The Golden Rule of accumulation in an economy with an endogenously determined growth rate of labor has been examined by Eric Davis. Davis finds that if the growth rate is an increasing function of per capita net income, steady-state per capita consumption is maximized not at the equality of the propensity to save and capital's share of output, but at a propensity to save smaller than capital's share of output and an interest rate which exceeds rather than equals the growth rate. The supply of labor in an economy is affected by both the growth and participation rates of its population. Davis' results and the traditional Golden Rule depend upon the implicit assumption that the latter rate is constant. Davis calls for a more flexible treatment of the participation rate, allowing the possibility of optimal unemployment in a theory of optimal savings. This note examines a simple model with a varying participation rate. It is seen that one common assumption describing the participation rate leads to a recommendation opposite that of Davis.

We study a population of agents, each of whom can be an Altruist or an Egoist. Altruism is a strictly dominated strategy. Agents choose their actions by imitating others who earn high payoffs. Interactions between agents are local, so that each agent affects (and is affected by) only his neighbors. Altruists can survive in such a world if they are grouped together, so that the benefits of altruism are enjoyed primarily by other Altruists, who then earn relatively high payoffs and are imitated. Altruists continue to survive in the presence of mutations that continually introduce Egoists into the population.

Hierarchical organizations often perform poorly in inducing the adoption of innovations. We examine a principal offering contracts to agents who make unobservable effort and adoption-of-innovation choices (yielding moral hazard), who occupy jobs of differing, unobserved productivities (yielding adverse selection), and who engage in a repeated relationship with the principal (causing a ratchet effect to arise). Increasing the rate of adoption of an innovation in such an organization causes the incentive costs of adoption to increase at an increasing rate. Relatively low rates of adoption may then be a response to the prohibitive incentive costs of higher adoption rates.

We consider an economy in which long-lived experts are matched with short-lived clients. Experts choose the type of client with whom they match, unobserved by the market. The interaction outcome depends on both the expert’s and the client’s type. We study the effects of supplying information about otherwise unobservable outcomes, such as “medical report cards,” to help clients identify better experts. Such information can lead to inefficient matches, as experts reject risky clients to build their reputation. Hence, information can reduce welfare. Withholding information can mitigate these perverse incentives at the cost of misallocating experts known to be inept. (JEL C78, D82, D83)

People reason about uncertainty with deliberately incomplete models. How do people hampered by different, incomplete views of the world learn from each other? We introduce a model of “ model-based inference.” Model-based reasoners partition an otherwise hopelessly complex state space into a manageable model. Unless the differences in agents’ models are trivial, interactions will often not lead agents to have common beliefs or beliefs near the correct-model belief. If the agents’ models have enough in common, then interacting will lead agents to similar beliefs, even if their models also exhibit some bizarre idiosyncrasies and their information is widely dispersed. (JEL D82, D83)

We examine the evolutionary foundations of intertemporal preferences. When all the risk affecting survival and reproduction is idiosyncratic, evolution selects for agents who maximize the discounted sum of expected utility, discounting at the sum of the population growth rate and the mortality rate. Aggregate uncertainty concerning survival rates leads to discount rates that exceed the sum of population growth rate and death rate, and can push agents away from exponential discounting. (JEL D11, D81, D91)