Some Notes on Golden Rules and Risk Aversion in a Merton Type Solow Model

Abstract

We consider Merton's (1975) version of the Solow Growth model, where capital per labor is assumed to follow the diffusion process dk(t ) = [sf (k(t ))- (n +l -s2 )k(t )]dt +sk(t )dW(t ), with constant per capita savings rate s. Merton defined a golden rule in this context as one for which expected utility from consumption c = (1- s)f (k ) under the equilibrium distribution of capital/output becomes maximal. One of the limitations of Merton's utility based setup, is that risk aversion and uncertainty have no effect on golden rule consumption. As an alternative we propose a setup in which mean-variance optimization is the objective. We then show, that in difference to Merton (1975), risk-aversion and uncertainty do have an effect on golden rule consumption, even if in the simple case of a Cobb-Douglas production function.