Some Notes on Golden Rules and Risk Aversion in a Merton Type Solow Model
11 Pages Posted: 8 Dec 2008 Last revised: 1 Feb 2010
Date Written: January 28, 2010
We consider Merton's version of the Solow model Merton (1975), where capital per labor is assumed to follow the diffusion process: dk(t)=[sf(k(t))-(n lambda-sigma2)k(t)]dt sigmak(t)dW(t), with constant per capital 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. We discuss some of Merton's results and their limitations and then provide an alternative setup, in which we consider a mean-variance optimizer. We show then, that unless in Merton, risk-aversion and volatility do have an effect on Golden rule consumption, even if a Cobb-Douglas production function is assumed.
Keywords: Economic Growth, Golden Rule, Solow model, Risk Aversion
JEL Classification: C63, G11, G31, G39
Suggested Citation: Suggested Citation