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Gray markets are unauthorized channels of distribution for a supplier's authentic products. We study a distribution channel that consists of a supplier who offers all-unit quantity discounts for batch orders to enjoy cost savings, and a reseller who may divert some goods to the gray markets. We show that the impact of gray markets depends on the reseller's inventory holding cost. When the reseller's inventory holding cost is high, diversion to the gray markets improves the channel performance by enabling the reseller to make batch orders. Because the reseller's order costs decrease through quantity discounts, diversion to the gray markets reduces the resale price and expands sales to the authorized channel. On the other hand, when the reseller's inventory holding cost is low, the reseller would make the batch orders even without the gray markets. In this case the diversion to the gray markets may improve the reseller's performance by shortening the order cycles and reducing the inventory holding costs. Interestingly, because diversion to the gray markets decreases the reseller's cycle inventory volume, the reseller has the reduced incentive to push its inventory, and, consequently, the resale price rises and sales volume decreases in the authorized channel. Moreover, there exists a range of reseller's inventory holding cost and supplier's cost of scale economy such that it is optimal for the supplier to induce reseller's gray market diversion through an all-unit discount. We show that these results are robust when the gray market overlaps with the authorized channel or when the gray market price is sensitive to reseller's diversion volume.
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