Pass-Through Pricing on Production Chains

We here want to analyze how the imperfect competition mark-up and pass-through are transmitted through the production chain and how they change, as a function of the number of firms existing at each production stage. In order to have an analytical closed form solution, we use the standard linear oligopoly framework. Without loss of generality and as first approximation, we assume an homogeneous good and constant returns to scale. The exercise, by using the well known standard results of Nash equilibrium with n firms and the monopoly double marginalization, obtains the mark-up solution parametric in the number of firms in S production stages. Results are mainly the followings, where the first two are just a confirmation of the two-stage results, the third is original: (i) Mark-up vanishes in the increasing number of firms, at any production stage. (ii) Pass-through increases in the number of firms, existing at each production stage, because competition transfers cost increases. (iii) Results are indifferent to the stage at which the larger number of firms happen. In other words, results do not discount the position in the sequence. Classical comparisons between integrated and decentralized chain have been computed with computed consequences on welfare results