Price of Identical Product with Gray Market Sales: An Analytical Model and Empirical Analysis

The sale of genuinely branded products through unauthorized channels (also known as gray markets) is a growing problem for many firms that operate in separate markets. It is generally believed that the existence of such unauthorized sales will cannibalize the profits of brand owners. In this paper, we develop a pricing model for a firm that sells an identical product in two distinct markets but faces the threat of potential gray market sales. The firm chooses prices in each market. A consumer chooses whether to buy the product from one of the markets including a gray market. We derive the optimal prices in the two markets and examine their effects on consumer demand and the total profit. We show that the higher price in one market transfers part of its demand into the gray market, thus influencing the consumer demand in the low-priced market as well. Additionally, the price gap between the two separate markets positively influences gray market sales and, under certain conditions, can lead to an increase in firm profit. Using authorized sales data from a Fortune 100 company and a separate data set on online gray market sales, we find empirical evidence in support of our model results.