Social Planner's Solution Research Articles

R&D competition and the direction of innovation

We propose a model to show that when innovation in a given field becomes more lucrative, its direction can be distorted even though its rate rises. Higher payoffs attract innovators, making the R&D supply side more competitive. This competition endogenously shifts effort toward less promising but quicker-to-invent projects. We empirically quantify the magnitude of this distortion, in the context of pharmaceutical innovation during the Covid-19 pandemic. In the social planner solution, 74 percent more firms would have worked on vaccines and 17 percent more on novel compounds. Policy remedies include advance purchase commitments based on ex-ante value, targeted research subsidies, and antitrust exemptions for joint research ventures.

Emission taxes vs. environmental standards under partial ownership arrangements

This paper analyzes two pollution control instruments, uniform taxes and absolute standards, when polluting firms engage in partial ownership arrangements (POAs). Specifically, we examine the case of a bilateral POA between competing firms in which both hold equity shares on each other's profits as silent investments. We show that taxes and standards are equally efficacious in affecting the firms' output decisions and pollution emissions. Compared to the social planner's solution, a bilateral POA results in suboptimal outcomes with lower industrial output and consumer surplus. Firm profits are higher and environmental quality improves (since emissions decline), but social welfare decreases. We compare the equilibrium results associated with two different types of POAs (bilateral vs. unilateral), and examine their differences in welfare implications for the choice of policy options between taxes and standards.

Regional climate policy under deep uncertainty: robust control and distributional concerns

AbstractWe study climate change policies using the novel pattern scaling approach of regional transient climate response in order to develop a regional economy–climate model under conditions of deep uncertainty. We associate welfare weights with regions and analyze cooperative outcomes derived by the social planner's solution at the regional scale. Recent literature indicates that damages are larger in low latitude (warmer) areas and are projected to become relatively even larger in low latitude areas than at temperate latitudes. Under deep uncertainty, robust control policies are more conservative regarding emissions and, when regional distributional weights are introduced, carbon taxes are lower in the relatively poorer region. Mild concerns for robustness are welfare improving for the poor region, while strong concerns have welfare cost for all regions. We show that increasing regional temperatures will increase resources devoted to learning, in order to reduce deep uncertainty.

Dynamic coordination with timing frictions: Theory and applications

AbstractWe present a general framework of dynamic coordination with timing frictions. A continuum of agents receive random chances to choose between two actions and remain locked in the selected action until their next opportunity to reoptimize. The instantaneous utility from each action depends on an exogenous fundamental that moves stochastically and on the mass of agents currently playing each action. Agents' decisions are strategic complements and history matters. We review some key theoretical results and show a general method to solve the social planner's problem. We then review applications of this framework to different economic problems: network externalities, statistical discrimination, and business cycles. The positive implications of these models are very similar, but the social planner's solution points to very different results for efficiency in each case. Last, we review extensions of the framework that allow for endogenous hazard rates and ex ante heterogeneous agents.

How much to share: Welfare effects of fiscal transfers

AbstractRecent sovereign debt crisis has challenged policy makers to explore the possibility of establishing a fiscal transfer system that could alleviate the negative impact of asymmetric shocks across countries. Using a simple labour production economy, we first derive an analytically tractable solution for optimal degree of fiscal transfers. In this economy, fiscal transfers can improve welfare by moving the competitive equilibrium with fiscal transfers closer to the social planner's solution. We then extend the model to a DSGE setting with capital, international bond and linear taxes, and we analyze how implementation of a simple revenue sharing rule affects welfare and macroeconomic variables over time. Simulation results show that risk sharing through fiscal transfers always improves welfare in the long run. However, under certain model specifications, short‐run transitional welfare loss can outweigh the long‐run benefits. These results suggest that, in designing fiscal transfers across countries, government should take into consideration the intertemporal nature of welfare gains.

