Trois essais en bio-economie dynamique

This dissertation is composed of three essays dealing with the economic dynamics of either the use of an antibiotic to combat bacterial infection or the use of a genetically modified crop to combat pests, when the efficacy of those instruments may decline with use. In each case, we model the efficacy variable as a renewable resource and its optimal use is determined as the solution of an optimal control problem.;In the second essay, we characterize the pricing policy of a monopolist who is protected by a patent for a finite period of time. We assume that once the patent expires, the monopolist becomes a competitive producer in the open-access industry which sells the generic version of the initially patented antibiotic. In order to maximize his inter-temporal profits, the monopolist manages, via his pricing policy, the levels of antibiotic efficacy and of the infected population. These can be viewed, respectively, as the quality of his product and his market size. We show that he tends to maintain a higher level of efficacy and a higher level of infected population than a hypothetically myopic monopolist who does not take into account the dynamic externalities. We also show that his pricing policy is characterized by a turnpike property. This means that the system approaches the steady state that would be reached by an infinitely-lived monopolist and remains in its neighborhood for a period of time, the length of which depends on the length of the patent life and on the bio-economic parameters. As the patent is about to expire, the monopolist begins to behave more and more myopically, leading to a continuous decrease in price until it finally reaches the price charged by a myopic monopolist. As soon as the open-access generic industry takes over, a discontinuous fall in price occurs.;Finally, in the third essay, we consider the use of a genetically modified crop to fight a pest population that feeds on the crop. We use an entomological model that captures the diversity of the pest population's gene pool, as well as the level of pest invasion itself. A refuge area is used as an instrument to control the evolution of the susceptibility of the pest's gene pool to the genetically modified crop. We characterize the refuge area that minimizes the sum of discounted costs related to the crop damage caused by the pest as well as the supplemental cost of the genetically modified crop. The model is calibrated for the use of Bt-corn to fight the European corn borer. Because of the linearity of the objective function, the optimal refuge consists of a bang-bang and a singular control. For the calibrated parameters, as well as reasonable variations of them, the bio-economic system tends to an interior steady state where the level of pest-susceptibility is renewable. However, when the control is restricted to being constant over time, as is currently done in the United States, the system generally tends to a steady state where the susceptibility is completely exhausted. In that case, it takes very particular parameter constellations for the system to reach an interior steady state. We are able to assess, for the calibrated model, the cost reduction attained by using refuge area that varies over time instead of a time-invariant one. (Abstract shortened by UMI.);In the first essay, we analyze the exploitation of an antibiotic in a market subject to open access on the part of antibiotic producers to the common pool of antibiotic efficacy and compare it to the social optimum. Demand for the antibiotic is derived under the assumption that individuals differ with respect to their valuation of being in good health. The dynamics of the antibiotic efficacy is based on an epidemiological model which describes the dynamic interaction between the level of efficacy of the antibiotic and the level of infection in the population, including the fact that antibiotic consumption tends to deplete the efficacy of the antibiotic in combating bacterial infections as the bacteria develop resistance to the antibiotic. The antibiotic producers care only about the variables that affect the instantaneous demand for the drug, namely the current stock of infected population and the current level of efficacy of the antibiotic, and enter the market until price is driven down to average cost. The social optimum, on the other hand, takes into account the welfare of the entire population, including that portion of the population which is in good health and that which is infected but chooses not to consume the antibiotic, as well as the effect of the current treatment rate on the future efficacy of the treatment and the future stock of infected population.