Glen Weyl at Marginal Revolution:
What Is “Price Theory”?: ... I have an unusual relationship to “price theory”. As far as I know I am the only economist under 40, with the possible exception of my students, who openly identifies myself as focusing my research on price theory. As a result I am constantly asked what the phrase means. Usually colleagues will follow up with their own proposed definitions. My wife even remembers finding me at our wedding reception in a heated debate not about the meaning of marriage, but of price theory.
The most common definition, which emphasizes the connection to Chicago and to models of price-taking in partial equilibrium, doesn’t describe the work of the many prominent economists today who are closely identified with price theory but who are not at Chicago and study a range of different models. It also falls short of describing work by those like Paul Samuelson who were thought of as working on price theory in their time even by rivals like Milton Friedman. Worst of all it consigns price theory to a particular historical period in economic thought and place, making it less relevant to the future of economics.
I therefore have spent many years searching for a definition that I believe works... This process eventually brought me to my own definition of price theory as analysis that reduces rich (e.g. high-dimensional heterogeneity, many individuals) and often incompletely specified models into ‘prices’ sufficient to characterize approximate solutions to simple (e.g. one-dimensional policy) allocative problems. This approach contrasts both with work that tries to completely solve simple models (e.g. game theory) and empirical work that takes measurement of facts as prior to theory. Unlike other definitions, I argue that mine does a good job connecting the use of price theory across a range of fields of microeconomics from international trade to market design, being consistent across history and suggesting productive directions for future research on the topic. ...
He goes on to explain.