Should the interest rate really be the unique motive to save in the standard Ramsey model ?

It goes to our mind almost systematically, that the flow of saving should never be included in the utility function along with consumption, to solve the inter-temporal maximization problem of the consumer. Two reasons can be stated precisely and may sound a bit obvious only at first glance. The first one which is to consider savings as having no intrinsic value for the individual, can arguably be contested in several ways. The second, a technical redundancy deduced from standard models of re-allocation of income, can be shown to be misleading and inappropriate for models of accumulation. The goal of this paper is to criticize the systematic neutrality of a utility effect of savings in the literature, and to report the relevant implications in the Ramsey growth model.

Clearly, in the standard Ramey model, the capital accumulation occurs mechanically thanks to the interest rate. When its value is low, the incentive to save disappears. The desire to save or invest in itself is neither explicitly nore implicitly involved in the mind of the representative agent. Yet, several motives other than the interest rate are actually present in that framework. Important ones are the necessity to renovate the capital that depreciates, and the necessity to increase it in order to absorb a growing household. We may eventually cite also, as in the literature of 'capitalist spirit', the desire to get richer one day, to increase in social status, to acquire power, notoriety, etc. ; see for example Weber (1930), Zou (1994), Bakshi and Chen (1996), or Carroll (2000).

In the exogenous version of Solow (1956), the desire to save is set independently of the interest rate by assumption. The agent can choose the one that meets the golden rule condition or any one that generates over-accumulation (which is technically impossible in the Ramsey model). We show in this paper that including the saving rate in the utility function allows, not only extension of capitalist spirit models, but also recovery of all basic properties known from the exogenous version. Using an additive Cobb-Douglas form for the utility function, we show that the dynamics and steady-state solution change as soon as the direct preference for saving is different from zero. We conclude that the standard Ramsey model, used as a central structure in macroeconomic models, is actually a particular and too restrictive version of the optimal growth model where individuals are not really conscious.