THE ROBUSTNESS OF EQUILIBRIUM ANALYSIS IN THE DUAL ECONOMY

Abstract

DIXIT (1971) has recently criticized earlier models of the dual economy for failing to specify fully the relationship between the two sectors. He argues that a general equilibrium approach is required if the interdependence between the supply price of labour and the intersectoral terms of trade is to be handled adequately, and more importantly, that this will make a significant difference to estimates of the shadow price of labour. The implication of his very elegant general equilibrium model is that the main determinants of the shadow price of labour are the degree of suboptimality of savings (the shadow price of savings in terms of consumption) and the price and income elasticities of demand for food, with the marginal product of labour in the traditional sector of minor importance. The strength of general equilibrium analysis is unfortunately often its weakness. If the interactions are to be handled simultaneously it becomes difficult to see how the results depend on the assumptions, and whether the tail is wagging the dog. The aim of this note is anatomical to dissect Dixit's model and examine its members, to test its robustness and to see to what extent the implications depend on the different features of dualism. The shadow wage will differ from the marginal product of labour in the traditional sector only if there is a savings constraint (Dixit, equations ( 11), (15)), in which case investment is more valuable than consumption. For simplicity consider the extreme case in which the immediate objective of the government is to maximize the rate of investment, so that the shadow price of consumption in terms of investment (1/q in Dixit's notation) is zero. The simpler of the two cases discussed by Dixit assumes that all goods produced in the economy are fully tradable abroad at prices which are independent of the quantity of trade and this forms the logical startingpoint. Take manufactured goods produced in the modern sector as numeraire,2 whilst 'food', the product of the traditional or agricultural sector, has a world price of po and an internal price of p. Dixit's notation