Knowledge that Transforms

SOME time ago, an attempt was made to develop a practical method for the appraisal of projects of road construction.1 The proposed method is one of comparative statics and compares the national product before and after the construction of a road. The essential elements of the method are the following. The whole economy is divided into a number of geographically separated centers. The movement of products from one center to another gives rise to transportation costs and, consequently, the price of the product of center i in center k depends on the costs of transportation from i to k. Supply and demand equations are assumed for each center and each product. The supply of each product i depends on the price of product i and the prices in i of all other products as cost elements. Two alternative assumptions are made with regard to the reactions of demand to price changes:

IT is widely believed that for some individuals saving may be negatively related to the rate of interest. The argument is usually put in terms of a person's desire to have a particular sum (or an annuity of a particular size) available at some future date. In such a circumstance a rise in the rate of interest will make easier (in terms of present abstention from consumption) the attainment of that particular future sum (or annuity). Therefore, the argument continues, the rise in the interest rate will reduce saving.' We do not wish to question the proposition that such perverse reaction to changes in the interest rate may adequately describe the behavior of some individuals; however, we do propose to criticize the extension of the proposition about individuals to the body of consumers in aggregate. This paper takes issue with those who contend that the aggregate saving-interest rate function for households may be perverse. 2 Our purpose is threefold. First, we wish to demonstrate that the use of the saving-for-a-fixedfuture-sum argument as support for the hypothetical negative relation between aggregate personal saving and the interest rate has unacceptable implications. In particular, it will be shown that it implies that aggregate personal saving is non-positively associated with aggregate real income.3 Second, we shall argue that a more general way to discuss a negative relation between saving and the rate of interest is in terms of the price elasticity of demand for future goods. Saving for a fixed future sum is a special case of this more general phenomenon. But third, we shall demonstrate that if the aggregate saving-interest rate relation is perverse, then the implied reaction of consumers to changes in expected future money prices would also be perverse.4 We shall treat these matters in turn after introducing the geometric tools.

(e) Net interest paid by government. The national income net interest total comprises total interest accruing to United States persons and governments less the total interest paid by United States governments to persons, governments, and businesses. The personal income interest total is obtained by adding to the national figure the excess of interest payments by governments over their interest receipts. Thus it measures total interest paid to United States persons.3 The share of the national total attributable to any one state is extremely difficult, if not impossible, to estimate by direct means, if this were desired. But allocation can be made more easily, although the method rests upon the same sort of fundamental and hazardous assumptions as in the case of allocating corporate income. Figures are availalble from the Department of Commerce of private interest received by residents of Texas and the United States. The Texas state income component of United States net interest paid by governments was obtained by applying the ratio obtained from the private interest figures to the United States net government interest total. The assumption here, of course, is that Texas residents' entitlement to a share of the national total of net government interest was the same as their entitlement to a share of the national total of private interest, as reflected in the payments actually made or imputed. The method also, as in the corporate income case, has the merit of conforming to the conceptual framework which emphasizes the wherereceived measure. TABLE 4.-GOVERNMENT AND BUSINESS TRANSFER PAYMENTS, TEXAS, I950-58 ($ million)

FORECASTS of productivity changes are usually made by extrapolating time series. For individual industries productivity fluctuates widely from decade to decade1 and the extrapolation method is vulnerable. An alternative is to use leading series. In an earlier study it has been shown that a well-defined time lag exists in the cotton textile industry among the estimates of productivity from engineering data, plant data, and industry data.2 Leading best-practice series, unfortunately, are hard to come by. But the results have suggested a third alternative: the forecast of productivity changes in industries by studying the diffusion of more advanced technology among plants.3 The present paper is an attempt to develop and test a framework by which productivity changes may be deduced from cross-section plant data. The cross section provides the initial conditions concerning the technological mix before changes. A simple set of rules on innovation and diffusion, also suggested by the crosssection information, then yields the expected changes of the mix. The cross-section approach has many virtues. It is unconstrained by the existence and quality of historical series, and moreover a suitably designed sample also catches the peculiar characteristics of an industry at a particular time or in a particular region. The possibility of refinement is virtually unlimited. From a theoretical point of view the opportunity afforded for testing the behavior of individual plants is also invaluable. These merits are ranged against some equally conspicuous difficulties, the most important of which are probably the difficulties in introducing time variables and in interpreting the results.4 In this paper a simple method for ordering technologies is suggested. After a tag is attached to each technology indicating its place on the scale running from obsolete to advanced, a rule of technology diffusion is introduced. In the third section the rule is applied to each of the two-digit Census Standard Industrial Classification (SIC) manufacturing industries in New England. The results forecasts of productivity, inputs, and outputs are evaluated in the last section of this paper. Although it would be desirable to use the model to predict the known data of some past year, the information at hand has not permitted such an endeavor without gross assumptions. It will therefore be argued only that the long-range forecasts based on the present model are reasonable and consistent in view of historical and present conditions.