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.

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)

Where do preferences come from? What determines their properties? Though traditionally reluctant to ask such questions, economists have recently turned to evolutionary models for answers. We focus on intertemporal preferences here, arising out of the evolutionary implications of different reproductive strategies or life histories. An agent’s life history specifies the agent’s number and timing (and in a richer model, quality) of offspring. Evolution will select the life history that maximizes the growth rate of the associated group of individuals. We begin with the simplest possible biological life history, that of a semelparous agent that, if it survives a fixed number of years, reproduces and then dies. We show the evolutionary criterion for success in this case entails hyperbolic time discounting of the log of the number of offspring produced. The rate of time preference is a function of age, however, not of time relative to the present, and there are no preference reversals in the sense of behavioral economics. At the same time, the optimal strategy maximizes the exponentially discounted number of offspring, provided we discount at the sum of the death rate and the maximal growth rate. Conventional discounting thus suffices to induce optimal choices from the agent. More generally, if the animal is iteroparous, that is, has a nondegenerate profile of offspring, we show the evolutionary indifference curves over offspring of various ages are hyperplanes that are not parallel, but tilt to reflect greater impatience as the growth rate increases. There is no additively separable function of the age profile of expected offspring that is globally equivalent to this basic biological growth-rate The Evolution of Intertemporal Preferences

We study transactions that require investments before trading in a competitive market, when forward contracts fixing the transaction price are absent. We show that, despite the market being perfectly competitive and subject to arbitrarily little uncertainty, the inability to jointly determine investment levels and prices may make it impossible for buyers and sellers to predict the prices at which they will trade, leading to inefficient levels of investment and trade.

We consider a market with “red” and “green” workers, where labels are payoff irrelevant. Workers may acquire skills. Skilled workers search for vacancies, while firms search for workers. A unique symmetric equilibrium exists in which color is irrelevant. There are also asymmetric equilibria in which firms search only for green workers, more green than red workers acquire skills, skilled green workers receive higher wages, and the unemployment rate is higher among skilled red workers. Discrimination between ex ante identical individuals arises in equilibrium, and yet firms have perfect information about their workers, and strictly prefer to hire minority workers. (JEL C70, D40, J30)