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

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

Treble Damage Awards in Private Lawsuits for Price-Fixing

The traditional model for assessing the effects on price fixing of trebel damage penalties is reexamined and shown to yield surprising results. Unless the probability of detection is extremely sensitive to the price charged, increasing the damage multiple will affect neither market efficiency nor expected distribution and will raise the market price.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100936/1/ECON383.pd

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.

For Sale by Owner: When to Use a Realtor and How to Price the House

By using a broker, the owner of a house can speed up his search for buyers but must pay a percentage of the sale price as a commission. Nonstationarities inherent in the housing market may make it optimal to market a house by-owner at the outset and to retain a broker only if the house remains on the market later in the selling season. This article investigates the optimal sequence of asking prices within the by-owner phase, within the broker phase, and at the transition between the two phases. The asking price declines within each phase but may jump up at the transition to cover part of the commission. The model implicity determines the demand for broker services as a function of the commission rate. When estimated, it may be useful in investigations of price fixing among brokers.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100935/1/ECON382.pd

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

When is Inducing Self-Selection Sub-optimal for a Monopolist

Stokey (1979) showed in an intertemporal context that, under reasonable assumptions, price discrimination is never optimal if a monopolist can pre-commit to a price path. This note explores the implications of Stokey's result for the optimality of inducing self-selection in the static quantity and quality contexts of Spence (1980) and Mussa-Rosen (1978). It is shown that Stokey's result carries over to these other contexts under appropriate curvature assumptions. Moreover, even under traditional curvature assumptions, inducing self-selection may be suboptimal. Necessary and sufficient conditions for discrimination to be optimal are derived for the two-type case.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100937/1/ECON384.pd

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

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.