In this paper we present a continuous time optimal control analysis of resistance buildup in agricultural chemicals when the supplier is a monopolist. We compare the monopolistic, competitive and socially optimal solutions after establishing the stability of each equilibrium. The central finding is that with a monopolistic supplier, resistance buildup is lower than socially optimal. This directly opposes the standard result in the resistance literature. This implies that policies to manage resistance should vary with the age of the chemical, with no intervention during the lifetime of a patent and an optimal tax once the patent expires.