Surplus Maximization Research Articles

Income distribution, implementation sequence, and equity in auto ownership rationing

Auto ownership rationing schemes, including lottery, auction and hybrid schemes, have been recognized as effective measures to mitigate urban traffic congestion. The implementation sequence of auction and lottery in the hybrid schemes has two possible scenarios: auction is implemented before lottery (i.e., A+L), and lottery is implemented before auction (i.e., L+A). This paper addresses the issues of income distribution, implementation sequence, and equity in the auto ownership rationing schemes. Expected social surplus maximization models are proposed for determining the optimal auto quota for each scheme and the optimal proportion allocated to the lottery and auction for the hybrid schemes. In the proposed models, a trade-off between positive externality (social contribution) and negative externality (traffic congestion) caused by auto industrial development is considered, together with effects of residents’ income distribution. Inequity issue incurred by the rationing schemes (who gains and who loses) is investigated, and Pareto-improvement strategy with self-financing constraint is presented to balance the equity and efficiency. The solution properties of the proposed models are analytically explored, and the solutions of different schemes are compared. The results show that (i) residents’ income distribution has no significant effects on the properties of the models; (ii) the optimal L+A hybrid scheme outperforms the optimal A+L hybrid scheme in terms of the expected social surplus; (iii) however, it is just reverse for the Pareto-improvement strategy that solves the inequity issue, i.e., the optimal A+L Pareto-improvement strategy is better than the optimal L+A Pareto-improvement strategy in terms of the expected social surplus.

Time and toll trade-off with heterogeneous users: A continuous time surplus maximization bi-objective user equilibrium model

This paper presents a continuous time surplus maximization bi-objective user equilibrium (C-TSmaxBUE) model, in which the users’ variability toward the time and toll trade-off in a tolled road network is explicitly considered. Different users are assigned with different ratios of the time saved per unit of money (RTSMs), the values of which represent the different expectations to trade more money for less travel time. Infinite indifference curves are then generated by considering continuously distributed RTSMs in the population. Accordingly, we extend the definition of the path-based time surplus for the C-TSmaxBUE model, which can be formulated as a Beckmann-type mathematical program operating in the space of RTSM boundaries. To solve the problem, we develop a path-based single-boundary adjustment (SBA) algorithm that fits the non-additive structure of the model. The algorithm involves a Newton-type flow equilibration procedure that simultaneously adjusts RTSM boundaries and path flows, as well as a column generation scheme that firstly enumerates all efficient paths and then identifies the paths that have the potential to reduce generalized travel times. Numerical results on a small network show the feature of the equilibrium flow pattern, whereas instances of practical size confirm that SBA is an efficient tool to obtain high-quality equilibrium solutions. Compared to the original TSmaxBUE problem, we found that a larger set of efficient paths will be used when the users’ heterogeneity is considered.

An Information Theory of Efficient Differential Treatment

When are differential treatment policies—such as preferential treatment, affirmative action, and gender equity policies—justified by efficiency concerns? I propose a nonparametric assignment model where a policymaker assigns agents to different treatments or positions to maximize total surplus, based on the agents’ characteristics and noisy information about their types. I provide necessary and sufficient conditions on the agents’ signal structures, which characterize whether surplus maximization requires differential treatment or not, and study how the bias and informativeness of signal structures determine the efficiency implications of differential treatment. I examine implications of this model for inequality, decentralization, and empirical work. (JEL D63, D82, D83, I23, I24, J71)

Reaping the Informational Surplus in Bayesian Persuasion

The Bayesian persuasion model studies communication between an informed sender and a receiver with a payoff-relevant action, emphasizing the ability of a sender to extract maximal surplus from his informational advantage. In this paper, we study a setting with multiple senders in which the receiver is restricted to choosing, at the interim stage, one sender with whom to interact. Our main result is that whenever senders are uncertain about each other’s preferences and, in particular, cannot dismiss with certainty the possibility that others are aligned with the receiver, the receiver receives all the informational surplus in all equilibria. (JEL C72, D82, D83)

