Some firms, particularly in high-tech, appear to view technology and cost leadership as separate and distinct ways of achieving high profiles within a given product market. In contrast, we develop a model of technology competition suggesting that a firm’s success in sustaining its technology leadership may hinge on its ability to produce the new product (resulting from the new technology) at lower cost, an ability we call firm’s “cost competence.” In our model, cost competence, above a critical hurdle level, is essential to the incumbent firm in its bid to retain technology leadership. The model also clarifies the role of “innovative competence,” which characterizes a firm’s ability to turn an investment in new technology into a marketable product. We present an example of a standard product market model (for determining prices and production quantities for two competing products in the aftermath of the technology competition) in which the assumptions of our technology competition model hold. An additional key finding is that there can be discontinuities in the returns that accrue from enhanced cost competence. If a firm is on the right side of a “jump point,” its expected profits can be dramatically more than if it were only slightly less competent. These jump points arise where the firm’s cost competence becomes sufficient to cause a competitor to decide against competing in the new technology, or to significantly drop its investment amount. When a potential competitor backs down, the prospect of high returns for the incumbent opens up.