The Silence of the Lambs: Payment for Carnivore Conservation and Livestock Farming Under Strategic Behavior

During the last few decades, the number of large carnivores (wolf, bear, lynx and wolverines) has increased significantly in Scandinavia. As a result of more predation of livestock, conflicts with livestock farmers have deepened. We model this conflict using sheep farming as an example, and in instances in which farmers are given compensation for the predation loss. The compensation scheme is composed of a fixed per animal loss value (ex-post), but also a compensation just for the presence of the carnivores (ex-ante). Ex-post compensation payment is practiced in many countries where farmers are affected by killed and injured livestock, but also damages to crops. Ex-ante payment implies payment for environmental services and is also widely practiced. In the first part of the paper, the stocking decision of a group of farmers is analyzed. In a next step, the Directorate for Natural Resource Management (DNRM), managing the carnivores and compensation scheme, is introduced. The strategic interaction between the sheep farmers and DNRM is modelled as a Stackelberg game with DNRM as the leader. We find that it is not beneficial for DNRM to use ex-post, but only ex-ante compensation. The solution to the game is compared to the social planner solution, and numerical illustrations indicate that the efficiency loss of the ex-ante compensation scheme to be small.

Product Homogeneity, Knowledge Spillovers, and Innovation: Why Energy Sector is Perplexed by a Slow Pace of Technological Progress

There is a growing body of literature mentioning the slow pace of energy technological progress as compared to other technologies like information technology (IT), but the reasons why energy sector is perplexed by slow innovation remain unexplained. Based on a variety-expanding endogenous technological change model, this paper provides a rigorous economic exposition of the mechanism that underlies the slow progress of energy technological innovation. We show that in decentralized market equilibrium the growth rate of energy technology variety is lower than that of IT variety. This stems from both market fundamentals where the homogeneity of end-use energy goods is less likely to harness the pecuniary externality embedded in the household’s love-for-variety preference, and technology fundamentals where the capital-intensiveness of energy technology inhibits the non-pecuniary technological externality due to knowledge spillovers. We further show that a social planner solution can promote energy technological progress, yet still cannot achieve an outcome in which energy technology variety grows faster than IT variety. By targeting subsidies on energy technology R&D and the use of intermediate primary energy inputs by secondary energy producers, the decentralized market equilibrium can achieve an outcome in which energy technology grows faster than IT.

Optimal growth through product innovation

In Lentz and Mortensen (2008), we formulate and estimate a market equilibrium model of endogenous growth through product innovation. In this paper, we provide quantitative equilibrium solutions to the model based on our parameter estimates, and compare them with a social planner's solution. We find that the socially optimal growth rate is double that of the market equilibrium growth rate when firm differences in the ability to create productive products are highly persistent as a consequence of the “business stealing” externality present in the model. The welfare loss of the decentralized economy relative to that of the planner is equivalent to a 21% tax on the planner consumption path. The planner's solution differs from the decentralized economy in that it discourages innovation by low ability innovators as well as entry.We introduce two mechanisms that temper the strength of the negative externality: Transitory firm types and the possibility of buyouts. We show that both sharply reduce the inefficiency due to innovation by low ability innovators. But with caveats: If firm types are completely transitory, then the notion of firm heterogeneity is for practical purposes lost. Buyouts improve efficiency, but the efficiency gain depends significantly on the strength of the innovator's ability to extract rents from incumbents through the buyout.

Political geography and income inequalities

We analyze political geography and the size of governments in the presence of income inequality. The social planner solution implies that income inequality is neutral on the size of countries but reduces the optimal provision of public goods within each country. Under additional conditions, a politico-economic equilibrium geography is characterized by suboptimal size of nations, but there may not be a stable equilibrium when inequality is high enough. Finally, we introduce globalization showing that inequality can increase the size of countries, reduce public good provision and, at the same time, decrease their degree of openness.

Optimality versus stability in water resource allocation

Water allocation is a growing concern in a developing world where limited resources like fresh water are in greater demand by more parties. Negotiations over allocations often involve multiple groups with disparate social, economic, and political status and needs, who are seeking a management solution for a wide range of demands. Optimization techniques for identifying the Pareto-optimal (social planner solution) to multi-criteria multi-participant problems are commonly implemented, although often reaching agreement for this solution is difficult. In negotiations with multiple-decision makers, parties who base decisions on individual rationality may find the social planner solution to be unfair, thus creating a need to evaluate the willingness to cooperate and practicality of a cooperative allocation solution, i.e., the solution's stability. This paper suggests seeking solutions for multi-participant resource allocation problems through an economics-based power index allocation method. This method can inform on allocation schemes that quantify a party's willingness to participate in a negotiation rather than opt for no agreement. Through comparison of the suggested method with a range of distance-based multi-criteria decision making rules, namely, least squares, MAXIMIN, MINIMAX, and compromise programming, this paper shows that optimality and stability can produce different allocation solutions. The mismatch between the socially-optimal alternative and the most stable alternative can potentially result in parties leaving the negotiation as they may be too dissatisfied with their resource share. This finding has important policy implications as it justifies why stakeholders may not accept the socially optimal solution in practice, and underlies the necessity of considering stability where it may be more appropriate to give up an unstable Pareto-optimal solution for an inferior stable one. Authors suggest assessing the stability of an allocation solution as an additional component to an analysis that seeks to distribute water in a negotiated process.

