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This paper is about the application of optimization methods to the analysis of three pricing schemes adopted by one manufacturer in a two-country model of production and trade. The analysis focuses on pricing schemes—one uniform pricing scheme, and two differential pricing schemes—for which there is no competition coming from the so-called parallel trade. This term denotes the practice of buying a patented product like a medicine in one market at one price, then re-selling it in a second so-called gray market at a higher price, on a parallel distribution chain where it competes with the official distribution chain. The adoption of pricing schemes under which parallel trade does not arise can prevent the occurrence of its well-documented negative effects. In the work, a comparison of the optimal solutions to the optimization problems modeling the three pricing schemes is performed. More specifically, conditions are found under which the two differential pricing schemes are more desirable from several points of view (e.g., incentive for the manufacturer to do Research and Development, product accessibility, global welfare) than the uniform pricing scheme. In particular, we prove that, compared to the uniform pricing scheme, the two differential pricing schemes increase the incentive for the manufacturer to invest in Research and Development. We also prove that they serve both countries under a larger range of values for the relative market size, making the product more accessible to consumers in the lower price country. Moreover, we provide a sufficient condition under which price discrimination is more efficient from a global welfare perspective than uniform pricing. The analysis applies in particular to the case of the European Single Market for medicines. Compared to other studies, our work takes into account also the possible presence in all the optimization problems of a positive constant marginal cost of production, showing that it can have non-negligible effects on the results of the analysis. As an important contribution, indeed, our analysis clarifies the conditions—which have been overlooked in the literature about the mechanisms adopted to prevent parallel trade occurrence—that allow/do not allow one to neglect the presence of this factor. Such conditions are related, e.g., to the comparison between the positive constant marginal cost of production, the parallel trade cost per-unit, and the maximal price that can be effectively charged to the consumers in the lower price country.

Welfare and research and development incentive effects of uniform and differential pricing schemes