Proof for a Case where Discounting Advances the Doomsday Get access Tjalling C. Koopmans Tjalling C. Koopmans International Institute for Applied Systems Analysis Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 41, Issue 5, December 1974, Pages 117–120, https://doi.org/10.2307/2296375 Published: 01 December 1974

I. Introduction, 355. — II. A model with two commodities, 359. — III. Growth paths and proportional growth paths, 361. — IV. Geometrical representation of the technology, 362. — V. Representation of proportional growth, 366. — VI. Determination of a maximal proportional growth path, 367. — VII. A price system sustaining a given von Neumann path, 370. — VIII. Is any proportional growth path sustained by a price system maximal? 374. — IX. A numerical example, 375. — X. The turnpike conjecture, 377. — XI. Access to or from the von Neumann path, 378. — XII. Rates of growth in von Neumann value, 379.— XIII. “Profit” effects of an interest rate reduction, 382. — XIV. A variant of Radner's turnpike theorem, 383. — XV. A catenary property of maximal growth paths, 385. — XVI. The turnpike conjecture in other cases, 387. — XVII. Concluding remarks, 391.

This paper surveys the results of mostly recent research on optimal aggregate economic growth models, and comments on the difficulties encountered and on desirable directions of further research.

This paper investigates Bohm-Bawerk's idea of a preference for advancing the timing of future satisfactions from a somewhat different point of view. It is shown that simple postulates about the utility function of a consumption program for an infinite future logically imply impatience at least for certain broad classes of programs. The postulates assert continuity, sensitivity, stationarity of the utility function, the absence of intertemporal complementarity, and the existence of a best and a worst program. The more technical parts of the proof are set off in starred sections.

A study of the efficient allocation problem in production by the evaluation of the merits of private or corporate enterprise versus a centrally directed economy. Presented before a joint meeting of the American Statistical Association, the American Economic Association, and the Econometric Society in New York City, December 29, 1949.