Aggregate Intertemporal Microfounded Models with Infinite Horizon

Solow’s model is of a great theoretical interest in a discussion of dynamic efficiency but does not specify any criteria for ascertaining whether a saving behaviour based on the golden rule propensity to save s = sg is optimal. This would require a theory of optimal individual saving. Modern theory offers the competing approaches of Ramsey (1928) and Fisher (1930). We shall begin here with Ramsey’s approach. His distinctive assumption is that a consumer’s objective is to maximize over a given horizon a utility functional which depends on an instantaneous utility function. Since instantaneous utility exhibits decreasing marginal utility of consumption, the individual has an incentive not to concentrate all the consumption in the current period, but to distribute it over time as uniformly as possible. In this intertemporal re-allocation, a rational agent must compare the marginal rate of substitution between current consumption and saving to what will be earned as future utility from future consumption. The optimal saving condition is dictated by the Ramsey-Keynes rule, according to which saving, or a wealth accumulation path, is optimal if the growth rate of marginal utility is equal to the difference between the utility discount rate and the real rate of return of saving.