A single period competitive model of pricing and inventory under reference price effect

Abstract

This research studies a single period combined inventory and pricing system. It is assumed that the demand which has a random additive term, is contingent on the firm’s own selling price, the rival firm’s selling price in the current period as well as the firm’s initial reference price. The mean deterministic demand is in a linear form and has an increasing price elasticity. The additive randomness has an increasing hazard rate. Furthermore, the salvage value to be obtained at the end of the period is an evolution of the initial reference price via an exponential smoothing model. This assumption is a novel way to bring in reference price effects to a single period model. First, optimal quantity and price policies to maximize profitability is analyzed, optimal production quantities are isolated and the quasi-concavity of the expected profit function in the space of possible prices is established. Then, insights about to what extent the marginal cost and initial reference prices effect the optimal price and inventory levels are analytically shown. Finally, a duopolistic game is considered by introducing competition over selling prices and the existence of Nash equilibrium is shown. A computational study is carried out to show some comperative static results.