Baumol was most famous for the notion of "cost disease." The idea is pretty simple, but powerful: Industries that experience more rapid productivity growth will see their relative costs– and therefore relative unit prices– fall. Conversely, industries in which productivity gains are difficult will see their relative prices rise and, assuming demand is relatively inelastic, will take up a growing share of the economy in value terms. This cost disease particularly afflicts high-skill service industries where mechanization and automation cannot readily displace skilled labor. It's one explanation for the growing share of health care in the economy, and for the tendency for education costs to rise more rapidly than inflation.
This post has an excellent discussion of Baumol's work on innovation and market structure. He also did interesting work on money, and on fairness theory. He was a very clear expositor of important economic ideas. For a while I taught using his fine little book, Perfect Markets and Easy Virtue: Business Ethics and the Invisible Hand, with Sue Anne Batey Blackman (1992). This book uses standard arguments from the literature on market imperfections to help the reader understand when markets do a good job steering the pursuit of profit toward the social good, and when they do not. It is an excellent antidote to the usual claptrap about socially responsible business and the unalloyed virtues of markets.
He was a prolific writer and a prolific painter. Not nearly as good an economistic painter as Wassily Kandinsky, but no doubt a better painting economist.
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