MEDIEVAL MATCHING MARKETS

AbstractWe study the regulation of brokerage in wholesale markets in premodern Central Western Europe. Examining 1,804 sets of rules from 82 cities, we find brokerage was primarily a centralized matchmaking mechanism. Brokerage was more common in towns with larger populations, better access to sea ports and trade routes, and greater political autonomy. Brokers' fee structures varied systematically: price‐based fees were more common for highly heterogeneous goods, quantity‐based fees for more homogeneous goods. We show theoretically that this was broadly consistent with total surplus maximization, and that brokerage was more valuable in markets with unequal numbers of buyers and sellers.

Optimal scheduling of a hybrid AC/DC multi-energy microgrid considering uncertainties and Stackelberg game-based integrated demand response

The emergence of solid-state transformers (SSTs) enriches the system structure and operation mode of the multi-energy microgrid (MEMG). This paper depicts a novel hybrid AC/DC MEMG structure based on a three-stage SST, and proposes a two-level optimal scheduling model considering generation and load uncertainties, as well as Stackelberg game-based integrated demand response. In the upper level model for the energy hub operator (EHO), the pricing strategy and equipment dispatch are optimized to maximize profit, and the two-stage adaptive robust optimization and reserve allocation are used to address the uncertainties of renewable generation and loads, respectively. In the lower level model for the demand response aggregator (DRA), the response strategy of different loads, including shiftable, adjustable and replaceable loads, is optimized for surplus maximization. To solve the proposed scheduling model, the two-level optimization problem is transformed to a single-level min–max-min problem according to Karush-Kuhn-Tucker conditions, then it is divided into two subproblems and solved by the column-and-constraint generation algorithm and CPLEX solver. Furthermore, a case study is carried out to validate the effectiveness of the proposed model, and it shows that the total benefit of EHO and DRA can be improved by 5.75% due to the demand response strategy.

Sorting expertise

We analyze the optimal sorting of experts who differ in their ability to acquire information, into production teams. Once a team is formed, experts individually acquire information about the joint project, communicate the information they acquired, and then engage in team production. Misalignment of preferences at the production stage creates incentives for belief manipulation at the communication stage. We show that the cost associated with misaligned incentives is minimized if experts of similar abilities are placed in the same team. Consequently, surplus maximization may lead to non-diversified teams, even if in the absence of misaligned incentives optimal sorting is negative assortative. Thus, our analysis provides a novel rationale for creation of non-diversified teams of experts.

The pivotal mechanism versus the voluntary contribution mechanism: an experimental comparison

We conduct an experimental comparison of two well-known mechanisms for undertaking a binary public project: the pivotal mechanism and the voluntary contribution mechanism. We compare the two mechanisms under complete information in which each subject knows the other subjects’ payoffs. We then observe that the voluntary contribution mechanism works better than the pivotal mechanism from the perspectives of Pareto efficiency, individual rationality, and surplus maximization. On the other hand, there is no significant difference between the two mechanisms in terms of decision efficiency. These results suggest that the voluntary contribution mechanism is more favorable than the pivotal mechanism in practical applications.

Horizontal mergers under uniform resource constraints

Resource constraints have a vertical influence on a firm's competition and it is important to address the issue of horizontal mergers with scarce resources. This article highlights the effects of uniform resource constraints on horizontal mergers with game theory methods. First, the threshold values for the firms to accept the merger, increasing consumer surplus, and increasing social welfare are presented and compared. Second, the threshold value to merge for consumer surplus maximization is larger than that for profit incentive mergers without resource constraints. Thus, under unbinding resource industries, mergers reduce consumer surplus and it is necessary to implement antitrust. Third, resource constraints deter mergers. Finally, under binding capacity (or resource) constraints, the threshold value for firms to merge is larger than that for the social optimality. Therefore, industries with scare resource should avoid antitrust.

