Study week on the econometric approach to development planning

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Monograph

Identifikator:: 1824422792

URN:: urn:nbn:de:zbw-retromon-217476

Document type:: Monograph

Title:: Study week on the econometric approach to development planning

Place of publication:: Amsterdam [u.a.]

Publisher:: North-Holland Publ. Co. [u.a.]

Year of publication:: 1965

Scope:: XLVII, 1259 S.; graph. Darst.

Digitisation:: 2022

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: On the concept of optimal economic growth / Tjalling C. Koopmans, Cowles Foundation for research in Econimics at Yale University New Haven, Conn. - U.S.A.

Collection:: Economics Books

SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE LETC. 237 It 2 represents the rate of growth of the labor force, Z repre- sents a capital stock per worker so large that the investment required to keep it at the same level absorbs all output, leaving nothing for consumption. If z,>2z, it will therefore be neces- sary to allow gz, to decrease at least to some level below Z. To avoid the uninteresting complication arising if z,>Z we shall from here on simply define « feasibility » so as to imply O< 2,52. Although we have not vet defined a maximand, it may be observed that the attainable set is now defined in a space where the « point » is a pair of positive functions x,, z, of time, defined for o=¢<oco. This is an infinite-dimensional space for the double reason that we use a continuous time concept and an infinite horizon. It remains infinite-dimensional if we limit ourselves (!) to twice differentiable functions z, and once dif- ferentiable functions x. 5. THE PATH OF THE GOLDEN RULE OF ACCUMULATION To answer an important preliminary question, we first con- sider a KANTOROVICH type restriction of the problem to a one- dimensional one. The latter problem has been formulated and solved in the last few years, independently and in one form or another, by (*) ArLaIs [1962], DESROUSSEAUX [1961], PHELPS [1961], JoAN ROBINSON [1062], SwAN [1060], VON WEIZSACKER [1962]. Remove from the definition of the attainable set the restric. (") Due to twice differentiability of the data functions f(z) above and u(x) below we will not be excluding any optimal paths by that requirement. However, a slightly weaker requirement will be found useful in the Appendix. (°) Dates are bibliographical only and refer to the list of references below. Some of these authors used somewhat more general models involving ar exponential technological improvement factor in the production funcHon ; € : Koopmans - pag. 13

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