Academic journal article Economic Inquiry

Elastic Capital Supply and the Effects of Fiscal Policy

Academic journal article Economic Inquiry

Elastic Capital Supply and the Effects of Fiscal Policy

Article excerpt


Perfectly elastic or perfectly inelastic supply or demand curves have much to recommend them. Equilibrium analysis which would otherwise be fraught with ambiguity yields forth sharp predictions when one assumes either demand or supply are either perfectly elastic or inelastic. Nonetheless, this is not the way we typically teach equilibrium analysis nor, in most circumstances, perform it. Neoclassical macroeconomics is an exception to this rule. Specifically, capital accumulation models in which a representative agent maximizes the standard additively-separable, fixed-discount-factor utility function - to which class most equilibrium business cycle models based on the neoclassical growth model belong - imply a long-run supply curve for capital which is perfectly elastic at the agent's fixed rate of time preference.

This property of what we will refer to as the "standard" model is, and has been, well-known and well-criticized, even by users of the standard model.(1) But, the question of exactly where and when this assumption ceases to be innocuous - i.e., for what sorts of experiments it is or isn't a harmless simplification-has been given surprisingly short shrift.(2) In this paper we explore the implications for the equilibrium analysis of the effects of changes in government purchases of relaxing this assumption. In particular, we explore the implications of replacing the fixed discount factor [Beta] in the standard utility specification

[summation of] [[Beta].sup.t] u([c.sub.t], [l.sub.t]) where t = 0 to [infinity]

where [c.sub.t] and [l.sub.t] denote consumption and leisure at date t, with an endogenous discount factor, [Beta]([c.sub.t], [l.sub.t]). In this way, discounting of future utility is allowed to depend on the agent's enjoyment of current consumption and leisure. The lifetime utility function that results from this modification is of the sort first formulated by Uzawa [1968] and Epstein and Hynes [1983]. The latter of these, in particular, demonstrated through a series of examples the extent to which models with endogenous discount factors can differ substantially from their fixed-discount-factor counterparts. While these earlier papers were primarily concerned with developing theoretical results, our analysis will be primarily quantitative.

The possibility that the rate of time preference varies across individuals and over time, or equivalently, that the rate at which the future is discounted responds to the current and previous decisions of individuals, is more than a theoretical curiosum. To start with, there is a substantial body of evidence that rates of time preference differ across individuals: people are not equally patient. Much of this evidence is summarized in table 1 of Becker and Mulligan [1997]. At the aggregate level, they point to the fact that rich countries have grown slightly faster than poor countries over the past 30 years as suggesting that the residents of rich countries may have lower rates of time preference than residents of poor countries. Differences between the United States and Japan in the age-consumption profile are also consistent with differences in the rate of time preference between the United States and Japan. And the fact that income is associated with consumption growth suggests that the rich may be more patient than the poor. Detailed micro evidence on differences in rates of time preference across households is also presented by Lawrance [1991]. She finds that the rates of time preference of poor consumers are three to five percentage points higher than those of rich consumers using panel data for the United States from the PSID. Ogaki and Atkeson [1997] estimate a model in which time preference is allowed to vary across rich and poor households using household level panel data from India. Furthermore there is evidence that rates of time preference vary not just across individuals at a point in time, but also over time. …

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