THE GOLDEN RULE OF ACCUMULATION UNDER ALTERNATIVE SAVINGS ASSUMPTIONS 1

Abstract

IN the early 1960s several economists enunciated a result called 'the neoneo-classical theorem' or 'the golden rule of accumulation' (GR).2 This is the proposition that consumption per head is maximized on a steady state path along which the rate of profit is equal to the rate of growth. In the context of the neoclassical one-commodity model it was left to Koopmans3 and Phelps4 to elicit the rather limited optimality implications of the GR. They established that paths along which the capital to labour ratio remains permanently bounded above the GR value are inefficient in the sense that there always exists another path which, starting from the same initial capital stock, provides more consumption at some time and never less consumption. In other words they showed that it was possible to 'over-save' and therefore to have too much capital. The present note inquires into the existence and significance of GR paths in a two-commodity long run equilibrium model. More specifically the well-known Hicksian model5 together with alternative savings assumptions is examined.6 The main result is that in the multi-technique case profitmaximizing capitalists may be unable to choose a path along which the rate of profit equals the rate of growth.