Socially optimal procurement with tight budgets and rationing

We investigate the behaviour of a social planner that secures the supply of a good, e.g. an environmental benefit, through contracting with private agents. While the social planner seeks to maximise net social benefits, she is also controlled with a fixed budget. Private agents are profit maximising and hold private information concerning their variable costs of production. They also have known fixed costs of contracting. We find that budget constraints and fixed costs change the optimal contract design in more than one way: the social planner minimises costs, rations high-cost contracts to reduce fixed costs and information rents, and distorts contracts for all agent types, including low-cost agents. We find that rationing improves social welfare. Also, even though social costs – including tax distortion – are explicitly taken into consideration, they do not affect the design of optimal contracts when budgets are tight. In those cases the budget constraint dominates the solution.     

Implementation with partial provability

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agents? preferences or beliefs and agents need little information about each others? preferences. Our results are robust to evidence forgery at any strictly positive cost.     

Social media networks,fake news,and polarization

We study how the structure of social media networks and the presence of fake news affects the degree of misinformation and polarization in a society. For that, we analyze a dynamic model of opinion exchange in which individuals have imperfect information about the true state of the world and exhibit bounded rationality. Key to the analysis is the presence of internet bots: agents in the network that spread fake news (e.g., a constant flow of biased information). We characterize how agents’ opinions evolve over time and evaluate the determinants of long-run misinformation and polarization in the network. To that end, we construct a synthetic network calibrated to Twitter and simulate the information exchange process over a long horizon to quantify the bots’ ability to spread fake news. A key insight is that significant misinformation and polarization arise in networks in which only 15% of agents believe fake news to be true, indicating that network externality effects are quantitatively important. Higher bot centrality typically increases polarization and lowers misinformation. When one bot is more influential than the other (asymmetric centrality), polarization is reduced but misinformation grows, as opinions become closer the more influential bot’s preferred point. Finally, we show that threshold rules tend to reduce polarization and misinformation. This is because, as long as agents also have access to unbiased sources of information, threshold rules actually limit the influence of bots.     

Randomization, revelation, and redistribution in a Lerner world

Summary. If total social income is fixed and a social planner is uninformed of the utility representations of different individuals, then Lerner showed that the social optimum is to equally distribute income across individuals. We show that the planner by the use of randomization can in some circumstances induce individuals to reveal information about the curvature of their utility functions and then use the information to move away from equality on average. However, whether this is optimal depends in part on unobservable beliefs of the planner. These may be viewed as an aspect of the planner's ethical judgements or as something entirely arbitrary. Received: January 11, 2000; revised version: June 26, 2001     

On the robustness of laissez-faire

This paper considers a model economy in which agents are privately informed about their type: their endowments of various goods and their preferences over these goods. While preference orderings over observable choices are allowed to be correlated with an agent's private type, we assume that the planner/government is both uncertain about the nature of this joint distribution and unable to choose among multiple equilibria of any given social mechanism. We model the planner/government as having a maxmin objective in the face of this uncertainty.Our main theorem is as follows: Once we allow for this kind of uncertainty and assume no wealth effects in preferences, the uniquely optimal social contract is laissez-faire, in which agents trade in unfettered markets with no government intervention of any kind.     

SOCIAL NORMS,LOCAL INTERACTION,AND NEIGHBORHOOD PLANNING*

This article examines optimal social linkage when each individual's repeated interaction with each of his neighbors creates spillovers. Each individual's discount factor is randomly determined. A planner chooses a local interaction network or neighborhood design before the discount factors are realized. Each individual then plays a repeated Prisoner's Dilemma game with his neighbors. A local trigger strategy equilibrium (LTSE) describes an equilibrium in which each individual conditions his cooperation on the cooperation of at least one “acceptable” group of neighbors. Our main results demonstrate a basic trade‐off in the design problem between suboptimal punishment and social conflict. Potentially suboptimal punishment arises in designs with local interactions since in this case monitoring is imperfect. Owing to the heterogeneity of discount factors, however, greater social conflict may arise in more connected networks. When individuals' discount factors are known to the planner, the optimal design exhibits a cooperative “core” and an uncooperative “fringe.”“Uncooperative” (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when the planner knows only the ex ante distribution over individual discount factors, then in some cases the optimal design partitions individuals into maximally connected cliques (e.g., cul‐de‐sacs), whereas in other cases incomplete graphs with small overlap (e.g., grids) are possible.     

Environmental risk and welfare valuation under imperfect information

Consumers are often uninformed, or unsure, about the ambient level of environmental risk. An optimal policy must jointly determine efficient levels of self-protection, information provision, and public risk mitigation efforts. Unfortunately, conventional welfare measures are not amenable to welfare analysis in the presence of imperfect information. We develop a theoretical welfare measure, called quasi-compensating variation, that is a natural extension of compensating variation (CV). We show that this welfare measure offers not only a money metric of the “value of information,” but also a means to appropriately evaluate the welfare effects of various policies when consumers are imperfectly informed about ambient risk. This welfare measure allows us to obtain a number of results that the traditional CV measure fails to offer. In particular, we show that the consumer’s willingness to pay for a (small) environmental risk reduction is higher for those who underestimate ambient risk than for those who overestimate or are perfectly informed if the marginal return to self-protection increases with ambient risk.     

