Waves and Cycles: Explorations in the Pure Theory of Price for Fine Art

This paper models price movements in the market for fine art. Consumers of art are assumed to value art for its own sake, but are also subject to externalities in consumption whereby the utility of consuming the work of a painter is affected by the consumption choices of other consumers of art. Painters are arranged in space, and positive externalities arise when the painter consumed is coming into fashion; negative externalities arise when the painter is going out of fashion. Because supply is fixed, popularity can be measured by price, so externality effects can be expressed through prices. Motion to the prices arises through the presence of some consumers who are fashion leaders, driving up the prices of coming artists. Rising prices indicate rising popularity, and the market moves towards these painters, shunning those who were previously popular. The paper makes reference to a companion paper by Peter Swann which is an empirical exploration of the same phenomenon. His paper suggests that painters can effectively be placed in a circular space, which makes the spatial assumptions of the analysis in the current paper reasonable. Results on trends in prices, and steady state prices under certain conditions are derived. The model is simulated numerically to illustrate some of the dynamics that arise.