Price or quantity? An analysis of strategies in the presence of gray markets

Gray markets, a double‐edged sword for the multinational firms' profitability, can boost the sales revenues of low‐end subsidiaries while cannibalizing the demands of high‐end arms. To counter the adverse effects of the gray market, firms can flexibly adjust between the two strategies of setting prices (the price strategy) and choosing quantity (the quantity strategy) for its products. This paper investigates the best strategy for responding to gray markets. We consider a firm that produces two substitute products, each sold in an independent market (country). A gray marketer purchases the product sold in the low‐priced market and resells it in the high‐priced market, thereby starting a gray market. By studying the conditions of determining when and which strategy is more profitable, we establish several findings that are absent in the current literature. For instance, we find that it is likely that the quantity strategy could also be the best one in the presence of the gray competition. Moreover, implementing the quantity strategy can even automatically eliminate the gray market, which will not happen if the price strategy is employed. In addition, we identify special cases in which implementing one of the two strategies can lead to profit improvements while employing the other will cause the firm to suffer in case a gray market exists. We also examine the robustness of these findings in several cases of extensions of our model.