On the functional equivalence of two perfectly competitive economies with negative exponential utility and linear utility with a quadratic holding cost

Abstract

In this paper, we analyze the functional equivalence of two perfectly competitive economies with negative exponential and linear utility with a quadratic holding cost. The two economies are said to be functionally equivalent if there exists a one-to-one correspondence between the vector of holding costs and the vector of risk aversion coefficients such that the resulting two economies have the same market equilibrium. If the information was symmetric, the equilibrium price reveals no new information and the functional equivalence between the two economies is straightforward. However, in the case of asymmetric information, the equilibrium price reveals some new information and an endogeneity issue arises. We establish the functional equivalence between the two economies with asymmetric information by resolving this endogeneity problem through a fixed-point argument.