The Multi-Level Marketing as a Two-Sided Market

The Multi-level marketing (MLM) can be identified as a two-sided market a la Rochet and Tirole (Rochet and Tirole, 2003, 2006; Weyl, 2010). The platform is represented by the promoter of the MLM and the sides are the recruitment activity and the selling activity. The recruitment side has negative network effect on the selling side, and the selling side generates positive network effect in favor of the recruitment side. We compare the social planner's solution with that of the profit-maximizer. We find that, like the newspapers and credit cards two-sided markets studied in Weyl (2010), the MLM business is characterized by some distortions. First, there is a distortion coming from the negative network effect from the recruitment side. The selling side is not a source of distortion or the profit-maximizer can internalize it. Second, there is another distortion due to the signal the promoter uses to increase artificially the valuation of the business and the product. However, this distortion can be mitigated by the recruitment side effect. Also, contrary to the newspapers two-sided market, there is no Spence distortion on the the MLM two-sided market.

Constant-utility paths in a resource-based economy

This paper analyzes a social planner's solution in a resource-based economy under a constant-utility criterion. The utility function includes social progress in a multiplicative form. The resulting paths of consumption include the patterns of growth that are conventionally used in the literature. A closed form solution, derived for the Dasgupta-Heal-Solow (DHS) model, includes the Solow–Hartwick result as a special case. This paper extends the link between the utilitarian criterion and the maximin for the cases with finite elasticity of marginal utility. The result also implies that economic growth in a resource-based economy may be slower than exponential; therefore, the expression for utility with social progress may become a more appropriate measure of sustainable growth than the percentage of consumption growth.

Who Benefits from Improved Search in Platform Markets?

Online platforms invest large sums in their search technology. Motivated by this observation, we investigate how lowering search costs affects the welfare of market participants, in a model where buyers with horizontally differentiated tastes search and then compete for differentiated goods in an auction. We identify a effect, whereby lower search costs lead to better matches; and a effect whereby lower search costs endogenously shift market participation in favor of some goods and against others. We prove that there is a unique equilibrium, and demonstrate that the decentralized market achieves the social planner's solution. Decreasing search costs thus improves joint welfare; and yet surprisingly it is possible for segmentation effects to dominate matching effects, and joint seller revenue to fall.

Optimal R&D subsidies in a model with physical capital, human capital and varieties

In this paper, we analyze the social planner solution of an endogenous growth model with physical capital, human capital and R&D. The model incorporates three sources of inefficiency: monopolistic competition in the intermediate-goods sector, duplication externalities and spillovers in R&D. A complete stability analysis for the optimal growth problem of this model is provided. We characterize the optimal policy that can decentralize the optimal solution and find that the path of the optimal R&D subsidy can be non-monotonic.

Brain Drain, Fiscal Competition, and Public Education Expenditure

AbstractA two‐country model is developed in this paper to examine the implications of fiscal competition in public education expenditure under international mobility of high‐skilled labor. The authors allow for educational choice, asymmetry of countries with respect to total factor productivity, and tax base effects of migration in source and host country. As the latter may give rise to multiplicity of equilibrium, alternative belief structures of mobile high‐skilled workers are carefully taken into account. The paper also looks at the consequences of bilateral policy coordination. While in line with other studies on tax competition, bilateral coordination can reduce the under‐investment problem in public education spending, it also tends to hinder migration or may even reverse the direction of the migration flow that materializes under non‐cooperative policy setting. As a result of its potentially adverse effects on migration patterns, bilateral coordination may therefore reduce global welfare and bring the world economy further away from the social planner's solution.

