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

Willpower and the Optimal Control of Visceral Urges

Common intuition and experimental psychology suggest that the ability to self-regulate, willpower, is a depletable resource. We investigate the behavior of an agent who optimally consumes a cake (or paycheck or workload) over time and who recognizes that restraining his consumption too much would exhaust his willpower and leave him unable to manage his consumption. Unlike prior models of self-control, a model with willpower depletion can explain the increasing consumption sequences observable in high frequency data (and corresponding laboratory findings), the apparent links between unrelated self-control behaviors, and the altered economic behavior following imposition of cognitive loads. At the same time, willpower depletion provides an alternative explanation for a taste for commitment, intertemporal preference reversals, and procrastination. Accounting for willpower depletion thus provides a more unified theory of time preference. It also provides an explanation for anomalous intratemporal behaviors such as low correlations between health-related activities.

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

Willpower and the Optimal Control of Visceral Urges

Common intuition and experimental psychology suggest that the ability to self-regulate ("willpower") is a depletable resource. We investigate the behavior of an agent with limited willpower who optimally consumes over time an endowment of a tempting and storable consumption good or "cake". We assume that restraining consumption below the most tempting feasible rate requires willpower. Any willpower not used to regulate consumption may be valuable in controlling other urges. Willpower thus links otherwise unrelated behaviors requiring self-control. An agent with limited willpower will display apparent domain-specific time preference. Such an agent will almost never perfectly smooth his consumption, even when it is feasible to do so. Whether the agent relaxes control of his consumption over time (as experimental psychologists predict) or tightens it (as most behavioral theories predict) depends in our model on the net effect of two analytically distinct and opposing forces.willpower, self-control, hotelling

Size Matters (in Output-Sharing Groups): Voting to End the Tragedy of the Commons

Individuals extracting common-pool resources in the field sometimes form output-sharing groups to avoid costs of crowding. In theory, if the right number of groups forms, Nash equilibrium aggregate effort should fall to the socially optimal level. Whether individuals manage to form the efficient number of groups and to invest within the chosen groups as theory predicts, however, has not been previously determined. We investigate these questions experimentally. We find that subjects do vote in most cases to divide themselves into the optimal number of output-sharing groups, and in addition do decrease the inefficiency significantly (by 50% to 71%). We did observe systematic departures from the theory when the group sizes are not predicted to induce socially optimal investment. Without exception these are in the direction of the socially optimal investment, confirming the tendency noted elsewhere in public goods experiments for subjects to be more “other-regarding” than purely selfish.catch-sharing, common-pool resources, efficient private provision, free-riding, laboratory experiment, partnership solution

Willpower and the Optimal Control of Visceral Urges

Common intuition and experimental psychology suggest that the ability to self-regulate, willpower, is a depletable resource. We investigate the behavior of an agent who optimally consumes a cake (or paycheck or workload) over time and who recognizes that restraining his consumption too much would exhaust his willpower and leave him unable to manage his consumption. Unlike prior models of self-control, a model with willpower depletion can explain the increasing consumption sequences observable in high frequency data (and corresponding laboratory findings), the apparent links between unrelated self-control behaviors, and the altered economic behavior following imposition of cognitive loads. At the same time, willpower depletion provides an alternative explanation for a taste for commitment, intertemporal preference reversals, and procrastination. Accounting for willpower depletion thus provides a more unified theory of time preference. It also provides an explanation for anomalous intratemporal behaviors such as low correlations between health-related activities.

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

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