Social Planner Research Articles

Mirage on the horizon: Geoengineering and carbon taxation without commitment

We show that, in a model without commitment to future policies, geoengineering breakthroughs can have adverse environmental and welfare effects because they change the (equilibrium) carbon taxes. In our model, energy producers emit carbon, which creates a negative environmental externality, and may decide to switch to cleaner technology. A benevolent social planner sets carbon taxes without commitment. Higher future carbon taxes both reduce emissions given technology and encourage energy producers to switch to cleaner technology. Geoengineering advances, which reduce the negative environmental effects of the existing stock of carbon, decrease future carbon taxes and thus discourage private investments in conventional clean technology. We characterize the conditions under which these advances diminish—rather than improve—environmental quality and welfare, and show that given current estimates of costs and environmental damages, these conditions are likely to be satisfied in our model.

Optimal liquidity allocation in an equity network

We study an optimal liquidity allocation problem in a distressed financial system when agents are embedded in a network of cross-ownership. We construct a model in which a benevolent social planner allocates a limited amount of funds to rescue agents facing liquidity shortages and whose liquidation can be avoided if the shortage is met. A discrete allocation problem arises in this setting and the “Balas” algorithm is employed to solve this problem. Solving the optimal liquidity allocation problem over a class of core–periphery equity network topologies, we establish the existence of a threshold value of exposures levels between core and peripheral nodes above which the social planner would allocate available funds to the periphery and below which to the core. The algorithm demonstrates how monetary and fiscal authorities may implement rescue plans when the size of the fund is limited and could thus serve as a new intervention tool in the arsenal of policymakers.

Fleet cost and capacity effects of automated vehicles in mixed traffic networks: A system optimal assignment problem

Automated vehicles can increase network capacity by leveraging connectivity with other vehicles and the infrastructure, but come at a larger operating and maintenance cost than other human-driven vehicles. This study investigates the trade-off in cost and capacity effects of automated vehicles when a social planner decides the optimal fleet mix for serving a given network demand. We present a system optimal assignment problem that is a non-linear program with linear constraints. Using second-order analysis, we label each link of the network as either “convex” or “concave”. The classification is done prior to any traffic assignment and is independent of demand patterns. According to the classification, a social planner benefits from increasing (decreasing) the automated vehicle ratio of traffic in convex (concave) links. We show that the proposed system optimal problem is non-convex and develop a Benders decomposition algorithm with a master problem that decides path flows and a sub-problem that finds the optimal automated vehicle ratio of each path. We further discuss the system optimal properties in three stylized networks with parallel, series, and mixed topology, and a larger Sioux Falls network. Results show that in parallel networks, the convex (concave) links have an automated vehicle ratio of one (zero), whereas in series networks, the optimal automated vehicle ratios depend on several network parameters.

Preferences for investment in and allocation of additional healthcare capacity

Policy makers need to make decisions regarding the allocation of scarce healthcare resources. We study preferences for investment in additional healthcare capacity and allocation between two regions, focusing on reducing waiting time for elective surgery for a physical health problem. We elicit preferences from a societal and an individual perspective, with unequal initial waiting times between the two regions. In an online survey, 1039 respondents were randomly assigned to one of three versions of the experiment: (1) a social planner perspective, placing respondents in the role of a policy maker; (2) an individual perspective where the respondent's own region was better off regarding initial waiting times; (3) an individual perspective where the individual's own region was worse off regarding initial waiting times. Respondents were asked to rank the status quo and five scenarios where the investment in additional capacity led to different distributions of shorter waiting times between regions. For all allocations we presented both the reduction in waiting time and the resulting final waiting time for both regions. We find that in version 1 of the experiment, preferences were in line with inequality aversion and Rawlsian preferences regarding final waiting time. In version 3, similar preferences were found, although here they also align with individualistic preferences. In version 2, preferences were more heterogeneous, with both individualistic and egalitarian preferences present. Concluding, individualistic and egalitarian preferences mostly concerned final waiting time. We therefore recommend policy makers to focus on the effect on final waiting time instead of the reduction of waiting time.

Sudden stops and reserve accumulation in the presence of international liquidity risk

We propose a small open economy model where agents borrow internationally and invest in liquid foreign assets to insure against liquidity shocks, which temporarily shut out the economy of short-term credit markets. Due to a pecuniary externality, individual agents overborrow and hold too little liquid assets relative to a social planner. This inefficiency rationalizes macroprudential policy intervention in the form of reserve accumulation at the central bank to stabilize trade and the real exchange rate. Our model quantitatively matches the depreciation of the real exchange rate and contractions in output, gross trade flows, and foreign reserve holdings during Sudden Stops.

