Using Lorenz curves to represent firm heterogeneity in Cournot games

We derive several comparative-static results for Cournot games when firms have nonconstant marginal-cost curves which shift exogenously. The results permit us to rank certain vectors of equilibrium marginal costs with the same component sum according to their associated social surplus or industry profit. We arrange the components of each vector in ascending order and then construct from the resulting ordered vector its associated Lorenz curve. We show that if two Lorenz curves do not cross, the one reflecting greater inequality is associated with higher social surplus and industry profit. A duality result permits a corresponding ranking of equilibrium output vectors. The same partial ordering is used in the literature on income inequality to rank certain distributions of income and in the literature on decision-making under uncertainty to compare the riskiness of certain probability distributions with the same mean.Lorenz curves, Herfindahl index, Cournot games

A Free Lunch in the Commons

We derive conditions under which cost-increasing measures -- consistent with either regulatory constraints or fully expropriated taxes -- can increase the profits of all agents active within a common-pool resource. This somewhat counterintuitive result is possible regardless of whether price is exogenously fixed or endogenously determined. Consumers are made no worse off and, in the case of an endogenous price, can be made strictly better off. The results simply require that total revenue be decreasing and convex in aggregate effort, which is an entirely reasonable condition, as we demonstrate in the context of a renewable natural resource. We also show that our results are robust to heterogeneity of agents and, under certain conditions, to costless entry and exit. Finally, we generalize the analysis to show its relation to earlier work on the effects of raising costs in a model of Cournot oligopoly.

Recurrence of a modified random walk and its application to an economic model

A modification of Chung and Fuchs’ (Mem. Amer. Math. Soc., 6 (1951), pp. 1-12) recurrence theorem for random walks leads to an analogous result for a different discrete parameter Markov process. This latter process is applicable to an analysis of price stabilization programs involving purchases and sales from a buffer stock.speculative attack

Regulating An Experience Good In Developing Countries When Consumers Cannot Identify Producers

In developing countries, consumers can buy many goods from either the formal sector or the informal sector and choose the sector to patronize based on the product's price there and anticipated quality. We assume that firms can produce in either sector and can adjust quality at a cost. In the long run, firms produce in the sector that is more profitable. As for the consumers, we assume they cannot assess quality prior to purchase and cannot, at a reasonable cost, identify the producer of what they are purchasing. Many products (meats, fruits, vegetables, fish, grains) sold both in formal groceries and, less formally, on the street fit this description. Using this model, we investigate how a change in regulations in the formal sector affects quality, price, aggregate production and the number of firms in each sector.experience good, formal sector, informal sector, quality

Diversify or focus: spending to combat infectious diseases when budgets are tight

We consider a health authority seeking to allocate annual budgets optimally over time to minimize the discounted social cost of infection(s) evolving in a finite set of R >= 2 groups. This optimization problem is challenging, since as is well known, the standard epidemiological model describing the spread of disease (SIS) contains a nonconvexity. Standard continuous-time optimal control is of little help, since a phase diagram is needed to address the nonconvexity and this diagram is 2R dimensional (a costate and state variable for each of the R groups). Standard discrete-time dynamic programming cannot be used either, since the minimized cost function is neither concave nor convex globally. We modify the standard dynamic programming algorithm and show how familiar, elementary arguments can be used to reach conclusions about the optimal policy with any finite number of groups. We show that under certain conditions it is optimal to focus the entire annual budget on one of the R groups at a time rather than divide it among several groups, as is often done in practice; faced with two identical groups whose only difference is their starting level of infection, it is optimal to focus on the group with fewer sick people. We also show that under certain conditions it remains optimal to focus on one group when faced with a wealth constraint instead of an annual budget.public health spending; nonconvexity; dynamic programming

Litigation of Settlement Demands Questioned by Bayesian Defendants

This paper analyzes a stylized model of pretrial settlement negotiations in a personal-injury case. It is assumed that the prospective plaintiff knows the severity of his injury but that the prospective defendant has incomplete information. As a result of this information asymmetry a proportion of slightly-injured plaintiffs are tempted to inflate their settlement demands and a proportion of such demands are rejected by suspicious defendants. By analogy with other models of adverse selection (e. g., Rothschild-Stiglitz (1976)), the presence of slightly-injured plaintiffs imposes a negative externality on plaintiffs with genuine severe injuries since defendant s cannot identify the severely-injured and sometimes reject their reasonable demands, forcing them into costly litigation. A filing fee imposed on minor claims is shown to displace the equilibrium but, paradoxically, to cause an increase in the frequency of litigation. This model differs from recent contributions to the literature on pretrial negotiations under incomplete information. Unlike P'ng (1983) and Bebchuk (1983), the uninformed litigant in this model learns from the observed equilibrium behavior of the informed litigant. Unlike Ordover-Rubinstein (1983) and Salant-Rest (1982), settlement demands are endogenous

Markets with untraceable goods of unknown quality: a market failure exacerbated by globalization

In markets for many fruits, vegetables, and an increasing number of imported goods, consumers cannot discern the quality of a product prior to purchase and can never identify its producer. Producing high-quality, safe goods is costly for a firm and raises the collective reputation for quality shared with its rivals. Minimum quality standards improve welfare. If consumers observe the country of origin of a product, quality, profits, and welfare increase. Exports from countries with more exporting firms are of lower quality and sell for lower prices. If one country imposes a minimum quality standard on its exports while other countries do not, consumers benefit. As for sellers, the regulation raises the profits of firms in the country with regulation and lowers the profits of firms in countries without regulation.globalization; quality; collective reputation; minimum quality standards

Markets with Untraceable Goods of Unknown Quality: A Market Failure Exacerbated by Globalization

In markets for fruits, vegetables, and many imported goods, consumers cannot discern quality prior to purchase and can never identify the producer. Producing high-quality, safe goods is costly and raises the "collective reputation" for quality shared with rival firms. Minimum quality standards imposed on all firms improve welfare. If consumers can observe the country of origin of a product, quality, profits, and welfare increase. If one country imposes a minimum quality standard on its exports, consumers benefit, the profits of firms in the country with regulation rise, and the profits of firms in countries without regulation fall.

Putting Free-Riding to Work: A Partnership Solution to the Common-Property Problem

The common-property problem results in excessive mining, hunting, and extraction of oil and water. The same phenomenon is also responsible for excessive investment in R&D and excessive outlays in rent-seeking contests. We propose a "Partnership Solution" to eliminate or at least mitigate these excesses. Each of N players joins a partnership in the first stage and chooses his effort in the second stage. Under the rules of a partnership, each member must pay his own cost of effort but receives an equal share of the partnership's revenue. The incentive to free-ride created by such partnerships turns out to be beneficial since it naturally offsets the excessive effort inherent in such problems. In our two-stage game, this institutional arrangement can, under specified circumstances, induce the social optimum in a subgame-perfect equilibrium: no one has a unilateral incentive (1) to switch to another partnership (or create a new partnership) in the first stage or (2) to deviate from socially optimal actions in the second stage. The game may have other subgame-perfect equilibria, but the one associated with the ``Partnership Solution'' is strictly preferred by every player. We also propose a modification of the first stage which generates a unique subgame-perfect equilibrium. Antitrust authorities should recognize that partnerships can have a less benign use. By organizing as competing partnerships, an industry can reduce the ``excessive'' output of Cournot oligopoly to the monopoly level. Since no partner has any incentive to overproduce in the current period, there is no need to deter cheating with threats of future punishments.partnerships;common property;tragedy of the commons;cartels