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SUPERIORITY OF ROUNDABOUT PROCESSES AND POSITIVE RATE OF INTEREST. A SIMPLE MODEL OF CAPITAL AND GROWTH *
Author(s) -
Bernholz Peter
Publication year - 1971
Publication title -
kyklos
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.766
H-Index - 58
eISSN - 1467-6435
pISSN - 0023-5962
DOI - 10.1111/j.1467-6435.1971.tb00628.x
Subject(s) - economics , production (economics) , capital (architecture) , depreciation (economics) , productivity , roundabout , production function , time preference , microeconomics , macroeconomics , capital formation , financial capital , engineering , profit (economics) , archaeology , transport engineering , history
SUMMARY The article explores in the framework of a two‐period model if and under what conditions B öhm ‐B awerk's pretention is correct, that the superiority of roundabout production processes leads to a positive interest rate. It is assumed that a central planning agency maximizes a social welfare function which has the available amounts of the single consumer good in both periods as its arguments. Production technique is given by three linear‐limitational production processes. In the first production process the consumer good is produced by labor only, in the second by labor and a capital good, in the third the capital good is produced by labor and the capital good. The produced capital good has an infinite life span (no depreciation) and can be used for production not earlier than in the following period. With the production technique described the meaning of greater productivity of roundabout production processes is exactly definable without the use of an average production period. Starting from this model the optimality conditions for optimal quantities and optimal shadow prices are derivcd, using the theorems of K uhn and T ucker . After defining the rate of interest it is shown that with greater productivity of roundabout production processes there is always a positive interest rate if not the highest possible capital good production takes place and if there is no capital good saturation. In these cases, too, a positive interest rate is possible, but this depends on other conditions than the superiority of roundabout production processes, e.g. a positive time preference. A stationary state without capital saturation can only come into being with a positive time preference and implies always a positive interest rate. Finally, some growth aspects of the model are considered. It is shown that population growth favours the existence of a positive interest rate because it tends to impede or remove capital saturation.