Does counterfeiting benefit genuine manufacturer? The role of production costs

A monopolist sells a luxury genuine product which can be illegally copied and sold by a competitive fringe of counterfeiters. Fines imposed on caught counterfeiters are pocketed by the genuine firm. We prove that if production costs are low, then the genuine manufacturer would lobbying for high penalties so that counterfeiters should be thrown out of the market. In this case, the presence of counterfeiters does not provide any benefit to the producer of the original product. Whenever the production cost is neither too high nor too low, the optimal fine guarantees a positive demand for the genuine product as well as for the fake; the genuine producer is better off than in a world without counterfeiters. If production costs are too high, the genuine firm has no more incentive to produce. Its remaining goal is to collect penalty money from counterfeiters. Again, the presence of counterfeiters provides a benefit to the genuine manufacturer. Finally, a comparison between full protection and null protection policies is performed.