since the algorithm needs the scenario projection of final sales structure as its input, we suggest a modified methodology that allows the calculation of scenario shifts in final consumer spending. To do this, we employ the generalized nonparametric method of demand analysis. As a result, we develop new technology for scenario calculation of a national input–output table, including shifts in final consumer spending. The technology takes into account a substitution of inputs in the network and is based on officially published national statistics data. The application of the methodology to study tax collection scenarios for Kazakhstan’s production network is demonstrated.

The role of green reputation, carbon trading and government intervention in determining the green bond pricing: An externality perspective

Green bonds, due to their inherent externalities, pose challenges in achieving equilibrium prices under optimal public resource allocation and social welfare without governmental intervention. While numerous studies have explored green bond pricing via government subsidies and other strategies, this paper diverges by targeting the equilibrium price of green bonds as the optimal public resource allocation, specifically from an externality's standpoint. We integrate factors such as the cap-and-trade system, carbon taxes, government subsidies, and green reputation into the fractional jump-diffusion model. This is further combined with real options theory and the fast Fourier transform method to derive the green bond pricing equation. Through optimization techniques, we delve into the influences of various factors and the interplay of different governmental strategies. Numerical findings suggest that, in an ideal scenario where the government grants adequate carbon allowances to green bond issuers, the carbon emission trading mechanism can facilitate the bond in achieving its ideal equilibrium price. Conversely, when the government is restricted by carbon constraints, preventing green bond issuers from acquiring ample carbon allowances, supplementary measures like government subsidies and carbon tax policies can complement the cap-and-trade system, ensuring green bonds attain their ideal equilibrium price. Furthermore, given the carbon emission reduction level of green projects, our model can determine the optimal government subsidy ratio and the ideal carbon tax price.

The Interaction Between Information Disclosure Strategy and Channel Structure in Platform Retailing: The Role of Product Returns

ABSTRACT Different information disclosure formats have been implemented to solve the severe product-return issue in platform retail. Considering the significant impact of channel structure choice on the information disclosure strategy, we explore their interaction by investigating the role of product returns. A multistage sequential game model is built in a supply chain comprising a platform and supplier. First, we derive the equilibrium pricing decisions in the short term and examine the role of product returns. Second, we study the optimal information disclosure strategy and channel structure choice in the long term. We also investigate the impact of the optimal strategy on the entire supply chain’s profits and consumer surplus. The following results were obtained: (1) Under the no information disclosure strategy, the presence of product returns weakens the impact of double marginalization in the wholesale model. Therefore, the information disclosure strategy improves product returns, but aggravates the double marginalization effect. (2) Information disclosure benefits the consumer and supply-chain members who disclose information, but may hurt the entire supply chain due to its negative spillover effect on other supply-chain members. (3) The optimal channel structure choice for the platform depends on the trade-off between these two effects of the information disclosure strategy on product returns. Therefore, platforms and suppliers should reexamine their attitudes toward product returns and be aware that more information is not always better, because of the impact of product returns.

Price equilibrium analysis based on the new theory of value

The universal measure of value has been always controversial in the traditional theory of value. Analogous to the research method of theoretical mechanics, developed from the traditional theory of value – labor theory of value, theory of surplus value and utility theory of value, the new theory of value has established a value complex variable function with labor value and use value as unknown functions, further in the mathematical logic of Euler equation and Euler formula, provided a universal measure of commodity value. On this basis, this paper focuses on the mathematical explicit expressions of value, exchange value, price and market equilibrium function that satisfy the principle of dimensional homogeneity, and the proof of the existence and stability of extremum solutions of market price equilibrium function, so as to help economics become a scientifi c theoretical system, integral with consistent logic, formed by qualitative theories, mathematical models, and computer models.

Technology of Input–Output Analysis with CES Production: Application for Studying the Kazakhstan Supply Chain during the COVID-19 Pandemic

Input–output analysis finds widespread application in estimating the shock effects on production networks within both local and global economies. We are developing a new technology for intersectoral analysis that takes into account the substitution of production factors within a complex supply network triggered by external or internal shocks. This technology is based on the explicit solution of a pair of convex programming problems: the resource allocation problem under the assumption of Constant Elasticity of Substitution (CES) technologies and the special dual Young problem. Solving these problems, we can ascertain the equilibrium inputs and price indexes of goods within the production network. In this paper, we apply this technology to analyze the economy of Kazakhstan in the context of the COVID-19 pandemic. Our calculations provide us with the means to discuss the macroeconomic responses of the multi-sectoral production network in Kazakhstan to both external and internal shocks stemming from the pandemic.

