Surplus Function Research Articles

Consumer strategy, vendor strategy and equilibrium in duopoly markets with production costs

We study consumer strategy, vendor strategy and their equilibrium in a duopoly market where vendors bear the costs in the production process. If consumers have an identical preference that is unknown, we obtain the equations satisfied by the total social surplus and the profit of each vendor. Moreover, we prove that the second derivatives of the total social surplus function and the profit function are continuous at the cutoff by the well-known conditions of value matching and smooth pasting. In a duopoly market, vendors can increase the total social surplus by adjusting their output, which causes fewer profits for vendors. However, rational vendors usually do not make such concessions, which implies that it is almost impossible to maximize total social surplus in a duopoly market. Thus, the planner needs to control vendors’ output to maximize the total social surplus. We obtain the planner’s optimal strategy and the socially efficient allocation. When vendors and consumers maximize their value, we find that the price of goods may be less than their costs due to price competition. By Bayesian learning and price competition model, we discuss a Markov perfect equilibrium and the relationship between the socially efficient allocation and the Markov perfect equilibrium.

A continuous model of strong and weak ties

AbstractWhen individuals interact in a network, links are often asymmetric and of varying intensity. I study a model whereby networks emerge from agents maximizing utility from continuous linking decisions and self‐investment. The joint link surplus function allows arbitrary, bounded heterogeneity in the benefit to forming links. Under decreasing returns to scale in link surplus, the set of Nash equilibria is well‐behaved. In contrast, with constant or increasing returns to scale, heterogeneity and returns to self‐investment limit the set of Nash equilibria. This model rationalizes equilibrium networks in which individuals simultaneously hold ties that are asymmetric and of varying intensity.

Estimation of Marketed Surplus Function of Milk in Madhya Pradesh

"The present study to estimate the factors affecting the marketed surplus of milk in Madhya Pradesh was carried out by collecting data from 80 producer households from two zones of Madhya Pradesh during 2020. The study revealed that milk production per animal was the most significant factor influencing the marketed surplus of milk followed by price of milk and operational land holding, respectively. Both in relative as well as in absolute terms, production and marketed surplus increased with the increase in the herd size implying positive relationship between production and marketed surplus of milk. Larger family size tends to decrease the marketed surplus as it is more consumed at producer level. This signifies that efforts should be made to improve the productivity of animals as states has highest indigenous cattle population whose productivity was found to be very low along with efficient marketing facilities to get remunerative price"

Local social interaction and urban equilibria

In this paper we investigate the effect of local interaction in a simple urban economics model. Agents interact with others if and only if their interaction benefit outweighs their travel cost and therefore meet others only within finite geographic windows. We show that two or more cites may co-exist at the equilibrium provided that they are sufficiently distant. For any interaction surplus function, there exists a unique spatial equilibrium on not too large city supports. The population density within a city is determined by a second order advance-delay differential equation, whose solutions are fully characterized for linear interaction surplus functions. Numerical analyses show that more localized interactions yield flatter population density and land rents over larger extents of the city support. They do not give support to the idea that multiple subcenters can be caused by small and finite geographic windows of interaction.

The even split rule in positive assortative matching

Many economic models, especially in two-sided matching literature, involve breaking down a supermodular function into two supermodular functions according to a certain allocation rule. The conventional wisdom is to invoke the Nash bargaining solution, which boils down to an even split rule within the transferable utility framework. This paper rationalizes the use of the Nash bargaining solution in a two-sided matching model by showing that the even split rule is the only allocation which allows the net benefit functions to inherit supermodularity from the joint surplus function, which is necessary to ensure positive assortative matching.

Transition to nestedness in multi- to one-dimensional optimal transport

We study a one-parameter class of examples of optimal transport problems between a two-dimensional source and a one-dimensional target. Our earlier work identified a nestedness condition on the surplus function and marginals, under which it is possible to solve the problem semi-explicitly. In the family of examples we consider, we classify the values of parameters which lead to nestedness. In those cases, we derive an almost explicit characterisation of the solution.

Stable Marriage with and Without Transferable Utility: Nonparametric Testable Implications

We show that transferable utility has no nonparametrically testable implications for marriage stability in settings with a single consumption observation per household and heterogeneous individual preferences across households. This completes the results of Cherchye, Demuynck, De Rock, and Vermeulen (2017), who characterized Pareto efficient household consumption under the assumption of marriage stability without transferable utility. First, we show that the nonparametric testable conditions established by these authors are not only necessary but also sufficient for rationalizability by a stable marriage matching. Next, we demonstrate that exactly the same testable implications hold with and without transferable utility between household members. We build on this last result to provide a primal and dual linear programming characterization of a stable matching allocation for the observational setting at hand. This provides an explicit specification of the marital surplus function rationalizing the observed matching behavior.

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives. We extend and analyze a previously proposed stochastic clearing formulation in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price bounded price distortions, and we show that adding a similar penalty term to transmission flows and phase angles ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities equal a quantile of their real-time counterparts. The undesired effects of price distortions suggest that stochastic settings provide significant benefits over deterministic ones that go beyond social surplus improvements. We propose additional metrics to evaluate these benefits.

Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium

This paper focuses on oligopolistic markets in which indivisible goods are sold by multiproduct firms to a continuum of homogeneous buyers, with measure normalized to one, who have preferences over bundles of products. By analyzing a kind of extended contract schedule (mixed bundling prices), the paper shows that pure strategy efficient equilibria always exist in such settings. While inefficient equilibria may exist, this can be ruled out by refining the equilibrium correspondence using the concept of subgame perfect Strong equilibrium. In addition, the paper shows that each principal's set of equilibrium contracts of minimum cardinality may contain at least three offers. When the social surplus function is monotone and unit costs are constant, only two offers are required at the equilibrium outcome.

Output subsidy of renewable energy power industry under asymmetric information

Subsidy given by the government for production is common to develop renewable energy enterprises. This article establishes a duopoly model including renewable energy enterprises and traditional energy enterprises based on market with both complete information and asymmetric information. A generalized consumer surplus (GCS) function is defined, and the assumption that the government maximizes generalized consumer surplus is provided. To identify the cost of enterprises precisely, the government gives incentive compatibility constraint. Firstly, this article found that optimal subsidy for renewable energy enterprises positively correlates with its cost under complete information. Secondly, under asymmetric information, the optimal subsidy values increase with the probability of firms with high costs. Thirdly, renewable energy enterprises may hide their cost to maximize their profits when the difference between subsidies for renewable energy enterprises with disparate cost is too large or too small. Finally, a mechanism to induce enterprises' truth based on incentive compatibility constraints is offered. Under this circumstance, a suggestion is provided that government should choose to screen the cost information of the enterprises or to maximize generalized consumer surplus as the preferred target.

Matching in closed-form: equilibrium, identification, and comparative statics

This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are normal, and when the heterogeneity in tastes is of the continuous logit type, as in Choo and Siow (J Polit Econ 114:172-201, 2006), we show that the optimal matching distribution is also jointly normal and can be computed in closed form from the model primitives. Conversely, the quadratic surplus function can be identified from the optimal matching distribution, also in closed-form. The closed-form formulas make it computationally easy to solve problems with even a very large number of matches and allow for quantitative predictions about the evolution of the solution as the technology and the characteristics of the matching populations change.

Two-Sided Matching in Physician-Insurer Networks: Evidence from Medicare Advantage

Many health insurance plans in the U.S. restrict enrollees to choose from a set of providers the insurer has contracted with. These provider networks are formed via bilateral bargaining between insurers and providers. Provider networks are an important tool for product differentiation and cost containment for insurers and also put real restrictions on consumer's choice of providers. In this paper, I analyze matching between insurers offering Medicare Advantage Plans and physicians, using a unique data set consisting of all insurer-physician links in several counties. I estimate parameters of a two-sided, many-to-many matching model which describes formation of provider networks, using the Maximum Score estimator of Fox (2010). This method uses implications of a pairwise stability condition to estimate a joint surplus function which depends on insurer-physician links. The surplus function accounts for the role of physician and insurer characteristics in determining their match values, and also for interactions between physicians linked to the same insurer, whose services may be complements or substitutes. The results indicate that insurers prefer on the margin to link with physicians who increase the specialty concentration of their network and who are located near other physicians in the network. Physicians are negatively affected by having a broader referral network, as defined by having a larger set of physicians with whom they have insurer links in common. These forces could lead to networks being undesirably narrow, excluding specialties, locations and specific physicians that would be valuable for some plan enrollees. Finally, compared with regional insurers, nationally active insurers have a larger number of exclusive links with physicians, and match with more physicians with U.S. medical degrees. This result suggests positive assortative matching.

Do Consumers Benefit from Dynamic Pricing?

Dynamic pricing is designed to increase profits by adjusting prices in respond to changes in the marginal value of capacity or changes in input costs. While thousands of papers have been written about dynamic pricing, this is to our knowledge the first paper to examine the impact of dynamic pricing on consumer surplus. Intuition suggests that dynamic pricing may be a zero-sum game, where additional profits are made by firms at the expense of reducing consumer surplus. Executives who subscribe to this hypothesis may be reluctant to implement dynamic pricing for fear of consumer backlash. In this paper, we show that dynamic pricing is often win-win, with both firms and consumers being better off relative to the alternative of offering an optimal static price. The intuition lies on the fact that for common demand functions, the surplus function is decreasing convex in price and so is the composite function that incorporates optimal prices as a function of cost.

Matching in Closed-Form: Equilibrium, Identification, and Comparative Statics

This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are normal, and when the heterogeneity in tastes is of the continuous logit type, as in Choo and Siow (2006), we show that the optimal matching distribution is also jointly normal and can be computed in closed form from the model primitives. Conversely, the quadratic surplus function can be identified from the optimal matching distribution, also in closed-form. The analytical formulas make it computationally easy to solve problems with even a very large number of matches and allow for quantitative predictions about the evolution of the solution as the technology and the characteristics of the matching populations change.

