Constant Absolute Risk Aversion Preferences and Constant Equilibrium Interest Rates

This paper constructs a general equilibrium model with endogenous stochastic production and establishes that the equilibrium interest rate can be constant in a closed production economy when the preferences are represented by constant absolute risk aversion utility functions. The results in this paper and their limitations are compared and contrasted with related contributions in the financial economics literature. IN THIS PAPER AN intertemporal allocation problem with endogenous stochastic production is solved for consumption function and the interest rate. Preferences are assumed to be of constant absolute risk aversion type. There are a number of stochastic constant returns to scale production techniques with independently and identically distributed shocks. It is shown that the wealth dynamics of agent can be then approximated by a "square root" diffusion process which is a special case of constant elasticity of variance diffusion. With this as the starting point the consumption function and interest rates are derived and discussed. At equilibrium the interest rate is shown to be a constant and consumption is shown to be drawn from a distribution which belongs to the constant elasticity of variance diffusion class. Restrictions are placed on the form of the problem so that results make economic sense. The assumption of a constant interest rate has been made frequently in the asset pricing literature. We provide a plausible equilibrium model in which this assumption is valid. The findings are compared with those of Bhattacharya [1], Constantinides [2], Rubinstein [8], and Stapleton and Subrahmanyam [10] in subsequent sections. This paper is organized as follows. In the next section the characteristics of the economy are described. Section II develops the dynamic optimization problem facing the consumer in the economy. In Section III, the optimal consumption function is derived and discussed. Section IV contains a result on the equilibrium interest rate. In this section it is shown that the equilibrium interest rate is a constant, and its properties are analyzed. In Section V a discussion of the results is provided.