Aging society, health and the environment

In a general-equilibrium OLG model with endogenous longevity, a political economy and a social planner solution are contrasted mainly with respect to public supplies of health care and environment protection. The latter is relatively more supported by the young because its beneficial effect on longevity takes more time to occur but then lasts longer; while the old relatively prefer health spending. With population aging, political claims for health care expenditure are self-reinforcing. This framework is able to generate a quite rich set of results. In the political economy larger health care/consumption and health care/environmental quality ratios are implemented. Changes in risk aversion, production pollution, health inputs’ elasticity of substitution may have opposite impacts across regimes. More complete annuity markets improve welfare. Further comparative statics is analyzed.

Welfare Effects of Trade Liberalization with Intra-Industry Reallocations: The Importance of Preferences and Market Failures

This paper shows that the novel gains from trade liberalization driven by intra-industry reallocations (Melitz (2003)) are not robust to changes in the preference structure. In the Melitz (2003) setting the unambigousness of the welfare effect depends crucially on the assumption of traditional CES preferences, which ensures equivalence of the market equilibrium and the social planner solution. For other preferences this equivalence is broken and trade liberalization may reduce welfare by magnifying market failures. An exact condition for trade liberalization to reduce overall welfare is derived under the assumptions of generalized CES preferences and a specific distribution (Pareto) of firm heterogeneity.

Spending natural resource revenues in an altruistic growth model

This paper examines how natural resource revenues interact with growth and welfare in an overlapping generations model with altruism. The revenues are allocated between public productive services and direct transfers to members of society by spending policies. We analyze how these policies influence the dynamics, and how the dynamics are influenced by the revenue. Abundant revenues may harm growth, but growth and welfare can be oppositely affected. We also provide the social planner solution under which revenues enhance growth. Overall, the analysis suggests that variation in the strength of altruism and in spending policies may be part of the reason why natural resources seem to affect economic performance across nations differently.

Optimal Fragile Financial Networks

We study a financial network characterized by the presence of depositors, banks and their shareholders. Belonging to a financial network is beneficial for both the depositors and banks' shareholders since the return to investment increases with the number of banks connected. However, the network is fragile since banks, which invest on behalf of the depositors, can gamble with depositors' money (making an investment that is dominated in expected terms) when not sufficiently capitalized. The bankruptcy of a bank negatively affects the banks connected to it in the network. First, we compute the social planner solution and the efficient financial network is characterized by a core-periphery structure. Second, we analyze the decentralized solution showing under which conditions participating in a fragile financial network is ex-ante optimal. In particular, we show that this is optimal when the probability of bankruptcy is sufficiently low giving rationale of financial fragility as a rare phenomenon. Finally, we analyze the efficiency of the decentralized financial network. Again, if the probability of bankruptcy is sufficiently low the structure of the decentralized financial network is equal to the e¢ cient one, yielding an ex- pected payo¤ arbitrarily close to the efficient one. However, the investment decision is not the same. That is, in the decentralized network some banks will gamble as compared to the socially preferred outcome.

CONJUNCTIVE SURFACE AND GROUND WATER MANAGEMENT IN THE JAKARTA REGION, INDONESIA1

ABSTRACT: This study investigates the degree of economic inefficiency of the current institutional arrangements for surface and ground water management in meeting urban water demand in the Jakarta region. A numerical model of integrated surface and ground water management is developed using GAMS (General Algebraic Modelling System) software. The model maximizes the net present value of social benefits from piped water and ground water consumption across all users over time from 1999 to 2025. Four policy scenarios are examined: the status quo, the social planner's solution, and two ground water pumping quota scenarios: an aggregate ground water pumping quota and a partial quota applied to commercial and industrial users. Three variations in each policy scenario are considered: investment in water infrastructure of the Jakarta water enterprise (PAM Jaya), water demand growth, and discount rates. The status quo, depending on the investment option, the growth of water demand, and the discount rate, results in a 7.4 to 47.8 percent loss in economic efficiency relative to the social planner's solution. The partial quota is the most feasible, applicable, and manageable scenario. The optimal investment option could increase the volume of piped water supply and reduce the cost of water production. The volume of water delivery could increase by up to 156 percent, but it implies only a 35 percent increase in the surface raw water demands above the current level. However, it does not significantly reduce cumulative ground water extraction over the time period considered.