The equity premium in a production economy; A new perspective involving recursive utility

Abstract

We study a rational expectations' competitive equilibrium in a production economy, i.e., a system of prices at which firms' profit maximizing production decisions and individuals' preferred affordable consumption choices equate supply and demand in every market. We derive the equilibrium price of the firm and the equilibrium short term interest rate, the optimal per capita consumption in society, as well as the risk premium on equity. First a simple linear production technology with constant coefficients is studied, then a more general technology, and finally a general production economy with recursive utility is analyzed by the use of the stochastic maximum principle. While the two first models can not explain the empirics well using conventional preferences, the latter model is found to be much more promising in this regard. Wa also demonstrate a simple proof for the ICAPM.