Optimal firm investment in security

In this paper, we analyze the problem of an individual firm that has to deal with losses from criminal activities. It is assumed that the firm can protect itself by investing in security equipment. Two different models are considered. In the first model, the firm has the possibility to spend money on production and on security investment. More production increases revenue but also criminal losses, while the latter can be decreased by investing in security. It turns out that the optimal production level increases with security equipment and is determined such that marginal revenue, net from criminal losses, equals marginal cost. For the optimal level of security investment it holds that, in the case of the existence of a long-run steady-state equilibrium, the properly discounted future reductions in criminal losses, which are due to an additional unit of security investment, exactly balances the initial outlay necessary to acquire an extra unit of security investment. In the second model, we extend this analysis by considering the effect that the firm's reputation has in the criminal world. If the firm has produced a lot in the past without having invested in security equipment, this firm is known to be a fruitful target for criminals. Therefore, more criminals will try to rob this firm, and this will increase future criminal losses.