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. While the market equilibrium depends only on current levels of antibiotic efficacy and infection of the epidemiological system, the social optimum accounts for the dynamic externalities which relate those levels to the intertemporal use being made of the antibiotic. 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 antibiotic 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. However, the paths leading to the steady state always differ.