General Utility Function Research Articles

Technological and Price Uncertainty in a Ricardian Model of International Trade

Despite the fact that international trade is one of the riskiest economic activities, there has been remarkably little attempt to incorporate uncertainty into the formal theory. One of the few published papers dealing with this issue is the important contribution by Brainard and Cooper [3]. However, their formal analysis is rather restrictive in that they deal only with the quadratic utility and focus primarily on the case where the country is required to make all its decisions-both production and consumption-before the uncertainties are resolved. The present paper introduces uncertainty into a Ricardian model of international trade. While this technology is somewhat more restrictive than the neoclassical production possibility frontier considered by Brainard and Cooper, it nevertheless is an interesting case to start with in view of the fundamental role the Ricardian case has played in the development of international trade theory. Furthermore, it is of considerable interest to determine to what extent the extreme implications regarding the patterns of specialization associated with the classical Ricardian model remain after the introduction of uncertainty. In other respects the present analysis is more general than the Brainard-Cooper model. In the first place we try as far as possible to derive propositions based on general utility functions, although where appropriate, we use special cases to illustrate particular propositions. In establishing these propositions a crucial role is played by the indirect utility function which enables us to analyse the behaviour most conveniently in terms of the familiar Arrow-Pratt measures of risk aversion. The model is developed for a small country, in which domestic technology and the international trading price (which it takes as given) are both subject to uncertainty. We develop a kind of two-stage analysis in which production decisions are made before the random technological parameters and the actual trading price are known, while trading and thus consumption decisions are made after the uncertainties are resolved. In view of the lags associated with production and the fact that most international trade takes place at previously established prices, this seems to be the most plausible case to consider. Brainard and Cooper did not consider it on the grounds of analytical intractability, but in fact the analysis is no more difficult than the case they examine where all decisions are made under uncertainty.

The Investment-Consumption Decision under Capital Rationing: An Efficient Set Analysis

The investment decision under capital rationing has been of intense interest to individuals in the field of finance. A major research problem in this area is the specification of a criterion function for solving the capital rationing problem. Lorie and Savage [8] and Weingartner [11] argued that when faced with capital rationing, the firm's objective should be the maximization of the present value of its investments' cash flows. What was troubling to some about this formulation is the assumption that the discount rate, necessary for the calculation of the present value of an investment's cash flows, is known before the problem of project selection is undertaken. Baumol and Quandt (B-Q) [1] confronted this problem directly. First, they reminded their readers that Hirschleifer [5] had shown that the appropriate discount rate in a pure capital rationing problem is given by the slope of the investment opportunity curve at its point of tangency with the investor's highest indifference curve, and this rate cannot be discovered until the utility function is specified fully and the final consumption vector determined. Hence, B-Q claim (as Hirschleifer does) that under capital rationing the discount rate cannot be an external variable but must be an internal variable, which, among other things, is a function of the available projects and the actual capital constraints.3 As a way to circumvent this problem, B-Q offer the individual's utility of consumption flows over time as a substitute objective function. However, in B-Q's formulation, one needs to specify fully the individual's utility function, a task which is difficult. The purpose of this paper is to focus on the efficient set of consumption vectors when the problem is the maximization of U(c1, c2, ..., cJ), where ci is consumption in period i, and U is some general utility function. We assume nothing about the specific form of the utility function. The only assumption we make is that more consumption is preferred to less. Our method attempts to determine how far analysis can

