If the historical average annual real interest rate is m 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year? Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process...

For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount...

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing," i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are...

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then...

Conventional economics supposes that agents value the present vs. the future using an exponential discounting function. In contrast, experiments with animals and humans suggest that agents are better described as hyperbolic discounters, whose discount function decays much more slowly at large...

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing," i.e., systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are...

We review an emerging body of work by physicists addressing questions of economic organization and function. We suggest that, beyond simply employing models familiar from physics to economic observables, remarkable regularities in economic data may suggest parts of social order that can usefully...

We enlarge the standard model of general equilibrium with incomplete market (GEI), to incorporate liquidity constraints as well as the possibility of bankruptcy and default. A new equilibrium results, which we abbreviate GELBI (general equilibrium with liquidity, bankruptcy and incomplete...

Arrow's original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but...

We show that if students care primarily about their status (relative rank) in class, they are best motivated to work not by revealing their exact numerical exam scores (100,99,...,1), but instead by clumping them in broad categories (A,B,C). If their abilities are disparate, the optimal grading...