Price competition between retailers under symmetric costs

Abstract

Integrating operations and marketing decisions are an important objective for retailers in today's competitive environment. An obvious problem common to the retail industry is the joint optimization of the lot size of a product to be stocked and the selling price in order to maximize profit. Pricing and inventory control strategies are closely related. Pricing decisions alter demand forecasts, which are used by inventory control systems. We note that in the classical economic order quantity (EOQ) model the demand is assumed as constant. A lot of important results have been obtained in this field of study. There are many studies which modify this condition, in particular with linear demand function. Further studies are related to the complexity of market structures, in particular, considering the horizontal competition between retailers. In this paper the Bertrand's price competition in the retail duopoly with symmetric costs is analyzed. Retailers sell substitute products in the framework of the classical EOQ model with linear demand function. Products are stored in a warehouse and are evenly sold in the retail network. We assume that every retailer maximizes profit per unit of time on the order size and the price at a current price competitor. The market potential is considered to be the bifurcation parameter of retailers. Level of the barrier to market penetration depending on the bifurcation parameter is analyzed. The conditions of Bertrand-Nash equilibrium in parametric and trigonometric forms are found. The theoretical results are illustrated by a numerical example. Based on the results obtained, retailers can plan the level of profitability of logistics costs and assess the level of the entry barrier to the market.