Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.

Varying Injurer Costs of Care, Negligence, and Self-Selection

Standard economic models of negligence set a single standard of care to which all injurers must conform. When injurers differ in their costs of care, this leads to distortions in individual care choices. This paper derives the characteristics of a negligence rule that induces optimal care by all injurers by means of self-selection. The principal features of the rule are (1) the due standard is set at the optimal care of the lowest cost injurer, and (2) liability increases gradually rather than abruptly as care falls below this standard. The results are consistent with the gradation in liability under certain causation rules and under comparative negligence.

On Negligence Rules and Self-Selection

Economic models of negligence ordinarily involve a single standard of care that all injurers must meet to avoid liability. When injurers differ in their costs of care, however, this leads to distortions in their care choices. This paper derives the characteristics of a generalized negligence rule that induces injurers to self-select their optimal care levels. The principal features of the rule are (1) the due standard of care is maximal, and (2) liability increases gradually as injurers depart further from this standard. The results are broadly consistent with the gradation in liability under certain causation rules and under comparative negligence.