ASSIGNMET

Assignment



Assignment

Part 1: How Solow growth model would analyze the effects of a fall in the household saving ratio

The Solow growth model is predicated on a constant saving rate. It would be more informative to specify the preference orderings of households (individuals), as in standard general equilibrium theory, and derive their decisions from these preferences. This specification would enable us both to have a better understanding of the factors that affect savings decisions and furthermore to discuss the optimality of equilibria—in other words, to pose and answer questions associated to whether the (competitive) equilibria of growth models can be improved. The notion of improvement here is based on the standard concept of Pareto optimality, which asks whether some households can be made better off without others being made worse off. Naturally, we can only talk of households being “better off” if we have some information about well-defined preference orderings (Solow, 2006, pp: 71).

In order to analyze the effects of a fall in the household saving ratio, let us consider an economy consisting of a unit measure of infinitely-lived households. By a “unit assess of households” I signify an uncountable number of households with total assess normalized to 1; for example, the set of households H could be represented by the unit interval [0,1]. This abstraction is adopted for simplicity, to emphasize that each household is infinitesimal and has no result on aggregates. Nothing in this book hinges on this assumption. If the reader instead finds it more convenient to think of the set of households, H, as a countable set, for example, H = N, this can be finished without any loss of generality. The advantage of having a unit measure of households is that averages and aggregates are the same, enabling us to economize on notation. It would be even simpler to have H as a finite set of the form {1,2,...,M}. While this form would be sufficient in numerous contexts, overlapping generations models require the set of households to be infinite (Solow, 2006, pp: 79).

Households in this economy may be truly “infinitely lived,” or alternatively they may consist of overlapping generations with full (or partial) altruism linking generations within the household. Throughout I equate households with individuals and therefore ignore all possible sources of conflict or distinct preferences inside the household. In other phrases, I assume that households have well-defined preference orderings.

As in basic general equilibrium theory, let us suppose that preference orderings can be represented by utility functions. In particular, suppose that there is a unique consumption good, and each household h has an instantaneous utility function given by:

Where ch (t) is the consumption of household h, and uh : R+?R is increasing and concave. I take the domain of the utility function to be R+ rather than R, in order that negative levels of consumption are not allowed. Even though some well-known economic models permit negative consumption, this is not easy to interpret in general equilibrium or in growth ...