Optimizing Manufacturer Profit in Downstream Retail Markets under Conditions of Uncertainty

INTRODUCTION AND LITERATURE REVIEW As the saying goes, "the only thing worse than a monopolist is two monopolists." Thus is the problem of double marginalization, first explored by Spengler (1950). The problem arises when a "downstream" monopolist is dependent on inputs from an "upstream" monopolist. The result is a sub-optimal solution: both of the monopolists suffer losses, and the resulting inefficiencies cause a "welfare loss," or loss of value to society as a whole. The double marginalization problem, which involves monopolists in both the upstream and downstream markets, has been viewed from a variety of perspectives. Bresnahan and Reiss (1985) extended the standard double marginalization model into a "successive monopoly" model, showing largely Stackelberg behavior, which is a situation in which one firm functions as a "leader," and the other as a "follower." The authors found that the most important factor influencing the manufacturer-retailer relationship was the curvature of the demand curve. Other studies have extended Bresnahan and Reiss' approach to evaluate its impact on certain other economic phenomena, such as price discrimination (Cowans, 2012), tax incidence (Weyl and Fabinger, 2013), and "cost pass through", or the extent to which price changes in response to a change in marginal cost (Adachi and Ebina, 2014), all finding similar results. Hegji and Moore (2006) evaluated a similar scenario under both Stackelberg conditions, described above, and Cournot conditions, which refers to a situation in which firms make decisions on output based on anticipated output decisions of the other firm. They found that under certain circumstances, franchise fees were an effective tool for manufacturers to maximize profits, and also control retail prices. The manufacturer's use of a franchise fee amounts to a two-part tariff; the manufacturer sells units to retailers and charges each retailer a franchise fee. The franchise fee is used by the manufacturer to capture the retailers' profits, thereby increasing the manufacturer's own profits. Hegji and Moore also found that such franchise fees could offset the potential welfare losses suffered under double marginalization. Some firms (and similar entities) address the problems of competing manufacturer/retailer incentives (including, inter alia, double marginalization) by engaging in resale price maintenance (RPM). RPM is an agreement between a manufacturer and dealer through which the dealer agrees to a retail price floor for the sale of a manufacturer's products. A substantial literature on RPM exists, including Hamilton (1990) and others, examining RPM as a solution to double marginalization and other problems. All of the studies cited above assume profit maximization at every stage by each firm in the analysis; Fershtman and Judd (1987), drawing upon Baumol (1958) and others, examine the possibility of alternative objective functions (such as sales maximization) in an imperfectly competitive environment. Specifically, Fershtman and Judd contemplated mixed objective functions in the context of a principal-agent problem faced by owners seeking to incentivize optimal behavior by managers. Fershtman and Judd found that in an oligopoly situation, owners may wish to provide incentives in order to shift their managers' incentives away from strict profit maximization. We extend the approaches cited above by considering cases involving a manufacturer interacting with downstream retailers in an imperfectly competitive retail market. Specifically, we examine how such a manufacturer can use sales incentives to encourage retailers to increase sales, with the manufacturer's ultimate aim being to increase its profit. This paper presents the results of 4 different scenarios, in models involving a manufacturer selling a product to Cournot-type retailers competing in the retail market. These include no sales incentive, a constant per-unit incentive, a sales incentive as a function of a retailer's own-sales, and an incentive as a function of the total retail sales of the manufacturer's product. …