The Economic Dynamics of Antibiotic Efficacy under Open Access

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. We show that depending on the parameters of the model, in particular the cost of production and the improvement in the recovery rate that results from treatment, the positive steady-state level of antibiotic efficacy to which the system tends under open access can be lower or higher than the level which should prevail in the socially optimal steady state. In fact there are parameter configurations for which the steady states can be exactly the same. But no matter how the steady states compare, the socially optimal and the open-access paths to steady state will differ and involve different paths for the treatment rates.