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Literatur
E. Mishan, “The Postwar Literature on Externalities: An Interpretative Essay,”The Journal of Economic Literature, IX (1971), p. 18.
For an interesting discussion of the formal interrelation of problems of congestion and pollution, see J. Rothenberg, “The Economics of Congestion and Pollution: An Integrated View,”American Economic Review, LX (1970), pp. 114–121.
A. R. Dobell and E. Burmeister,Mathematical Theories of Economic Growth (New York: Macmillan Company, 1970) F. H. Hahn and R. C. O. Matthews, “The Theory of Economic Growth: A Survey,”Economic Journal, LXXIV (1964), pp. 825–832; Koichi Mera, “A Multi-Regional Multi-Sector Model of Equilibrium Growth,” inPapers of the Regional Science Association, XXI (1968); H. Ryder, Jr., “Optimal Accumulation and Trade in an Open Economy of Moderate Size,” in Karl Shell, ed.,Essays on the Theory of Optimal Economic Growth (Cambridge, Mass.: The M.I.T. Press, 1967).
The optimal control of industrial pollution in the context of a closed growth model is studied by R. Zeckhauser, M. Spence, and E. Keeler, “The Optimal Control of Pollution,” Discussion Paper No. 1, Public Policy Program, Kennedy School of Government, Harvard University, June, 1970. Their interest, however, is with the more technical aspects of the control problem.
WhenR=0,R=1/η (VL+G).
Ovadia Salama, “Stochastic Control and Multilevel coordination Models for Air Quality Management within a Region,” Regional Science Group, Graduate School of Design, Harvard University, April, 1971.
L. H. S.—left-hand side. R.H.S.—right-hand side.
F. Ramsey, “A Mathematical Theory of Savings,”Economic Journal, XXXVIII (1928), pp. 543–559.
M. Inagaki,Optimal Economic Growth (Amsterdam: North Holland Publishing Co., 1970).
In short, “social energy.” See W. Isard, ‘Social Energy: A Relevant New Concept for Regional Science?”, paper presented to the British section of the Regional Science Association, London, 1971.
When attached to a function, subscripts denote partial differentiation with respect to the variable indicated. When attached to a parameter, as inP x , or to a multiplier (P R ), they simply provide economy of notation.
Primes are attached to the shadow price of capital here in order to emphasize that these shadow prices may vary from theP K 's of, for example, setA throughD because the influence of pollution may lead to a different evaluation of capital in equilibrium. This problem does not arise with the other prices (P x ,y, a, Z, I) inasmuch as they are dictated by interregional trade.
R. McKean, “The Use of Shadow Prices,” inProblems in Public Expenditure Analysis, ed. Samuel Chase (Washington, D.C.: Brookings Institution, 1968).
R. Coase, “The Problem of Social Cost,”Journal of Law and Economics, III (1960), pp. 1–44.
K.J. Arrow, “The Organization of Economic Activity: Issues Pertinent to the Choice of Market Versus Nonmarket Allocation,” inThe Analysis and Evaluation of Public Expenditure: The PPB System, Vol. I. Joint Economic Committee, 91st Cong., 1st Sess. (Washington, D.C., 1969), pp. 47–66.
D. Starrett and R. Zeckhauser, “Treating External Diseconomies—Markets or Taxes?”, Discussion Paper No. 3, Public Policy Program, Kennedy School of Government, Harvard University, June, 1970.
W. D. Montgomery, “Market Systems for the Control of Air Pollution,” unpublished doctoral dissertation (Harvard University, 1971).
For the significance ofP ′ K , see n. 12.
This definition follows that used by D. Jorgenson, “The Demand for Capital Services,” in K. A. Fox, J. K. Sengupta, and G. V. L. Narasimham,Economic Models, Estimation, and Risk Programming: Essays in Honor of Gerhard Tintner (Berlin, New York: Springer-Verlag, 1969), pp. 35–57.
Council on Environmental Quality,Environmental Quality, First Annual Report, Office of the President (Washington, D.C., 1970), pp. 76–77.
“House Approves Clean Air Bill,”New York Times, Friday, November 3, 1967.
If locations are fixed and there are no economies of scale over the significant range of goods movement, transportation charges will be a constant per unit addition to the price.
I. M. Gelfand and S. V. Fomin,Calculus of Variations (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963).
K. J. Kurz and M. Kurz,Public Investment, The Rate of Return, and Optimal Fiscal Policy (Baltimore: The Johns Hopkins Press, 1970).
When attached to a function, subscripts denote partial differentiation with respect to the variable indicated. When attached to a parameter, as inP x , or to a multiplier (λ, ρ), they simply provide economy of notation.
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This paper was supported by Environmental Protection Agency Grant No. A. P. 00842-02 to the Regional Science Group, Graduate School of Design, Harvard University, and was undertaken while the author was postdoctoral fellow in Regional Science, Harvard University. The author is indebted to Walter Isard for stimulating his interest in the subject and for introducing him to the tools of dynamic analysis herein employed. The author has benefited greatly from the constructive criticism of the Regional Science Seminar and particularly from the insights of V. K. Mathur and H. Yamada, who were simultaneously concerned with a similar problem of environmental control.
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Walter, G.R. Intertemporally optimal urban pollution. Papers of the Regional Science Association 28, 237–254 (1972). https://doi.org/10.1007/BF01961464
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DOI: https://doi.org/10.1007/BF01961464