Knowledge that Transforms

' . when p 0 (i.e., the elasticity of substitution is less than unity), the isoquants have asymptotes which do not coincide with the axes. The exact formula for the asymptotes is given by K val/p K =

Although the validity of quoted prices is an important issue and must not be slighted, it is suggested here that there are also other important problems in the steel industry which need to be considered. These problems relate to the various ways the industry can respond to changes in external conditions which are made possible by very close relationships among the large number of products it sells. The purpose of the present article is to indicate the importance of these responses for steel price change analysis and then to develop and test a new kind of price change index which attempts to measure these responses. While the orientation of the present article is perhaps somewhat unfamiliar, it is not new. For example, some of the following can be traced to a suggestive

where G is the growth rate of aggregate demand, and gi and Ei are the actual growth rate and the income elasticity of output for the ith sector respectively. GEi is defined as the expected growth rate of the ilh sector.2 Measure (2) is preferred to (1) as the latter is unnecessarily sensitive to extreme deviations in sectoral growth rates. Swamy then correlated both measures of imbalance with the aggregate growth rate, G. Coefficients were positive and statistically significant for all periods except 1938-1948. He concludes that the 'statistical evidence does not corroborate the balanced growth theory.' 3 Swamy's results have to be interpreted carefully. In the first place there are weaknesses in the statistical techniques he adopts. These result from his reliance on the correlation between G and V. This correlation is questionable on two counts. Firstly, where the k sectors form a large proportion of aggregate output, we would expect high sectoral growth rates to be accompanied by a high growth of overall output. The association between V and G merely reflects a mutual component in both (i.e., gi). However, since Swamy disaggregated into 13 manufacturing sectors, this spurious element may not be important. Secondly, variations in G automatically affect V since one of the elements of the latter is GEi. This will generate a positive correlation between G and V when the sign of (gi GEj) is negative (and a negative correlation when the sign is positive). Take the limiting case,

T HIS is an empirical study of what determines the flotation of Canadian municipal and provincial bonds denominated in States dollars. The determinants of foreignpay flotations are important for two reasons: (1) States purchases of these flotations result in a significant inflow of capital to Canada from the States; and (2) a large part of States portfolio investment abroad is States purchases of new Canadian securities denominated in States dollars. This paper presents an analysis of individual issue data in order to establish the determinants. Many empirical studies of international portfolio investment have been conducted. Some of them are based largely on the Canadian-United States flows while others concentrate on the aggregate flows in and out of the States.' They are founded completely on aggregate economic data and are devoted to the analysis of time series. This paper is the first study to the author's knowledge that uses micro-economic data and cross-section analysis to investigate portfolio capital flows. If Canadian bond issuers behave rationally they will float their securities to enable their costs for any given issue to be minimized. These costs include both underwriting fees and interest payments. If the security is floated in the States and is denominated in States dollars, a subjective adjustment factor is included in the cost calculations to incorporate exchange rate risks. When Canadian issuers do make use of the States capital market to raise capital, they are expressing their preference for this market over the domestic market for these issues.2 During any given period does the States capital market appeal to a particular group of Canadian issuers or is the economic incentive to raise funds abroad spread evenly across Canadian issuers? If the incentive to raise funds abroad is equally great for each Canadian issuer, then foreign-pay issues will be selected from domestically floated issues by a random process; they will have no characteristics which distinguish them from domestic flotations. Alternatively, foreign flotations may appeal to a distinguishable group of issuers. If so, then what are the characteristics differentiating these issuers from domestic issuers? In part II of this paper foreign bond flotations are found to be statistically distinguishable from domestic bond flotations, and their differentiating characteristics are discussed. What factors give rise to the groupings observed in part II? The Canadian capital market may subject issues with certain characteristics to cost premiums so that the States market is especially attractive to these issues. Alternatively, the States market may offer these issues particular cost advantages. Thus, the grouping arises as a result of market characteristic configurations in Canada and in the States. * This article is based on the author's doctoral dissertation, United States Investment in Canadian Securities, 1958-1965, Harvard University, 1969 (unpublished). The research for this dissertation was financed by the Ford Foundation and by the National Science Foundation. The author accepts complete responsibility for the views expressed in the paper. 'For example see Robert Baguley, International Capital Flows and Canadian Monetary and Fiscal Policies, 1951-1962, unpublished Ph.D. dissertation, Harvard University, 1969; Gerald K. Helliner, Connections Between the States' and Canadian Capital Markets, 19521960, Yale Economic Essays, II (No. 2, 1962), pp. 351400; William Branson, Financial Capital Flows in the U.S. Balance of Payments (Amsterdam: North-Holland Press, 1968). 2 The distinction between the States capital market and the Canadian capital market is one between two regional markets. Each market is part of the world capital market but has characteristics which differentiate it from other components of the world market. This paper discusses the movement of capital from one regionally defined market to another.