A dynamic analysis of a monopolist's efforts for improving product quality and process innovation with reference price effects under linear demand

AbstractThis paper examines a monopolist's innovation efforts for improving product quality and process innovation with reference price effects. Our main results show that the system can achieve saddle‐point steady‐state equilibrium; the two efforts increase with the increase of reference price; although the price is still determined by the monopolist, the price under the social planner regulation is higher than that under the monopolist decision‐making; there is always a negative relationship between the product quality and the price; and memory parameter affects the complementarity (substitutability) relationship between these two efforts.

A novel price-driven energy sharing mechanism for charging station operators

To address the deviations of energy schedules and increase benefits, charging station operators (CSOs) hope to trade energy in a low-cost and efficient way. Energy sharing has been noticed as a way to improve social welfare. When energy has commodity attributes, designing a better sharing mechanism from energy scarcity to stimulate prosumer flexibility and achieve optimal social welfare needs to be studied. In this paper, a novel price-driven energy sharing mechanism is designed for prosumers. A prosumer surplus model including energy utility is established to extend the prosumer flexibility. Value identity based on the “shared electricity price” enables prosumers to agree on a price voluntarily. It is proven that the new mechanism has the same unique optimal solution as the social planner's problem. Unlike the existing sharing mechanisms based on the generalized Nash game, the new mechanism can achieve optimal social welfare in a market with finite prosumers. On this basis, a local energy sharing model of CSOs is established, where the network constraints of the local system and time-varying utility are considered in the sharing process. The simulations show that the new mechanism can efficiently use the prosumers' generation and load flexibility to achieve better social welfare.

Optimal electric vehicle subsidy and pricing decisions with consideration of EV anxiety and EV preference in green and non-green consumers

Electric vehicles (EVs) are an important part of the solution to climate change due to their reduction in carbon emissions. Purchase subsidies have been efficient tools in overcoming the cost barrier. In this paper, we formulate an analytical model to study the impact of EV anxiety and EVs’ environmental benefits on optimal subsidy and pricing decisions. We consider a market consisting of a vehicle manufacturer, a social planner and two segments of consumers: green and non-green. Both segments have EV anxiety. The manufacturer produces and sells both EVs and traditional vehicles. EV purchase decisions are influenced by consumers’ EV anxiety, preference for EVs, EV subsidy amounts, and retail prices for both EVs and traditional vehicles. Our results justify the necessity of a subsidy program in promoting EV sales. We identify the optimal subsidy under various market conditions. We further analyze how environmental benefit and consumers’ EV anxiety impact the optimal subsidy decisions. We find that it is optimal to offer the maximum level of subsidy when the environmental benefit is above a certain threshold value. Our results also show that the optimal subsidy either decreases or increases in consumers’ EV anxiety, depending on the level of environmental benefit of EVs. In addition, we show that EV anxiety has both positive and negative effects on the demand for EVs, but overall harms EV adoption.

Renewable resource dynamics: A Web-based classroom experiment

The authors adapted a lab-in-the-field experiment emulating the dynamic extraction of a fishery to create a Web-based classroom experiment. The game includes a multi-player version analogous to an open-access problem and a single-player version analogous to the social planner problem. This game is helpful in introductory microeconomics courses to teach about dominant strategies and the consequences of resource rivalry. In elective courses, the game helps teach bio-economics concepts, including logistic growth functions and optimal extraction paths. Instructions for game deployment and creating the sessions are provided. Conducting the game takes about 20 minutes, and because the game is Web-based, students can access it from their laptops, tablets, or smartphones.

Joint Design for Electric Fleet Operator and Charging Service Provider: Understanding the Non-Cooperative Nature

This work proposes a new modeling framework for jointly optimizing the charging network design and the logistic mobility planning for an electric vehicle fleet. Existing literature commonly assumes the existence of a single entity – the social planner, as a powerful decision maker who manages all resources. However, this is often not the case in practice. Instead of making this assumption, we specifically examine the innate non-cooperative nature of two different entities involved in the planning problem. Namely, they are the charging service provider (CSP) and the fleet operator (FO). To address the strategic interaction between entities, a bi-level mixed integer program is formulated, with the CSP/FO’s problem expressed in the upper/lower levels respectively, in a joint decision making process. These decisions involve the CSP’s infrastructure siting, sizing, substation capacity upgrades, the FO’s fleet composition, vehicle routing, charging, and delivery assignment. To solve the problem, an iterative fashion is adopted to solve and reach optimality. We conduct detailed numerical studies on a synthesized small network and the simulation results reveal the unique aspects of this two-entity framework. This modeling perspective can be generalized to other system design problems with two interacting agents planning and operating resources across networks.

