Knowledge that Transforms

The economic gradient method is designed to provide guidance for the analysis and recommendation of change when information is available only over so narrow a range as to preclude a credible calculation of the global optimum. Using as data the gradients of the relevant functions evaluated at the current point of operation, the procedure calculates the direction of change from the status quo that yields the greatest feasible local rate of increase in the objective function of the decision maker. The calculation should be viewed as a benchmark because proposed movements of practical size must be assessed for feasibility. Under structural assumptions (standard for second-order conditions), the procedure can also be used to obtain an upper bound on the gain from effecting any particular (nonlocal) set of feasible changes in the decision variables. In Section I, we present the economic gradient method in a general form. We specialize the formulae in Section II to apply to pricing under a budget constraint with aggregate consumer welfare as the objective function.' Pilot empirical applications to U.S. Postal Service and long distance telephone rates are summarized in Sections III and IV.

The article investigates the Ronald Findlay-Stanislaw Wellisz and T. N. Srinivasan-Bhagwati (F-W-S-B) two-by-two small-country model of traditional international trade theory. Section I recapitulates the basic F-W-S-B analysis, retaining the two-by-two model but distinguishing between the with-distortion and the no-distortion cases. Section II examines the many-good-and-factors cases: goods equal factors, no distortion; good equal factors, with distortion; goods outnumber factors, no distortion; goods outnumber factors, with distortion; factors outnumber goods, no distortion and factors outnumber goods, with distortion. Section III offers concluding observations, indicating the applicability of the analysis to other problems in trade theory and the relationship of the results to mathematical programming. The F-W-S-B model is characterized by three key features: constant-returns-to-scale production functions; two primary factors producing two graded goods; and fixed foreign prices for the two traded goods. The uniqueness and stationarity of the marginal variational shadow prices in the two-by-two F-W-S-B model, with and without the specified distortions, do not necessarily carry over to the cases with unequal numbers of goods and factors that need to be analyzed as soon as the author consider many goods and factors. The analysis leads to many observations. First, the relative numbering of factors and goods is of signifiance. Second, the analysis has clear applicability to the transfer problem, conceived not as a transfer of purchasing power, but rather as a transfer of factors of production as may be the case when reparations payments have to be made in barter. Third, the analysis has applicability therefore to the theory of international factor mobility.

There appears to be an inconsistency Morton Paglin's recent article this Review. The effect of that inconsistency is to exaggerate the difference between the traditional Gini coefficient and a Gini coefficient which is adjusted for the average age-earnings relationship. Paglin observes that the Gini coefficient is often used normative evaluations of the income distribution. What begins as a measure of inequality is finally treated, with or without intervening statements of qualification, as if it were a measure of inequity. This being so we must ask whether all deviations from the mean income of the population-the inequalities that give magnitude to the Gini coefficent, G-are unjustifiable. For Paglin the answer is no, and on this point one suspects that he belongs, to a comfortable majority. The question is what to do. Paglin proposes that use be made of the average age-income relationship. Perfect equality or equity exists when all families at the same stage their life cycle have the same annual income. The deviation of any one family's income from the mean income for its age cohort is taken to be an unjustifiable deviation that gives magnitude to some adjusted Gini coefficient. Since the actual age-income profile has a definite hump, it is expected that the adjusted Gini coefficient will be less than G. My points will be that Paglin, giving mathematical expression to his normative position, has made a structural change the Gini formula which does not fully conform with the logic of the Gini measure, and that consequence the magnitude of inequality which he has measured is determinately too small. Suppose that the income scale and the age scale are partitioned into a finite number of segments. Each family belongs to one of the income ranges and to one of the age (of head) ranges so defined. Let nii represent the number of families that have an annual income income range i and whose family heads are age range j. They will be said to be in cell (i, j). The income level of every family cell (i, j) is denoted by yij.' The mean income level for all families age range j is denoted mj, and the grand mean is m. There are N families the population. The Gini coefficient,

Business cycles appear to reflect predominantly the effects of changes in aggregate demand for output on real variables such as aggregate employment. The measurement of the magnitude and timing of these effects is not a trivial problem. However, recent work, for example, by Robert Hall and by Robert King, supports the impression that the response of aggregate employment to aggregate demand is prompt and large, apparently peaking within a few months of the disturbance at a level equalling or exceeding the value of the disturbance, but also temporary, giving way over time to adjustments in wages and prices. These observations suggest that cyclical fluctuations in aggregate employment are not symptoms of the familiar nonneutralities that arise in analyzing the effects of changes in the stock of money or its velocity of circulation in a Walrasian general equilibrium context. Rather, the characteristics of the relation between aggregate demand and aggregate employment suggest that the actual economy differs in significant respects from the imaginary Walrasian economy, in which exchange takes place only under market-clearing conditions that emerge from a tatonnement process conducted with all agents in possession of complete information about wages and prices. This conclusion that the Walrasian paradigm does not do justice to the real world does not seem controversial. However, research in macroeconomics has witnessed persistent disagreement about the usefulness of specific non-Walrasian paradigms for modelling the determination of aggregate employment. This disagreement reflects basic differences in perceptions of the essential characteristics of the actual economy that are responsible for the non-Walrasian behavior of aggregate employment. The discussion that follows evaluates the current state of this controversy, focusing on recent disenchantment with the popular nonmarket-clearing approach and, more positively, on the prospect that a resolution of this paradigm conflict is presently at hand. As explained below, this impending settlement involves recognition that incomplete information is the critical factor in the generation of non-Walrasian fluctuations in employment, together with explicit allowance for the implications of implicit contractual arrangements for efficient shifting and pooling of risk in labor and product markets. The present discussion is not concerned with the causes of fluctuations in aggregate demand or, in particular, with the relative importance of variations in the stock of money and its velocity of circulation. Rather, the focus is only on why such fluctuations in aggregate demand cause observed nonWalrasian fluctuations in aggregate employment, taking this causal link to be a matter of fact.

Although demand for money equations have traditionally been regarded as exceptionally stable, the literature abounds with empirical evidence of structural shifts and apparent trends in some of the coefficients over time. Subperiod estimates of long-term studies often yield different coefficients or suggest secular trends in the coefficients. Other studies report structural shifts or variables which are significant only during particular periods. And while numerous other instabilities have vanished along with revisions in the data, the 1974 instability is too large to be so obliging. Thus, the latest apparent instability is hardly without precedent. One possible source of these instabilities is the omission from the estimated equations of a measure of technological change which reduces over time the real cost of transactions in the management of money balances. The real cost of transactions plays a substantial role in explaining money holdings in the standard inventory theoretic models of money demand. The omission of a key explanatory variable from the estimation produces a misspecified equation which may result in biased coefficient estimates. While the sources of the most recent instability in money demand equations may be due to a structural shift, as suggested in several studies, it may also be due in part to an omitted technological change measure. This paper tests the usefulness of some technological change proxies and examines the forecasting ability of these modified models over the difficult post-1974 period. A Shiller lag specification is employed to obtain a better specification of the dynamic properties of money demand. Although the technological change proxies do improve the equations, the findings support the existence of another structural shift in money demand. The results nevertheless provide some hope that a fairly standard money demand equation, with only minor adjustments, may once again be capable of providing satisfactory forecasts, at least for the present.