Some wildlife species are agricultural pests but these populations are often valued by other than agriculturalists. For non-farmers, the population levels of such wildlife are frequently pure public goods. This is one source of market failure in the economically optimal social control of an agricultural pest of this type. Secondly, if the species is geographically mobile, externalities occur between farmers in the control of the species, and this reduces the incentives of farmers as individuals to control the pest species. It is shown that depending on the relative strength of these opposing types of market failure, farmers may excessively reduce or insufficiently decrease the population of a species from a social economic point of view.