Optimal assignment mechanisms with imperfect verification

Objects of different quality are to be allocated to agents. Agents can receive at most one object, and there are not enough high‐quality objects for every agent. The value to the social planner from allocating objects to any given agent depends on that agent's private information. The social planner is unable to use transfers to give incentives for agents to convey their private information. Instead, she is able to imperfectly verify their reports through signals that are positively affiliated with each agent's type. We characterize mechanisms that maximize the social planner's expected payoff. In the optimal mechanism, each agent chooses one of various tracks, which are characterized by two thresholds. If the agent's signal exceeds the upper threshold of the chosen track, the agent receives a high‐quality object, if it is between the two thresholds, he receives a low‐quality object, and if it is below the lower threshold, he receives no object.

A dynamic analysis of a monopolist's quality improvement, process innovation and goodwill

<p style='text-indent:20px;'>Although there are many literatures on firms' product and process innovation in recent years, the effects of advertising-based goodwill and consumers' reference quality on firms' product and process innovation are rarely considered. Therefore, the significant features of our study are: (i) introducing the concept and definition of the consumers' reference quality; (ii) considering the effect of product quality on goodwill; (iii) the customers' demand function depends on product quality, product price, advertising-based goodwill and the difference between product quality and reference quality, and the demand function takes a linear form. Our results suggest that (i) the system admits unique saddle-point steady-state equilibrium under the monopolist decision-making and the social planner regulation; (ii) with the increases of the product quality and goodwill, the corresponding investments also increases; however, with the increase of marginal cost and reference quality, the corresponding investment decreases; (iii) the monopolist's investment in one direction boosts the other in the neighborhood of the steady-state investments in product innovation, process innovation and advertising-based goodwill, respectively; and (iv) the monopolist will have an underinvestment problem as compared with the social planner.</p>

Product innovation, process innovation and advertising-based goodwill: A dynamic analysis in a monopoly

<p style='text-indent:20px;'>In this paper, we develop a dynamic control model to investigate a monopolist's investment strategies in product innovation, process innovation and advertising-based goodwill. The significant features of our study are: (ⅰ) considering the effect of product quality on goodwill; (ⅱ) considering the instantaneous cost of producing a quality using machinery and/or skilled labour; (ⅲ) the customers' demand function depends on product quality, product price and goodwill in a separable multiplicative way between the state variables and control variables. Our results suggest that (ⅰ) the system admits unique saddle-point steady-state equilibrium under the monopolist optimum and the social optimum; (ⅱ) and the monopolist will have an underinvestment problem as compared with the social planner; and (ⅲ) although the product price is still determined by the monopolist under the social planner optimum, the product price is higher under the monopolist optimum than that under the social planner optimum.</p>

Robust optimal macroprudential policy

We consider how fears of model misspecification on the part of the planner and/or the households affect welfare gains from optimal macroprudential taxes in an economy with occasionally binding collateral constraints. In this setup, the decentralized equilibrium may differ from the social planner's equilibrium both because of the pecuniary externalities associated with the collateral constraint and because of the paternalistic imposition of the planner's beliefs when designing policy. When robust agents have doubts about the model, they create endogenous worst-case beliefs by assigning a high probability to low-utility events. The ratio of worst-case beliefs of the planner over the household's captures the degree of paternalism. We show that this novel channel could render the directions of welfare gains from a policy intervention ambiguous. However, our quantitative results suggest that doubts about the model need to be large to make a “laissez-faire regime” better than an intervention regime.

Impact of customer bounded rationality on on-demand service platforms

We consider an on-demand platform connecting independent agents and delay-sensitive boundedly rational customers. By adopting a queueing-game framework, we analyze the equilibrium joining behaviors of customers and agents, the platform’s optimal pricing strategy, and the resulting profit and social welfare. Moreover, we investigate how the bounded rationality level affects these results. We obtain the following main insights. First, when customers are irrational, the positive externality between the agents and the customers becomes weak. In other words, increasing the same number of agents attracts fewer boundedly rational customers than fully rational ones. Second, we distinguish two types of equilibria in terms of agent participation: one in which all or none of the agents participate and the other in which it is possible that a fraction of the agents may participate. We show that in the latter case, a social planner and a platform can easily align their goals since they are affected by the bounded rationality in the same direction. We attribute the insight to the interactions among the cross-side effect, bounded rationality, and the pooling effect embedded in a queueing system. Next, we characterize the platform’s optimal pricing decisions and prove that the increase in the bounded rationality level does not always lead to higher optimal prices and wages. Finally, we examine the agent side bounded rationality and the social welfare maximizing decisions in the extended models.

Optimal vaccination in a SIRS epidemic model.