Our analysis has shown that the allocative branch and the income distribution branch, to use Musgrave's terminology, in conjunction determine a Pareto optimum. It was shown that an insistence on conform solutions with tax prices equal to marginal rates of substitution, will guide us to the proper initial income distribution. The optimum can be found directly. However, in a setting in which all preferences are known and allocations are made according to the market principle, not much is gained by introducing the concept of income before-tax and tax prices. No new insights for the conduct of fiscal policy can be derived from this. We obtain an elegant general solution. In this case the distinction between an Allocation Branch and an Income Distribution Branch becomes blurred, because both branches simultaneously affect allocation and distribution. Another and more realistic possibility is to think of the economy as a computer which finds an optimum in a number of steps. We start out with a given income distribution and some system of tax prices. For the pricing rule to be chosen three criteria should be used, (1) it should induce preference revelation for public goods, (2) it should be effective with respect to adjustments in distribution and (3) it should be possible to approximate it through the political process. The income should be adjusted in line with such a pricing rule. In this process a case can be made for conceptually different branches. To have or not to have a division between the allocation branch and the income distribution branch thus depends on how one believes an economy grinds out an optimal solution. If we assume that all adjustments are simultaneous, smooth and in the right directions, we get a direct solution in an elegant grand manner. In it there is little room for distinct branches. Yet, it is more realistic perhaps to think of the way towards an optimum as a series of consecutive adjustments in distinct allocation and distribution branches. Many of the adjustments are cumbersome, involving trial and error as well as feedback and learning and, to this extent, reflecting the true nature of fiscal decisions.

The purpose of this paper is to explore within the context of several simple macroeconomic models the magnitude and significance of the structural changes that have taken place since the 1930's. The method that is used to examine the structural-change hypothesis is first to estimate separately for 1921-41 and 1946-66 the parameters of a macroeconomic model of income determination. The parameter estimates are then compared to see if there are any significant differences between the two periods. Finally, the dynamic properties of the systems for each of the subperiods are derived and compared. The presumption is that the parameter estimates and the implied system behavior will reflect the structural changes that have been effected since the great depression. (Author)

Joseph L. Balintfy, John Neter, William Wasserman, Binary and Chain Comparisons with an Experimental Linear Programming Food Price Index, The Review of Economics and Statistics, Vol. 52, No. 3 (Aug., 1970), pp. 324-330

ANY attempts have been made to assess the relevant forces affecting the variation of the relative factor share since the monumental work of Hicks, The Theory of Wages. Some of the outstanding research on this subject has been conducted by Murray Brown and his associates [1, 2, 3]. Their analyses have been based on the Schumpeterian idea of discrete technological changes and on Hicksian propositions contained in [6]. Although the assumption of discrete technological changes facilitates the assessment of the impact of nonneutral technological changes as well as other forces, the reality of the assumption is questionable, particularly at the aggregate level of economy. In the present study, technological changes are regarded as continuous instead of discrete. Furthermore, technological changes are classified as factor augmenting and nonfactor augmenting, the rates of which follow exponential time paths. The former arise from the increases in education and training, improved health, and research and development, whereas the latter arise from managerial and organizational improvements. The production function system which includes a CES production function and the marginal productivity relations are used as the bases on which the subsequent model is derived. The model is applied to the selected manufacturing industries in the United States for the period 1947-1963.

T has long been recognized that the provision of nonpecuniary rewards to a of production creates a corresponding reduction in the observed market price of the factor. But the effect of the provision of nonpecuniary rewards on marginal products and thus on the relationship between marginal products and observed prices, has long remained an open, albeit unpressing, question in economic theory. This neglected question has recently grown in importance as several influential papers concerned with the estimation of production functions (e.g., Solow [ 7 ] and ACMS [2]) have been crucially based on the identification of marginal products with observed prices. Section I of this paper contains a generalization of the usual theory of the firm which allows for (1) joint production in a general form and (2) the existence of outputs which are not separately marketed. Differences between private marginal products and competitive prices, hereafter called discrepancies, are seen to be possible when and only when some of the firm's outputs are sold or evaluated in markets as nonpecuniary rewards. A factor's observed price is seen to equal its marginal product, its marginal product plus the reduction in payments to other factors made possible by a unit addition of the factor. Since the latter part of the net marginal product is not a derivative of an observed production function, the following empirical proposition becomes obvious: A factor's marginal product cannot be identified with its observed competitive price; nor can the magnitude or direction of the actual discrepancy be casually specified. This proposition immediately implies the existence of a fallacy, probably a crippling fallacy, in the modern approach to the estimation of production functions. Section II, which builds on the analysis of discrepancies in section I, contains the key result that any discrepancy can be considered a disaggregation biasthat when all firms are combined to form a competitively determined industry production function and all inputs are suitably grouped to form a single input index, the marginal product of the input index is equal to its average cost! To establish this, it is shown that for given relative output prices and given conventions on the indirect marketing of outputs, an ordinary industry production function generally exists in neoclassical, competitive equilibrium, that this aggregate production function is linearly homogeneous, and that observed payments exhaust the product; yet there are, in general, no equalities between prices and marginal products. This surprising result is used to show that the identification of the aggregate marginal product of a with its observed cost can be justified on neoclassical grounds only when the factor is a single index of all of the various factors of production. Thus, while the modern techniques of studying technology based upon identifying marginal products of individual factors with observed prices are theoretically groundless in the presence of nonpecuniary rewards, the techniques of testing for scale economies and measuring technical change introduced by CobbDouglas and by Abramovitz [ 1 ] and Kendrick [5] are valid applications of neoclassical theory under suitable treatments of the relevant input indices. Also rationalized is a technique devised by the present author [8] of estimating both the degree of aggregate returns to scale and the annual rate of technical change with a single index of all inputs.1 * This work was supported by the Institute of Government and Public Affairs at the University of California at Los Angeles and by the National Science Foundation under Grant G-16239. The author benefited substantially from a discussion with Karl Brunner and from the comments by a Referee on an earlier draft. 1 The empirical results of [8] strongly confirm a hypothesis suggested by the present paper; viz., that there is a great deal of inequality between the marginal products and prices of separate inputs but there is an equality between