The equity premium and the risk free rate in a production economy. A new perspective

We study a 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 consumption in society, as well as the risk premium on equity. Both a linear, and a nonlinear production technology are considered. For the linear one applied to the Standard and Poor’s composite stock price index for the last century, a risk premium of 0.062 corresponds to a relative risk aversion of 2.27. The model provides a riskfree interest rate for the period of 0.8%. The nonlinear model, however, highlights a hedging demand for the investors related to the real economy, which would, if taken into account, make the stock market of the last century less risky than it was perceived to be.