# On some methods and problems in the study of metropolitan economies

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- 1.I would guess that the present
*marginal*contribution to the GNP generated by metropolitan areas is at least*80 percent*of the total; this indicates the height of the “ceiling” to which the present average of 70 percent is geared. A metropolitan area in the U. S. is defined as a “county or group of contiguous counties which contain at least one city of 50,000 inhabitants or more in 1950 or subsequently”.Google Scholar - 2.For an interesting set of recent data, see Kingsley Davis,
*The World's Metropolitan Areas*, University of California Press, Berkeley, 1959.Google Scholar - 3.
*Guiding Metropolitan Growth*(A Statement on National Policy by the Research and Policy Committee of the CED; August, 1960) p. 31.Google Scholar - 4.For clarity of exposition, numerical quantities (scalars) will be denoted by Greek letters, vector quantities will be denoted by Roman letters, and matrices will be denoted by capital letters A, B, C,....Google Scholar
- 5.Compare Raymond Vernon,
*Metropolis 1985*, Harvard University Press, Cambridge, Mass., 1960, pp. 2, 222, and 239.Google Scholar - 6.Compare, however, the actual model used in the New York Study, where a more comprehensive input-output model than the one so far discussed was applied. For further comments, see the following pages.Google Scholar
- 7.Barbara R. Berman, Benjamin Chinitz, and Edgar M. Hoover
*Projection of a Metropolis*, Harvard University Press, Cambridge, Mass., 1961.Google Scholar - 8.For a description of the characteristics of such models, and for a penetrating analysis of their strength and limitations, see Walter Isard,
*Methods of Regional Analysis*, John Wiley and Sons, 1960, pp. 345–49 and pp. 647–51.Google Scholar - 9.Actually, household expenditure was determined as a linear and homogeneous function of two variables, namely population and personal disposable income. But each of these two variables was considered a homogeneous function of total employment.Google Scholar
- 10.K. Miyazawa, “Foreign Trade Multiplier, Input-Output Analysis and the Consumption Function,”
*Quarterly Journal of Economics*, vol. 74, 1960, pp. 53–64.Google Scholar - 11.This statement is seemingly contradicted in a recent article by a long-time proponent of the theory of the economic base. The article deals with procedures for estimating the value of imports into an urban area (as such, very interesting and helpful procedures). But surprisingly enough these estimates are not used to analyze the characteristics of importation into an urban area. They merely serve the purpose of indicating the value of exports from the urban area, on the assumption that imports should equal exports in total value! (Besides, and needless to say, such an assumption could be far off the mark for such a short period as a year.) See H. Hoyt, “A Method for Estimating the Value of Imports into an Urban Community,”
*Land Economics*, vol. 37, 1961, pp. 150–61.Google Scholar - 12.For the pioneering model of international trade along this line, see R. Frisch, “Circulation Planning: Proposal for a National Organization of a Commodity and Service Exchange,”
*Econometrica*, vol. 2, 1934, pp. 259–336; and R. Frisch, “Circulation Planning: Mathematical Appendix,”*Econometrica*, vol. 2, 1934, pp. 422–35.Google Scholar - 13.David Gale,
*The Theory of Linear Economic Models*, McGraw-Hill, New York, 1960, pp. 263–80.Google Scholar - 14.Richard Meier,
*The Theory of Urban Growth in a Communications Perspective*(forthcoming).Google Scholar - 15.L. Moses, “An Input-Output, Linear Programming Approach to Interregional Analysis,” Harvard Economic Research Project Report 1956-57; and L. Moses, “A General Equilibrium Model of Production, Interregional Trade, and Location of Industry,”
*Review of Economics and Statistics*, vol. 42, 1960, pp. 373–97.Google Scholar - 16.B. Stevens, “An Interregional Linear Programming Model,”
*Journal of Regional Science*, vol. 1, 1958, pp. 60–98.Google Scholar - 17.Isard,
*op. cit. Methods of Regional Analysis*, John Wiley and Sons, 1960 in particular, pp. 444–91, 638–41, and 720–30.Google Scholar - 18.With reference to this problem of the choice of criteria or objectives, see also the interesting discussion in W. Hirsch, “A General Structure for Regional Economic Analysis” in Werner Hochwald (ed.),
*The Design and Use of Regional Accounts*, Johns Hopkins Press, Baltimore, 1961.Google Scholar - 19.Needless to say, the very same problems exist in applications of say, the export base model, but there these problems are hidden in the multiplier.Google Scholar
- 20.Of course, there is nothing intrinsically open about the metropolitan phenomena; the openness depends on the conceptual framework in terms of which we try to comprehend the phenomena concerned.Google Scholar
- 21.For some interesting attacks on this problem, I would again like to refer the reader to Hirsch,
*op. cit.*“.Google Scholar - 22.Meier,
*op. cit. The Theory of Urban Growth in a Communications Perspective*(forth-coming). “The Measurement of Social Change,” in the*1959 Proceedings of the Western Joint Computer Center*. See also Melvin Webber,*Spatial Patterns of Human Interaction*(unpublished manuscript), 1959.Google Scholar - 23.The reader should see this last sentence as an apology for my failure to formulate this communications model in a mathematical form which could be manipulated.Google Scholar

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© The Regional Science Association 1962