Intertemporal Utility Function Research Articles

On the Uniqueness of Steady States in an Economy with Heterogeneous Capital Goods

It well known that in multisector models of optimal growth, optimal paths converge to a unique steady state when future utilities are not discounted. Sutherland [1970], Kurz [1968], and Liviatan and Samuelson [1969] gave examples of multiple steady states when future utilities are discounted. Beals and Koopmans [1969] and Iwai [1972] used intertemporal utility functions, which also yield multiple steady states. The uniqueness of steady states with multiple consumption goods when future utility discounted has been studied by Brock [1973]. He showed tlhat if we assume that none of the goods are inferior in consumption (he calls this the normality condition for the utility function) the uniqueness of the steady state assured. Brock did not allow for pure consumption goods. Later Brock and Burmeister [1976] generalized Brock's result to allow pure consumption goods as well (Morishima [1974] type). Brock also formulated an alternative approach where uniqueness assured under the of a non-vanishing Jacobian for every non-negative discount rate. He writes however that the non-singularity of the Jacobian is an obscure assumption and that it would be worthwhile to relate it to the normality condition of the utility function. We first propose to weaken Brock's of non-vanishing Jacobian for every discount rate. Then in Section 3, Theorem 2, we show that the normality condition on the utility function implies a non-vanishing Jacobian. In Theorem 3 we weaken the normality condition for the uniqueness of the steady state by investigating the conditions for a non-vanishing Jacobian. We then clarify the economic content of our weaker conditions. In the final section we observe that the normality theorem can be proved for the joint production case (Mirrlees [1969] type) using a technique due to McKenzie [1963, 1973].

A method for constructing an intertemporal utility function from a Friedmanian consumption function

Abstract It is shown that the intertemporal utility function can be reconstructed from data on demands if they are restricted to be linear in wealth, or Friedmanian.

Windfalls and Consumption Under a Borrowing Constraint

The emphasis here is on a micro-economic derivation of the theoretical propensity to consume windfalls under limited borrowing capacity. This is done in the next section by means of a comparative static analysis employing a reduced intertemporal utility function. The final section reports a test whose results conform to the prediction of the analysis that the propensity to consume windfalls is negatively related to size of the windfall.

Increasing risk and nonseparable utility functions

Assuming that the intertemporal utility function is separable, conditions are established which determine when an increase in risk with respect to the rate of interest is likely to increase or decrease savings and the supply of work effort. Without assuming intertemporal separability similar results are derived for the case where present and future consumption of both leisure and commodities are complements. A heuristic interpretation of the results concerning the behavior of the Arrow-Pratt measure of relative risk aversion is provided.

A Dynamic Programming Model of Demand for Money with a Planned Total Expenditure

RECENT CONTRIBUTIONS BY Eppen and Fama [6, 7], Girgis [10], Miller and Orr [13], Tsiang [21] as well as the present author [5] apply inventory theory to analyze an economic agent's demand for cash arising out of an uncertain time course of cash needs. A feature common to all of them is an implicit assumption that either the economic agent has no plan whatever regarding his total income and expenditure over the period of his planning horizon or, as in Tsiang, his plan over the income period, need not necessarily be realized. Leaving the economic agent's total income and/or expenditure over the planning horizon random in this way, keeps the density functions of net payments due independent from period to period, and no doubt, makes the analysis simpler. It may also have some practical relevance, especially when the income and expenditure plans of the economic unit over the planning horizon are not exact. From a theoretical point of view, however, it seems somewhat unsatisfactory to leave the economic agent's total income and especially his total expenditure over the horizon as random and unplanned. In this paper, we shall, therefore, develop a model of demand for money based on the idea that the economic agent has some income-expenditure plan for the period of his horizon and yet he is not entirely certain about the time course of his cash needs during this period. Patinkin [14] has presented a similar model incorporating the intra-period uncertainty of receipts and payments. Restricting the uncertainty of payments and receipts only with respect to their time course during the leaves Patinkin free to determine the individual's expenditures on goods and services as well as his income for each week by using the well-known Fisherine framework of maximizing the intertemporal utility function of the individual subject to his wealth-constraint, now modified to take into account the (minimum) cost of cash management during each week.2 In this paper, we consider an individual who plans to make a given total

