On the optimal production capacity for influenza vaccine

This paper analyzes the profit maximizing capacity choice of a monopolistic vaccine producer facing the uncertain event of a pandemic in a homogenous population of forward-looking individuals. For any capacity level, the monopolist solves the intertemporal price discrimination problem within the dynamic setting generated by the standard mathematical epidemiological model of infectious diseases. Even though consumers are assumed to be identical, the monopolist will be able to exploit the ex post heterogeneity between infected and susceptible individuals by raising the price of vaccine in response to the increasing hazard rate. The monopolist thus bases its investment decision on the expected profits from the optimal price path given the infection dynamics. It is shown that the monopolist will always choose to invest in a lower production capacity than the social planner. Through numerical simulation, it is demonstrated how the loss to society of having a monopoly producer decreases with the speed of infection transmission. Moreover, it is illustrated how the monopolist's optimal vaccination rate increases as its discount rate rises for cost parameters based on Swedish data. However, the effect of the firm discount rate on its investment decision is sensitive to assumptions regarding the cost of production capacity.