On vertical restrictions and the number of franchises: comment.

• Author: Schaffer, Greg
• Position: Response to Owen R. Philips, Southern Economic Journal, p. 423, October 1991

1. Introduction

   In a recent issue of this Journal, Phillips [3, 423-29] examines the vertical control problem of an upstream monopoly when the number of its retailers is endogenous. He compares a situation in which the upstream firm chooses a two-part tariff contract to maximize its profit with one in which the upstream firm combines a two-part tariff contract with resale price maintenance. Phillips finds that resale price maintenance increases the upstream firm's profit, and in both situations, concludes that the "monopolist will set the wholesale price below its marginal cost in order to maximize profits through the franchise fee" [3, 423]. However, his analysis is incorrect.

   In this note, I solve Phillips's model and find that the profit maximizing two-part tariff contract never exhibits a wholesale price below marginal cost. Furthermore, I show that resale price maintenance does not increase the upstream firm's profit. The intuition for this latter finding is that the upstream firm's profit maximizing two-part tariff contract suffices to control perfectly the number of retailers and the retail price, yielding the same profit as would be earned by a vertically integrated firm. Resale price maintenance in this instance is redundant.

2. Phillips' Model and Notation

   Phillips considers a market in which an upstream monopolist sells its product through multiple retailers each with its own distinct geographic territory. The upstream firm is initially restricted to choosing a two-part tariff contract, that is, to setting a franchise fee (F) and wholesale price (P). Although the upstream firm cannot directly determine the number of retailers that will sell its product or the retail price, it recognizes that both variables are indirectly influenced by its choice of two-part tariff. According to Phillips, "As P and F are set, the number of franchises is determined under the conditions that franchisees maximize profits through their choice of [retail price] and that they break even in the downstream market" [3, 425].

   The retail equilibrium is summarized in reduced form by N(F, P), which is the equilibrium number of retailers as a function of the franchise fee and wholesale price, and S(F, P), which is the equilibrium sales made by the upstream firm to each retailer. Several sign restrictions are imposed. First, N(F, P) is assumed to be decreasing in both the franchise fee and wholesale price, as both decrease the profitability of owning a franchise. Second, S(F, P) is assumed to be increasing in the franchise fee - because increasing F reduces the total number of retailers thereby increasing each retailer's market area - and decreasing in the wholesale price - because higher wholesale prices lead to higher retail prices and thus less sales to consumers.

   The...