We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible individuals via a vaccination campaign, while minimizing the social and economic costs related to the infectious disease. As a theoretical contribution, we provide a technical non-smooth verification theorem, guaranteeing that a semiconcave viscosity solution to the Hamilton-Jacobi-Bellman equation identifies with the minimal cost function, provided that the closed-loop equation admits a solution. Conditions under which the closed-loop equation is well-posed are then derived by borrowing results from the theory of Regular Lagrangian Flows. From the applied point of view, we provide a numerical implementation of the model in a case study with quadratic instantaneous costs. Amongst other conclusions, we observe that in the long-run the optimal vaccination policy is able to keep the percentage of infected to zero, at least when the natural reproduction number and the reinfection rate are small.

Optimal menu when agents make mistakes

This paper studies how an optimal menu chosen by a social planner depends on whether agents receive imperfect signals about their true tastes (imperfect self-knowledge) or the properties of available alternatives (imperfect information). Under imperfect self-knowledge, it is not optimal to offer fewer alternatives than the number of different tastes present in the population, unless noise is infinite (agents have no clue about their true preferences). As noise increases, the social planner offers menu items that are closer together (more similar). However, under imperfect information, as noise increases, it could be optimal to construct a menu with more distinct alternatives, restrict the number of options, or, for some finite noise, offer a single item.

The impact of line-sitting on a two-server queueing system

In the presence of multiple lines, customers can often occupy the lines simultaneously with the help of someone else, so as to reduce their wait times. To understand the impact of such line-sitting behavior on the service system with multiple lines, we establish a queueing game-theoretic model to capture the interactions among customers, line-sitting firm and service provider. In particular, we consider a congested-prone service system with two dedicated queues, where arriving customers can join the two queues simultaneously by hiring a line-sitter to wait in one of the line on behalf of them, enabling them to receive service in any one of the queues. Our main results are as follows. First, contrary to our conventional wisdom that line-sitting firm could be more profitable when the system is more congested, we find instead that a queue with an intermediate demand volume can be most susceptible to line-sitting, whereas queues with either a very small or a very large demand volume may not be financially attractive to line-sitters. Second, our result discloses that the provision of line-sitting service in multiple lines can efficiently increase the system throughput. In the short run, both revenue of service provider and the customer surplus can be improved with the provision of line-sitting, which leads to a win-win situation. However, in the long run, line-sitting will stimulate a higher service fee charged by the service provider, reversing its short-run beneficial effect on customers, which results in a lower customer surplus. To restore the efficiency of line-sitting, we propose a centralized regulation policy from the perspective of social planner to maximize the social welfare without detriment to the customer population.

Energy harvesting cognitive radio networks with strategic users: A two-class queueing model with retrials

Motivated by the rapid growth in wireless communication systems, we develop a single-server queueing model with service retrials for the cognitive radio network (CRN). A key appeal of CRN is its flexible allocation scheme of limited spectrum for two user groups: (1) the licensed user, hereby referred to as primary user (PU), and (2) unlicensed users, referred to as secondary users (SUs). The PU take priority over SUs: when a PU arrives and observes a busy server currently occupied by an SU, it will take over the server by preempting the SU out of service. SUs are strategic and delay sensitive: they decide immediately upon arrivals on whether to join the CRN or to balk, based on the anticipated expected utility (service reward minus delay cost). In case the server is unavailable, SUs temporarily join an orbit queue where they wait for future accesses to service. Another realistic feature of our model is that, after successfully serving a user (PU or SU), the server becomes unavailable and undergoes an energy harvesting phase of a random time. We characterize the equilibrium system performance in the following three steps: First, we obtain the equilibrium joining behavior for utility-maximizing SUs; second, we derive the optimal joining strategy from the perspective of a social planner; and finally, we enforce that users adopt the socially optimal strategy by imposing an admission fee. We also investigate the impact of the energy harvesting time on users?? equilibrium strategies and report numerical experiments to provide qualitative and quantitative insights of our results.

Spatial growth theory: Optimality and spatial heterogeneity

Spatiotemporal dynamics are introduced in a standard Ramsey model of optimal growth in which capital moves toward locations where the marginal productivity of capital is relatively higher and initiate a study of the effects of nonlinear capital transport in terms of a linearized analysis around steady state solution solutions.The potential spatial heterogeneity of optimal growth, as seen from the point of view of an optimizing social planner, is examined. Our results suggest that for a high utility discount rate, the spatial capital flows induce the emergence of optimal spatial patterns, while for a low utility discount, a flat earth steady state is socially optimal. Furthermore, when spatial heterogeneities exist due to total factor productivity differences across locations, we identify conditions under which the spatial capital flows could intensify or weaken spatial inequalities.