Theory of Inverse Demand: Financial Assets

While the comparative statics of asset demand have been studied extensively, surprisingly little work has been done on the behavior of equilibrium asset prices and returns in response to changes in the supplies of securities. This is despite considerable interest in the equity premium and interest rate puzzles. In this paper, we seek to fill this void for the classic case of a representative agent economy with a single risky asset and risk free asset in both one and two period settings. It would seem natural to suppose that in response to an increase in the supply of the risky asset, its price would fall and the gross equity risk premium would increase. We show that in standard settings where preferences are represented by frequently assumed forms of expected utility, one can obtain the opposite result. The necessary and sufficient condition for prices (gross equity premium) to increase (decrease) with supply is determined by the sign of the slope of the asset Engel curve. This observation allows us to derive (i) sufficient conditions directly in terms of the representative agent's risk aversion properties for general utility functions and (ii) necessary and sufficient conditions for the widely used HARA (hyperbolic absolute risk aversion) class.