Consumer surplus and budget constrained preference maximization: A note

The paper attempts to rectify what appear to be popular but elementary misconceptions about the concept of consumer surplus in the context of Marshallian demand curves. It is primarily addressed to teachers of microeconomics at the undergraduate level or in MBA programs of business schools. The main text informs the reader about the model/context and the results we are concerned with, all of the latter being a comprehensive teaching note, relegated to an appendix of the paper. Thus, the potential instructor may use the main text to motivate himself/herself and at the same time inform his/her students as to the topic i.e. the rehabilitation of consumer surplus as an exact measure of welfare from the stand-point of cost benefit analysis. Thereafter the appendix can be referred to for a more formal presentation. The technical results contained in the appendix begin by showing that willingness to pay is the area under the demand curve if and only if consumers are surplus maximizers. The last result in the appendix is a theoretically ‘happy ending’ since it shows that for purposes of applied economics, budget constrained preference maximization implies surplus maximization and hence for such consumers, willingness to pay is indeed the area under the demand curve up to the quantity consumed.

Distributed Time-Sensitive Task Selection in Mobile Crowdsensing

With the rich set of embedded sensors installed in smartphones, we are witnessing the emergence of many innovative commercial mobile crowdsensing applications, which combine the power of mobile technology with crowdsourcing to effectively collect time-sensitive and location-dependent information. Motivated by these real-world applications, we consider the distributed task selection problem for heterogeneous users with different initial locations, destinations, costs, speeds, and reputation levels. We design a Bayesian asynchronous task selection (BATS) algorithm to help the users plan their task selections based on the incomplete information of the task popularity statistics. We prove its convergence and characterize the computation time for the users' updates. As a performance benchmark, we consider the ideal case that the service provider centrally allocates the tasks to the users for social surplus maximization. We show that it is an NP-hard problem and propose a greedy centralized algorithm with a lower complexity as the benchmark performance. Simulation results suggest that the BATS scheme achieves the highest Jain's fairness index and coverage, while yielding a user payoff similar to that with the greedy centralized benchmark. Finally, we evaluate the schemes based on some real-world movement time and distance data from Google Maps.

Reaping the Informational Surplus in Bayesian Persuasion

The Bayesian persuasion model studies communication between an informed sender and a receiver with a payoff-relevant action, emphasizing the ability of a sender to extract maximal surplus from his informational advantage. In this paper we study a setting with multiple senders, but in which the receiver interacts with only one sender of his choice: senders commit to signals and the receiver then chooses, at the interim stage, with which sender to interact. Our main result is that whenever senders are even slightly uncertain about each other's preferences, the receiver receives all the informational surplus in all equilibria of this game.

Intra-port coopetition under different combinations of terminal ownership

An intra-port coopetition model is proposed, which simultaneously characterizes both competition and cooperation among terminal operators in a port when competing with operators from external ports. Terminal operators make cooperative efforts to increase port competitiveness, while simultaneously making competitive efforts for price adjustment, cost and/or time reduction at individual terminals. Numerical analysis is performed considering private and public terminals characterized by different profit and social surplus maximization objectives. The results show that operator incentives change depending on the combinations of terminal ownership, and the private terminal tends to behave as a free rider in a public-private combination.

Buyer-Optimal Information Under Uncertainty

This paper explores the buyer-optimal information structures in a monopolistic screening context with nonlinear production technology. It shows that the buyer's optimal surplus may increase even when the production cost becomes more uncertain or when the efficient surplus decreases. Under a binary prior, this paper further shows that the buyer-optimal information structures must lie in a family described by truncated Pareto distributions. Such characterization effectively reduces the surplus maximization problem to a monopsony's pricing problem, which further implies that the buyer-optimal surplus is quasi-convex in technologies that are ranked by the rotational order.

