The traditional model of taste discrimination in labor markets presumes perfect substitution, making it unsuitable for the measurement of discrimination across job assignments. We extend the model to explain cross-assignment discrimination and test it on data from Major League Baseball. A competitive firm with a Generalized Leontief production function fills each job assignment with whites and nonwhites in an environment of customer prejudice. According to the model, cross-assignment discrimination depends upon racial productivity differences, the productivity x prejudice interaction, technology, relative labor supply and racial integration. We find strong evidence of ceteris paribus racial salary differences between hitters and pitchers.