One prominent aspect of recent developments in science studies has been the increasing employment of economic concepts and models in the depiction of science, including the notion of a free market for scientific ideas. This gives rise to the issue of the adequacy of the conceptual resources of economics for this purpose. This paper suggests an adequacy test by putting a version of free market economics to a self-referential scrutiny. The outcome is that either free market economics is self-defeating, or else there must be two different concepts of free market, one for the ordinary economy, the other for science. Both conclusions will impose limits on the applicability of the ordinary economic concept of the market to the study of science.