Maximal Paths in the von Neumann Model

Lionel McKenzie

Chapter Chapter 2 in Activity Analysis in the Theory of Growth and Planning, 1967, pp 43-63 from Palgrave Macmillan

Abstract: Abstract I shall concern myself with the problem of optimal accumulation in the von Neumann model as it was initially posed by Dorfman, Samuelson, and Solow (1958) (DOSSO).2 In this problem the objective is to reach a point on a prescribed ray through the origin which is as far out as possible in a given number of periods. Let the prescribed ray be ( y ¯ ) $$ \left( {\bar y} \right) $$ . Then, if there is free disposal, and accumulation occurs over N periods from y 0 as a starting-point, it is equivalent to maximize the minimum of y i T y ¯ i $$ \frac{{y_i^T}}{{{{\bar y}_i}}} $$ over i such that y ¯ i > 0 $$ {\bar y_i} > 0 $$ . We may define ρ ( y ) = min y i y ¯ i f o r y ¯ i > 0 $$ \rho (y) = \min \frac{{{y_i}}}{{{{\bar y}_i}}}\,for\,{\bar y_i} > 0 $$ . Then ρ (y)is a utility function which is maximized.

Keywords: Utility Function; Growth Theory; Angular Distance; Production Cone; Price Vector (search for similar items in EconPapers)
Date: 1967
References: Add references at CitEc
Citations: View citations in EconPapers (3)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pal:intecp:978-1-349-08461-6_2

Ordering information: This item can be ordered from
http://www.palgrave.com/9781349084616

DOI: 10.1007/978-1-349-08461-6_2

Access Statistics for this chapter

More chapters in International Economic Association Series from Palgrave Macmillan
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().