A NOTE ON THE MATHEMATICAL DERIVATION OF TOTAL FACTOR PRODUCTIVITY (TFP) AND ITS DECOMPOSITIONS

Abstract

This article is written with a two-fold objective: to prove the equivalence between Total Factor Productivity (TFP) and technological change when the production function exhibits constant returns to scale, and to decompose the TFP into several components. Toward this end, we established a linkage between the theory of production (specifically the cost of production), and TFP. Prior to that, however, we showed how the TFP is computed using the Divisia indexes or the Tornqvist index. Finally, we showed that if the production is subject to constant returns to scale, the TFP growth rate is identical to the rate of technological change. Otherwise, with the existence of scale effects, the TFP may be decomposed into technological change and scale effects, the two major sources of TFP.

JEL classification: C23, D24, O39

Key words: Total Factor Productivity, Technical change effects, Scale effects