Dynamic relational contracts under complete information

This paper considers a long-term relationship between two agents who both undertake an action or investment that produces a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. Agents have quasi-linear preferences. Two cases are considered: where agents are risk averse but where limited liability constraints do not bind, and where agents are risk neutral and subject to limited liability constraints. We ask how to structure the investments and division of the surplus over time to avoid expropriation. In the risk-averse case, the dynamics of actions and surplus may or may not be monotonic depending on whether or not a first-best allocation can be sustained. Agents may underinvest but never overinvest. If the first-best allocation is not sustainable, there is a trade-off between risk sharing and surplus maximization; surplus may not be at its constrained maximum even in the long run and the “amnesia” property of pure risk-sharing models fails to hold. In contrast, in the risk-neutral case there may be an initial phase in which one agent overinvests and the other underinvests. Both actions and surplus converge monotonically to a stationary state, where surplus is maximized subject to the self-enforcing constraints.

How many educated workers for your economy? European targets, optimal public spending, and labor market impact

This paper studies optimal taxation schemes for education in a search-matching model where the labor market is divided between a high-skill and a low-skill sector. Two public policy targets - maximizing the total employment level and optimizing the social surplus - are studied according to three different public taxation strategies. We calibrate our model using evidence from thirteen European countries, and compare our results with the target from the Europe 2020 Agenda for achievement in higher education. We show that, with current labor market characteristics, the target set by governments seems compatible with the social surplus maximization objective for some countries, while being too high for other countries. For all countries, maximizing employment would imply higher educational spending than that required for the social surplus to reach its maximum.

Surplus, Contractibility and Theory of the Firm

A theory of the firm is advanced as a unified property rights for surplus created by cooperative activity. This differs from traditional transaction cost literature which views the firm as a governance structure. Individual purposive entities act in their own interests, within or without a firm. Only contractible inputs are coordinated for joint surplus maximization. Each party determines her non-contractible inputs for her own benefits, which explain many observed firm phenomena. An equilibrium models are developed for the firm and used to explain the questions of firm existence, boundary, and ownership.

The optimal minimum wage with regulatory uncertainty

AbstractFor two different regulatory standards, we examine the optimal minimum wage in a competitive labor market when the government is uncertain about supply and demand. Solutions are related to underlying supply and demand conditions, and to the extent of uncertainty and of rationing efficiency. With expected earnings maximization, greater uncertainty widens the range of parameter values for which a minimum wage should be set. With expected worker surplus maximization and sufficiently efficient rationing, a minimum wage should always be set. However, in both cases regulatory uncertainty may require a low minimum wage that may not bind in equilibrium.

A Route Choice Model with Context-Dependent Value of Time

This paper proposes a route choice model that incorporates the various behavioral mechanisms in route choice proposed in the literature including the shortest path, bounded rationality, asymmetric preference, and the time surplus maximization. In the proposed model, travelers are assumed to compare travel cost to their status quo (travel cost of the currently used path) in deciding whether to switch to another alternative, and the underlying value of time is adaptive in the sense that it varies across different route choice contexts. We find that the status quo-dependent route choice model can handle the route choice inertia resulting from different sources (e.g., travelers’ misperceptions, satisficing behavior, asymmetric preference). Moreover, the inertia is path-specific and can incorporate the scaling effect of travel cost on travelers’ route choices. Examples are provided to illustrate the proposed status quo-dependent route choice model as well as its connection with various existing route choice models.

Search Design and Broad Matching

We study decentralized mechanisms for allocating firms into search pools. The pools are created in response to noisy preference signals provided by consumers, who then browse the pools via costly random sequential search. Surplus-maximizing search pools are implementable in symmetric Nash equilibrium. Full extraction of the maximal surplus is implementable if and only if the distribution of consumer types satisfies a set of simple inequalities, which involve the relative fractions of consumers who like different products and the Bhattacharyya coefficient of similarity between their conditional signal distributions. The optimal mechanism can be simulated by a keyword auction with broad matching. (JEL C78, D44, D82)