Marginal pricing equilibrium with externalities in Riesz spaces

Marginal pricing equilibrium with externalities in Riesz spaces

Identifying generalizable equilibrium pricing strategies for charging service providers in coupled power and transportation networks

Transportation electrification, involving large-scale integration of electric vehicles (EV) and fast charging stations (FCS), plays a critical role for global energy transition and decarbonization. In this context, coordination of EV routing and charging activities through suitably designed price signals constitutes an imperative step in secure and economic operation of the coupled power-transportation networks (CPTN). This work examines the non-cooperative pricing competition between self-interested EV charging service providers (CSP), taken into account the complex interactions between CSPs' pricing strategies, EV users' decisions and the operation of CPTN. The modeling of CPTN environment captures the prominent type of uncertainties stemming from the gasoline vehicle and EV origin-destination travel demands and their cost elasticity, EV initial state-of-charge and renewable energy sources (RES). An enhanced multi-agent proximal policy optimization method is developed to solve the pricing game, which incorporates an attention mechanism to selectively incorporate agents' representative information to mitigate the environmental non-stationarity without raising dimensionality challenge, while safeguarding the commercial confidentiality of CSP agents. To foster more efficient learning coordination in the highly uncertain CPTN environment, a sequential update scheme is also developed to achieve monotonic policy improvement for CSP agents. Case studies on an illustrative and a large-scale test system reveal that the proposed method facilitates sufficient competition among CSP agents and corroborates the core benefits in terms of reduced charging costs for EV users, enhancement of RES absorption and cost efficiency of the power distribution network. Results also validate the excellent generalization capability of the proposed method in coping with CPTN uncertainties. Finally, the rationale of the proposed attention mechanism is validated and the superior computational performance is highlighted against the state-of-the-art methods.

Pricing strategies in a dual-channel green closed-loop supply chain considering incentivized recycling and circular economy

In recent years, significant attention has been dedicated to the design of closed-loop supply chains. However, opportunities exist to refine modeling approaches in alignment with circular economy principles. This refinement could foster the collaborative involvement of customers and retailers, resulting in a more sustainable operational framework. This study aims to address this gap, fostering waste reduction, resource conservation, and collaborative engagement in closed-loop supply chains. Thus, a multi-level, dual-channel green closed-loop supply chain that integrates circular economy principles is examined. We focus on implementing an incentive-based recycling program and examining various closed-loop supply chain settings: centralized, decentralized, and collaborative. We aim to determine optimal equilibrium prices, greening levels, and advertising strategies while considering the concurrent aspects of greening and incentivized recycling in today environmentally conscious era. By developing a demand function that integrates price elasticity, cross-price impacts, sustainability, and advertising, we evaluate performance through numerical examples and a case study in the clothing industry. The findings indicate that a collaborative approach surpasses a decentralized one regarding sustainability, guaranteeing profitability across the supply chain. The study also underscores the trade-offs between centralization and decentralization, with the former failing to ensure maximum individual profitability despite augmenting overall chain profits. Our findings can guide managers in reconciling profitability with sustainability when choosing supply chain structures, accentuating the value of collaborative strategies and green cost-sharing contracts. Furthermore, our results highlight that targeted advertising can stimulate demand for green products, and incentivizing circular economy practices through collaboration can yield positive environmental and economic outcomes.

Empirical Test of CAPM Model in Stock Market

The rapid development of the economy has brought about the continuous accumulation of personal assets, and at the same time, the concept of financial management is rapidly budding and spreading. People's rapidly expanding consumer desire makes stocks, funds, and other products more appealing, leading them to prefer the financial route. However, stocks and funds need investors to bear certain risks, generally speaking, the greater the risk, the more lucrative the investment returns. The CAPM model was born for this reason, and its main content is the relationship between yield and risk and equilibrium pricing. The application of the CAPM model in the stock market has always been the focus of attention. As a core part of the stock market, the banking sector has an inseparable relationship with finance. Therefore, this paper selects eight stocks of banks with long listed times and top market capitalization rankings, conducts empirical analysis on their trading data from 2018 to 2021, and employs the time series detection method to test whether the single factor CAPM model is effective in the Chinese stock market.

Sequentially mixed search and equilibrium price dispersion

Many markets feature sequentially mixed search (SMS), which is search directed toward a price distribution followed by noisy matching with multiple offers. I construct a tractable model of SMS, establish existence of a unique equilibrium, and prove that the equilibrium is constrained efficient. Although individuals on each side of the market are homogeneous and search is directed, the equilibrium has a non-degenerate and continuous distribution of posted prices on a connected support. Despite the possibility of multiple offers, the highest price is lower than the joint value of a match so that both sides of the market obtain strictly positive surpluses of trade at all equilibrium prices. This feature captures the common practice that searchers restrict search below a price bound. Moreover, I show that an increase in the meeting efficiency widens price dispersion, which helps explain the puzzling fact that the increased use of the Internet has not reduced price dispersion.

DEMAND AND COMPETITION IN THE RETAIL MARKET OF DIESEL FUEL IN BULGARIA

The purpose of the article is to evaluate the parameters of demand for diesel fuel by households in Bulgaria, the structure of the retail fuel market and the effectiveness of competition. Based on statistical data, the parameters of the demand function for diesel fuel by households were estimated and the price and income elasticity was determined. Models of market behaviour are applied and theoretical values of equilibrium quantities and prices are estimated. The hypotheses of cartel existence, revenue maximization, competitive market with low market concentration and perfect competition are tested.

Shopping for Information: Implications of Consumer Learning for Optimal Pricing and Product Design*

I study a seller's pricing problem where consumers perform costly product research about value before purchase. They buy the product when sufficiently optimistic about value and cease research when sufficiently pessimistic. I find that the seller encourages product research when prior belief about value is high, even though he could sell immediately for a high price. The prior affects both expected value and how additional information changes consumers' beliefs. I show that an increase in research cost affects equilibrium price nonmonotonically. Finally, when the seller chooses price and product value dispersion, the optimal level of dispersion need not be extremal.