We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optimal control, we find the optimal harvesting strategy which maximizes the asymptotic yield of harvested individuals. To our knowledge, ergodic optimal control has not been used before to study harvesting strategies. However, it is a natural framework because the optimal harvesting strategy will never be such that the population is harvested to extinction-instead the harvested population converges to a unique invariant probability measure. When the yield function is the identity, we show that the optimal strategy has a bang-bang property: there exists a threshold [Formula: see text] such that whenever the population is under the threshold the harvesting rate must be zero, whereas when the population is above the threshold the harvesting rate must be at the upper limit. We provide upper and lower bounds on the maximal asymptotic yield, and explore via numerical simulations how the harvesting threshold and the maximal asymptotic yield change with the growth rate, maximal harvesting rate, or the competition rate. We also show that, if the yield function is [Formula: see text] and strictly concave, then the optimal harvesting strategy is continuous, whereas when the yield function is convex the optimal strategy is of bang-bang type. This shows that one cannot always expect bang-bang type optimal controls.

I examine a model of long-term contracting in which the buyer is privately informed about the discrete probability distribution for his future value for a divisible product, and fully characterize the optimal long term contract that will be offered by a monopolistic seller in a simple case where two types of buyers can have two types of utility in any period. In such a case, the buyer more likely to have a high utility type will receive the first-best allocations indifferent of his value report, while the lower type will receive the first best only if he makes a high utility report. The paper also supplements the current literature on infinite dynamic games with continuous buyer types, which relies on the use of a distribution of types with full support and an envelope theorem. With discrete types, the number of compatibility constraints considered can be greatly reduced by sandwiching the border of the space of solutions allowed by constraints: formulate the maximization problem in a wider space with fewer constraints and prove that the solution obeys a simpler set of stronger constraints that places it in the allowed region.

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We use an annual household panel to conduct a comparative analysis of which decision theory explains life satisfaction better. We consider expected utility theory and prospect theory. We consider the effects of three domains on life satisfaction: income, health, and (un)employment. Using a fixed effects estimator we find that life satisfaction contains features of both expected utility theory and prospect theory. However, the elements of expected utility theory are stronger predictors of life satisfaction. Life satisfaction depends positively on income, good health, and employment. It also depends positively on income and employment improvements, however the reverse is true for health improvements. Life satisfaction is concave in income gains and convex in income losses, and it exhibits loss aversion in income and employment status, but not in health. The results suggest that life satisfaction is best described by expected utility theory, but also contains some aspects of prospect theory.