The Consumer's Demand for Money: A Neoclassical Approach

Since the appearance of the contributions of Modigliani and Brumberg (1954), and of Friedman (1957), series of writers has derived new theories of the consumption from the neoclassical, or Fisherian, analysis of intertemporal resource allocation under assumptions of everincreasing generality. According to this approach, the consumer is viewed as maximizing an intertemporal utility function, having as arguments the levels of aggregate consumption at each point in time, subject to an overall resource constraint. The solution to this maximization problem yields the time path of consumption as function of total resources and the time path of forward prices. In this capital-theoretic approach, the household stock of nonhuman wealth enters only indirectly. First, the services of real assets (for example, homes and cars) are included in consumption, and forward prices of aggregate consumption are defined to include the prices of these services rather than the prices of the assets themselves. Second, in the ModiglianiBrumberg formulation, expected labor income and nonhuman wealth (= present value of expected property income) are entered as separate arguments in the consumption function. However, neither Friedman nor Modigliani and Brumberg (nor their successors) stress the fact that the intertemporal maximization process also yields, as by-product, the time path of savings and of household nonhuman wealth (which includes stocks of financial as well as of real assets). Parallel to this work on the consumption function, Friedman and others have argued that the demand for money should also be regarded as a special topic in the theory of capital (Friedman 1956, p. 4). Money

Rational Choice and Patterns of Growth

Concluding his excellent survey of recent monetary theory, Harry Johnson [4] suggested that future developments in this field should come from attempts break monetary theory loose from the mould of short-run equilibrium analyses, conducted in abstraction from the process of economic growth and accumulation, and to integrate it with the rapidly developing theoretical literature on economic growth. This paper summarizes an attempt to deal with these issues. Like most theoretical work in rapidly growing fields, it is incomplete and the assumptions on which it is based are relatively crude abstractions. These abstractions, however, allow us to explore certain aspects of the interaction of the real and the monetary phenomena in a model of economic growth in which money, being government noninterest bearing debt, is introduced as an alternative asset to real capital. Most of the recent work in this field 1 has centered on the analysis of the patterns of growth of a monetary economy by postulating alternative plausible saving functions and demand functions for money. What differentiates this product is the fact that, in line with Patinkin's [6] presentation of the neoclassical theory of money, and with the classical Fisherian theory of saving [2], it is based on an explicit analysis of individuals' saving behavior, viewed as a process of wealth accumulation aimed at maximizing some intertemporal utility function. The first part of the paper describes the representative economic unit

Per Capita Consumption and Growth: Comment

In recent paper 1 J.C.H. Fei attempts to derive conclusions on efficient transitional growth towards the steady state solutions characteristic of growth models with constant technology, without assuming an intertemporal utility function. The criterion he uses is that a feasible per capita consumption stream C* (t) is inefficient if there is another feasible per capita consumption stream G* (t) such that G* (t) > C* (t) for all t and G* (t) > C* (t) for some t. By comparing the growth path of the C.P.C.S. (constant per capita consumption standard) model and that of the Solow constant average propensity to save model, Fei concludes that for the attainment of target steady states reflecting (rather extreme) capital assets preference 2 on the part of the community (i.e. higher capital/labor ratio K* than that corresponding to the maximum per capita consumption solution), the Solow growth path will be inefficient. The Fei argument is illustrated in Figure I (based on Figure III in the Fei article.) With community preference function yielding the indifference curves shown in Figure I, the optimum steady state will be point Z on the VS curve locus of feasible steady states. The C.P.C.S. and Solow paths corresponding to this solution are also plotted in Figure I. In the transition to the steady state, with the actual capital/labor ratio increasing towards the terminal capital/labor ratio K*,, (a rightward movement in the diagram), the per capita consumption stream of the Solow model is, at every time period, less than that of the C.P.C.S. model. Therefore, by the Fei criterion, the Solow path is inefficient. Several points, however, may be raised concerning the validity of this theorem. Firstly, this conclusion is based on the use of inconsistent welfare criteria. The per capita consumption target is derived on the basis of community utility function reflecting strong capital assets preference while the Fei theorem on transitional growth paths is based on welfare criteria which solely reflect per

Intertemporal Utility Functions and the Long-Run Consumption Function

Intertemporal Utility Functions and the Long-Run Consumption Function