Optimal and Sustainable City Size by Estimating Surplus Function for Metropolitans of Iran

By shouldering the burden of a big chunk of global production, and giving Shelter to half of the world’s population, currently cities play an important role in national economies. Benefits of agglomeration in cities have played a major role in the process of economic development of different countries, however, the expansion of urbanization has produced some problems including environmental and noise pollutions and traffic problems. Therefore many of the Metropolitan residents blame the population growth for the problems they face while urban governors have to find an answer to the question that if there is an optimum size for their cities, what is that size? This essay reflects on the optimal and sustainable size of the metropolitans in Iran and gives separate estimation for each. Due to scarcity of statistical information this article includes five metropolitans of Tehran, Isfahan, Mashhad, Shiraz and Ahvaz, within the time span of 1999 to 2012. This survey is based on the estimation of surplus function including the pollution externalities. The results show that Tehran is overpopulated to the excess of 71 percent of its optimum size, and also it has exceeded its sustainable size by five percent. Also other four metropolitans of Isfahan, Mashhad, Shiraz and Ahvaz have exceeded their optimal size but they still are in their relevant sustainable limits.

One-to-many bargaining when pairwise agreements are non-renegotiable

We study a model where a central player (the principal) bargains bilaterally with each of several players (the agents) to create and share the surplus of a coalitional game. It is known that, if the payments that were previously agreed (with each of the remaining agents) are renegotiated in case any bilateral negotiation permanently breaks down, then the Shapley value is the unique efficient and individual rational outcome consistent with bilateral Nash bargaining. Here we show that when instead the agreed payments cannot be renegotiated the outcome is also unique but it now coincides with the Nucleolus of an associated bankruptcy problem. We provide a strategic foundation for this outcome. Then we study how such renegotiation affects the principal's payoff according to the properties of the surplus function. We find, for example, that renegotiation benefits the principal when agents are complements and it hurts him when they are substitutes (situations with, respectively, increasing and decreasing marginal contributions).

Stability Induces Pre-Matching Gambles

This paper initiates the investigation into pre-matching gambles. Examples of pre-matching gambles include occupational choices before the marriage market, college major choices before the labor market, and financial portfolio management to attract future investors. Surprisingly, people take risky investments they would have not taken if not for the subsequent participation in competitive matching markets. A fundamental and unique feature of the competitive matching market, which I call the competitive rematching effect, drives pre-matching gambles. The competitive rematching effect drives gambling independently of the shape of the surplus function, contrary to the possible misconception that surplus supermodularity and positive-assortative matching play a role. Finally, the paper discusses implications to efficiency and inequality associated with gambles, and to occupational choices with marital concerns.

Risk-cost-based generation scheduling smartly mixed with reliability-driven and market-driven demand response measures

Because of potential benefits of demand-side management (DSM) at operation and economic levels, DSM is introduced as the first choice in all energy policy decisions. Under deregulation, DSM programs have been expanded to include demand response programs (DRPs). In the present study, in order to investigate and utilize the reliability-driven and market-driven measures of demand response, a model of risk-cost-based unit commitment (UC) problem mixed with demand-side resources (DSRs), that is, UCDSRs model considering economic model of responsive loads, is presented. In this study, the economic model of responsive load is derived on the basis of price elasticity of demand and consumers' surplus function. The proposed method is intelligently applied on a test power system to determine the optimal scheme for implementing DRPs, the optimal commitment status of units, the optimal risk level of system, the modified demand level of system, and the minimum total cost of system. Copyright © 2014 John Wiley & Sons, Ltd.

The Macrodynamics of Sorting between Workers and Firms

We develop an equilibrium model of on-the-job search with ex ante heterogeneous workers and firms, aggregate uncertainty, and vacancy creation. The model produces rich dynamics in which the distributions of unemployed workers, vacancies, and worker-firm matches evolve stochastically over time. We prove that the surplus function, which fully characterizes the match value and the mobility decision of workers, does not depend on these distributions. This result means the model is tractable and can be estimated. We illustrate the quantitative implications of the model by fitting to US aggregate labor market data from 1951–2012. The model has rich implications for the cyclical dynamics of the distribution of skills of the unemployed, the distribution of types of vacancies posted, and sorting between heterogeneous workers and firms. (JEL E24, E32, J24, J63, J64)

Optimal power and subcarrier allocation with partial side information for downlink OFDMA system

In this paper, we investigate the power and subcarrier allocation issue in the case of partial side information for downlink orthogonal frequency division multiple access (OFDMA) system. Relaxation method is utilized to characterize the necessary conditions of the optimal solution and the uniqueness of the optimal solution is proved. The game theoretical concept, surplus function is also introduced to analyze the optimal solution. Based on the theoretical analysis, we propose iterative surplus balancing algorithm (ISBA) that can jointly assign the power and subcarriers in multiple rounds, and then the optimality of ISBA is proved. Simulation results are presented to show the characteristics of the theoretical analysis and ISBA.