We consider the problem of identifying the supply and demand of a single homogeneous good when markets have rich forms of unobserved heterogeneity. We introduce market types---collections of potential equilibrium outcomes across values of an excluded instrumental variable---and use them to develop a new approach to analyzing identification. Through graphical examples, we show how nonparametric, economically-motivated assumptions---such as downward-sloping demand---provide empirical content about natural target parameters. We show that comparable linear IV estimators are systematically attenuated measures of demand, a theoretical prediction confirmed in a well-known dataset. We then analyze random coefficient models with linear supply and demand curves that have heterogeneous slopes and develop a computationally tractable method for computing and estimating sharp bounds. We apply the method to estimate the welfare incidence of sales taxes in the United States.