Optimal Harvest in an Age Structured Model with Different Fishing Selectivity

An age structured model of a fishery is studied where two fishing fleets, or fishing agents, are targeting two different mature age classes of the fish stock. The agents are using different fishing gear with different fishing selectivity. The model includes young and old mature fish that can be harvested, in addition to an age class of immature fish. The paper describes the optimal harvesting policy under different assumptions on the objectives of the social planner and on fishing selectivity. First, biomass yield is maximized under perfect fishing selectivity, second, equilibrium profit (rent) is maximized under perfect fishing selectivity, and third, equilibrium profit is maximized under imperfect fishing selectivity. The paper provides results that differ significantly from the standard lumped parameter (also surplus production, or biomass) model.     

Price Discrimination by a Many-Product Firm

Determining the optimal selling strategy for a multiproduct firm facing consumers with unobservable tastes is a difficult task. This paper aims to show how almost optimal nonlinear tariffs can often be found when the number of products is large. Moreover, such tariffs take a simple form: (i) when taste parameters are independently distributed across products, the almost optimal tariff is a single cost-based two-part tariff which can extract virtually all consumer surplus; (ii) when tastes are correlated across products, perhaps because of income differences across consumers, the almost optimal tariff can be implemented as a menu of two-part tariffs each of which has prices proportional to marginal costs.     

Pessimistic information gathering

An agent gathers information on productivity shocks and accordingly produces on behalf of a principal. Information gathering is imperfect and whether it succeeds or not depends on the agent's effort. Contracting frictions come from the fact that the agent is pessimistic on the issue of information gathering, and there are both moral hazard in information gathering, private information on productivity shocks and moral hazard on operating effort. An optimal menu of linear contracts mixes high-powered, productivity-dependent screening options following “good news” with a fixed low-powered option otherwise.     

Negative Externalities and Evolutionary Implementation

We model externality abatement as an implementation problem. A social planner would like to ensure efficient behaviour among a group of agents whose actions are sources of externalities. However, the planner has limited information about the agents' preferences, and is unable to distinguish individual agents except through their action choices. We prove that if a concavity condition on aggregate payoffs is satisfied, the planner can guarantee that efficient behaviour is globally stable under a wide range of behaviour adjustment processes by administering a variable pricing scheme. Through a series of applications, we show that the concavity condition is naturally satisfied in settings involving negative externalities. We conclude by contrasting the performance of the pricing mechanism with that of a mechanism based on direct revelation and announcement dependent forcing contracts.     

Sequential decisions with several agents

Summary. We consider k agents who have different subjective probabilities and are utility maximizers. A planner, who knows the beliefs of the agents, maximizes the social expected utility, which is increasing and symmetric in the utilities of the agents. She does that by optimally stopping the flow of information released to the agents. The explicit form of the optimal stopping time is given. Received: October 23, 1995; revised version: June 25, 1997     

Imports, Status Preference, and Foreign Borrowing

This paper considers the implications of consumption and borrowing externalities in a small open economy framework. The former reflect the assumption that status conscious agents care about the relative consumption of imported goods, while the latter arise because agents do not take into account the effects of their borrowing decisions on the interest rate on debt. We analyze in the paper the impact of an increase in the degree of status preference on the saddlepath adjustment of the decentralized economy. In addition, the contrasting steady‐state and dynamic properties of the social planner’s economy are derived, along with the corresponding optimal tax and subsidy policies.     

Intertemporal self-selection with multiple buyers

Summary We consider a monopolist selling durable goods to consumers with unit demands but different preferences for quality. The seller can offer items of different quality at the same time to induce buyers to self-select, as in Mussa-Rosen (1978), but is not artificially constrained to offer only one such menu. Instead the seller can offer without precommitment asequence of menus over time. In the two-buyer case where the seller has complete information about each buyer's marginal valuation for quality, the seller's profits exceed what can be obtained from a single menu and sometimes approximate the profits of a perfectly discriminating monopolist. In companion papers (Bagnoli et al., 1990, 1992), we show that these conclusions continue to hold (1) in the infinite-horizon case with any finite number of buyers and (2) in two-period examples where the seller has incomplete information about buyer preferences.     

