Abstract: All-units discount (AUD) is a pricing scheme that lowers a buyer's marginal price on every unit purchased when the buyer's purchase exceeds or is equal to a pre-specified threshold. The AUD and its variations (e.g., market-share discounts and quantity forcing) are commonly used in both final-goods and intermediate-goods markets. In the recent FTC v. Intel case, FTC challenged the so-called ˇ°first-dollar rebateˇ± in which Intel offered its customers a retroactive rebate if their purchase of microprocessors from Intel exceeded a pre-specified target level. One might argue that Intel's rival AMD was capacity- constrained and might not be able to match Intel's AUD contract. The existing literature has so far focused on interpreting AUD as a price discrimination tool or rent-shifting instrument. In this paper, we investigate the strategic effects of the AUD used by a dominant firm in the presence of a smaller, capacity-constrained rival. In particular, we consider a three-stage game in which the dominant firm and the small firm make price offers to a buyer sequentially before the buyer purchases. In addition, we allow the dominant firm to offer AUD while the smaller firm only uses linear pricing. We show that, in equilibrium, the dominant firm uses an AUD to limit its rival's supply strictly below its capacity level and to squeeze the rival's profit. This result holds even when the rival has lower marginal cost. Thus, AUD may lead to partial foreclosure of a more efficient, capacity-constrained competitor (full foreclosure is likely too if there are fixed costs or scale economies). When the rival's capacity level is small, the buyer is worse off under the AUD as compared to linear pricing. The limited capacity of firm 2 implies that the dominant firm has a "captive" portion of the buyer's demand. The dominant firm is able to use the AUD to leverage its market power on the "captive" portion to the "competitive" or "contestable" portion of the demand, much like the tied-in selling strategy in the context of multiple products. We further explore antitrust implications of the AUD. Bio: Guofu Tan is professor of economics at USC. His research focuses on auction theory, industrial organization, and antitrust economics. His most recent work is concerned with collusion, entry, investments and resale in auction markets; all-units discounts and other loyalty programs in retail contracts; Nash bargaining with log-convexity; platform competition with complementary products; and economics and private antitrust litigation in China.