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An Input-Output System Involving Nontransferable Goods

Michio Morishima
Yasuo Murata

Abstract

This paper presents a dynamic input-output model explicitly allowing for the durability and nontransferability of capital goods. The fact that capital goods are durable and hardly transferable once they have been installed in some factories requires that different vintages of capital goods should be distinguished. The traditional nonvintage input-output systems by Leontief and others are compared with our vintage model; it is seen that they are identical only when capital goods are "perfectly malleable" in the sense defined in the text. This is, of course, a very stringent and unrealistic condition. When it does not hold, the replacement coefficients cannot be constant and deviate from Leontief's (constant) flow coefficients. The capital coefficients obey the Sectoral Flexible Acceleration Principle instead of the simple one; it is seen that that level of activity of an industry i at which the acceleration principle ceases to work for a capital good j (because of loss of acceleration) depends on the age composition, as well as the total amount of the stocks of capital good j installed in industry i. It is seen, however, that the equilibrium rate of growth calculated from the traditional model would not be very far from the one calculated from our more general and realistic model; so that from the long run point of view, there is little difference between the two. This means that the vintage and nontransferabilit of capital goods would not be so far reaching in the long run growth analysis as they are in the discussion of cyclical movements.