HIS paper presents a model of T which is an extension to n sectors of the original one-sector equilibrium paths developed by R. F. Harrod and E. D. Domar.1 Following Harrod, we employ discrete periods of time and hence a (first-order) difference equation technique. However, in order to give the model a prescriptive rather than a predictive overtone, the first differences refer to the immediate future instead of the immediate past. In addition, an allowance for depreciation is included in the model. By balanced growth we simply mean the existence of equilibrium (the equality of supply and demand) in every market in every time period. Equiproportionate of each market is a special case of as used in this paper. Prices do not explicitly enter the model. Supply in each market is an increasing linear function of the existing capital stock in that sector or industry, and hence the model refers to a one-factor economy. However, capital is not transferable from one sector to another. The single factor of production (capital) is produced by a single industry, the investment-goods industry, the input into which is also capital. Demand for the output of each industry, with the exception of the investment-goods sector, is an increasing linear function of net real income. By definition, these industries are producers of consumption goods, all of which are non-inferior from the point of view of the income-demand relation. The demand for investment goods is a mixed accelerator-multiplier relation. The solution of the system expresses net aggregate output as a function of integral values of time. The output of each sector at any time can then be determined from the structural equations of the model.

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.

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.