A real option approach to the protection of a habitat dependent endangered species

We use a real option approach to determine when a social planner has to stop or resume logging in situations where an endangered species relies on forest habitat for its survival. Logging affects the stochastic process followed by the habitat of the endangered species, which disappears irreversibly if its habitat reaches a critical extinction level. As long as the endangered species is still in existence, the social planner manages logging in such a way as to balance the risk of extinction against the benefits from commercial wood exploitation. The model incorporates economic, ecological, and social features. It is solved analytically to characterize the optimal forest management rule. Then it is applied to the case of the Rangifer tarandus caribou, an endangered species in Central Labrador (Canada). The parameters of the habitat process are estimated by Monte Carlo methods. The policy implied by the model – alternatively banning and resuming logging according to appropriate habitat threshold levels – turns out to be quite attractive; it does not require long banning periods while it drastically reduces the extinction risk and increases forest value.     

Asymmetric information and contract design for payments for environmental services

In contractual relationships involving payments for environmental services, conservation buyers know less than landowners know about the costs of contractual compliance. Landowners in such circumstances use their private information as a source of market power to extract informational rents from conservation agents. Reducing informational rents is an important task for buyers of environmental services who wish to maximize the services obtained from their limited budgets. Reducing informational rents also mitigates concerns about the “additionality” of PES contracts because low-cost landowners are least likely to provide different levels of services in the absence of a contract. Paying low-cost landowners less thus makes resources available for contracts with higher opportunity cost landowners, who are more likely to provide substantially different levels of services in the absence of a contract. To reduce informational rents to landowners, conservation agents can take three approaches: (1) acquire information on observable landowner attributes that are correlated with compliance costs; (2) offer landowners a menu of screening contracts; and (3) allocate contracts through procurement auctions. Each approach differs in terms of its institutional, informational and technical complexity, as well as in its ability to reduce informational rents without distorting the level of environmental services provided. No single approach dominates in all environments. Current theory and empirical work provides practitioners with insights into the relative merits of each approach. However, more theoretical work and experimentation in the laboratory and the field are necessary before definitive conclusions about the superiority of one or more of these approaches can be drawn.     

DESIGNING POLLUTION MARKET INSTRUMENTS: CASES OF UNCERTAINTY

This paper examines design alternatives for emissions trading credits and assesses their relative performance given several sources of uncertainty endemic to market-based environmental regulatory programs. Facilities regulated in such programs face significant uncertainty about their total emissions. Uncertainty arises due to changes in production-demand schedules for their product, imperfect knowledge of abatement efficiency, and other informational lags. Depending on the design of the trading credit, this uncertainty can result in significant market price volatility and undesirable increases in peak emissions (in the absence of additional costly market institutions, such as contingent contracts and brokered insurance). In addition to the design alternatives, the paper considers allocation alternatives to alleviate these unintended effects and also discusses the value of properly designed reconciliation markets .     

Discounting Nordhaus

This paper evaluates Nordhaus's neoclassical complaints about the Stern Review from the vantage point of classical growth theory. Nordhaus criticizes the Stern Review because it uses a discount rate that is well below the market rate of return on capital. From the perspective of classical growth theory, Nordhaus's belief in choosing preference parameters for the social planner based on observed market rates of return is equivalent to assigning the preferences of the capitalist agents to the social planner. This equivalence is an implication of the Cambridge Theorem, which interprets the Ramsey equation as the saving function of the capitalist agents.     

Incentive mechanisms for cost revelation with intermodal competition

To set regulated utility prices that are sustainable against uneconomic bypass alternatives, regulators must estimate the costs of the alternative bypass technologies; this entails a series of theoretical and institutional problems that regulators cannot practically resolve. This paper now develops a simple incentive mechanism that effectively solves those problems associated with producing an optimal amount of bypass. In the suggested procedure, regulators use readily available accounting data to specify one two-part tariff that covers the utility's revenue requirements and is deemed fair by regulators and consumers; as long as it offers this fair tariff, the company may subsequently offer as many alternative tariffs as it sees fit, including some particularly aimed to deter bypass. This procedure gives a utility the correct incentive to determine its own and its rivals' cost structures; with accurate cost information, the utility will design a menu of tariffs that would eliminate uneconomic bypass and would be responsive to changing cost conditions in the emerging bypass markets.     

Learning Dynamics with Private and Public Signals

This paper studies the dynamics of learning in a model of technology adoption. Firms learn about an unknown technology by observing both private and public signals. Because of the externality associated with the public signal, the social planner has firms experiment more in the initial period of the model, relative to the market equilibrium. In certain cases, this more rapid generation of information results in the planner experimenting less in later periods of the model. In contrast, typical models with public signals result in the planner inducing more experimentation in all periods of the model relative to the market equilibrium. I would like to thank Matt Mitchell and Tom Holmes for their advice and encouragement. I would also like to thank Thor Koeppl, Cyril Monnet, John Stevens, and Jason Cummins, and two anonymous referees for their helpful comments. This paper is the second chapter of my dissertation. The views expressed herein are my own and not necessarily those of the Bureau of Economic Analysis or the US Department of Commerce.