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 ECONOMETRIQUE ETC. 255 but some weight is explicitly given to population size, it will always increase utility to delay still further the time at which the fruit of the initial sacrifice is reaped. In the proofs of Propositions (A) - (K), given in the Ap- pendix, one common characteristic of the problems considered is repeatedly used without explicit mention. At any time in an optimal path (%,, £,), the capital stock #, is the only link between the past and the future. This is due, on the one hand, to the utility function being an integral over time of instan- taneous utilities (discounted or not). On the other hand, it arises from the fact that the feasibility constraint (10 a) restricts z, but not %,. Hence the function x, is in principle free to vary discontinuously (even though it is found optimal for it not to do so). However, Z, is bounded by (10 a, b), hence z, can only vary continuously. The resulting property can be expressed. formally as follows: If (£,, #,) is an optimal path for given then, for any T, the path (-"* ” defined +- is optimal for <- 7. ADIUSTING PREFERENCES TO OPPORTUNITIES What have we learned from our « logical experiments »? We have confronted a simple model of production with a utility function representing a sum of future per-capita utilities, dis- counted by a positive, zero, or negative instantaneous rate of discount p. We have found that g=o0 is the smallest rate for which an optimal path exists 41 Koopmans - pag. 29

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