Optimum consumption and portfolio rules in a continuous-time model

Publisher Summary A common hypothesis about the behavior of limited liability asset prices in perfect markets is the random walk of returns or in its continuous-time form the geometric Brownian motion hypothesis, which implies that asset prices are stationary and log-normally distributed. A number of investigators of the behavior of stock and commodity prices have questioned the accuracy of the hypothesis. In an earlier study described in the chapter, it was examined that the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the “geometric Brownian motion” hypothesis. Under the additional assumption of a constant relative or constant absolute risk-aversion utility function, explicit solutions for the optimal consumption and portfolio rules were derived. The changes in these optimal rules with respect to shifts in various parameters such as expected return, interest rates, and risk were examined by the technique of comparative statics. This chapter presents an extension of these results for more general utility functions, price behavior assumptions, and income generated also from noncapital gains sources. If the geometric Brownian motion hypothesis is accepted, then a general separation or mutual fund theorem can be proved such that, in this model, the classical Tobin mean-variance rules hold without the objectionable assumptions of quadratic utility or of normality of distributions for prices. Hence, when asset prices are generated by a geometric Brownian motion, the two-asset case can be worked on without loss of generality.

A Note on Simon Patten's Contribution to the Concept of Consumer's Surplus

Historians of economic thought have failed to notice the contribution of Simon Nelson Patten to the development of the concept of consumer's surplus. Patten, a professor of economics at the University of Pennsylvania from 1888 to 1917, a founder and president of the American Economic Association, was a recognized leader of the nascent economics profession in the United States;1 but he has been all but forgotten by contemporary economists. This Note attempts to correct that historical oversight by recognizing Professor Patten's ideas on the concept of consumer's surplus. Patten disputed briefly with Marshall over the meaning and measurement of consumer's surplus and may have induced Marshall to make a minor alteration in his statement of the concept in the third (1895) and subsequent editions of the Principles. Unlike the founders of marginal utility theory (Jevons, Menger, and Walras) and unlike Marshall, Patten considered the utility of a good to a consumer to be a function of the quantities of all goods he consumed. In his Theory of Dynamic Economics (1892) Patten treated extensively the cases of complementary and substitute consumer goods. In this analysis he should be credited with some originality, since he seems to have developed on his own the concepts of complementary and substitute consumer goods from the discussion by the Austrian economists, particularly Wieser, of complementary factors of production. These concepts were not new when Patten wrote his Dynamic Economics, but, as far as can be determined, he was unaware of any prior discovery. For example, he apparently was unaware of the mathematical formulation of a generalized utility function by Edgeworth in 1881 and of the discussion of consumer's surplus, which

Taxation and Risk-Taking: An Expected Utility Approach

It is a popular notion that higher taxes tend to discourage risk-taking. In economic theory, however, the conclusions in this respect have been somewhat different. Thus, Tobin in his celebrated Liquidity Preference as Behavior Towards Risk [3] and Musgrave in his text-book [2]1 come to the conclusion that an increase in a proportional tax rate will, with full loss offset, increase the holding of the risky asset in a portfolio of a given size. Musgrave's analysis of the no-loss-offset case leads to the result that the direction of the effect is indeterminate. In this article these problems are re-examined on the basis of expected utility theory. There are two reasons why such a re-examination is justified. One is that it seems desirable to develop the analysis under assumptions about the investor's preference structure less restrictive than those made by Musgrave and Tobin. The other is that in spite of the greater generality of the expected utility approach, it is possible to sharpen some of the old conclusions, to derive some new ones, and to correct some erroneous ones. The analysis is inspired largely by the elegant treatment of portfolio choices by Arrow in [1]. The Pratt-Arrow measures of absolute and relative risk aversion are employed at various points in the analysis, and some familiarity with these concepts is assumed. (See Appendix.) Without any serious loss of generality, the discussion is restricted to portfolio choices involving two assets only. It is assumed, however, that the yield on one of these is non-stochastic, i.e. known with certainty. It may be true that in the real world no such asset exists, but when a general utility function is used this assumption is necessary in order to get a relatively simple measure of risk-taking, simply by using the amount invested in the riskless asset. One might of course compute and compare, say, the means and variances of two portfolios; but when it is not assumed that the investor is satisfied by letting himself be guided by the portfolio mean and variance only, it is clearly not to be expected that his behaviour can be summarized by these alone. The following notation is employed: