Complementarity and Long-Range Projections - Verdoorn, P. J. (Econometrica, 1956)
This article studies the implications of complementarity on the problem of the long-term forecast. The conditions for maintaining long-run equilibrium between factor demand and factor supply are derived and illustrated with the help of a three-factor model, so as to bring out the particular problem of foreign trade. Equilibrium for all of the three factors appears possible only if the parameters of the system satisfy a set of specific relations or certain policy variables are introduced. Finally the complete system as used by the Central Planning Bureau is presented, together with the numerical values chosen for the parameters. 1. SOME IMPLICATIONS OF COMPLEMENTARITY 1.1. FOR THE PURPOSE of long-range projections a choice must be made as to the nature of the production function. Two extreme assumptions are possible, viz., perfect substitutability and strict complementarity. Most long-range projections published hitherto are based explicitly or implicitly upon the hypothesis of complementarity. Some of the implications of this hypothesis will be discussed in the first and second sections of this paper. In the third a model based on complementarity as has been used by the Central Planning Bureau for projections covering the period 1950-1970 will be presented. 1.2. The type of model to be considered will cover a period of only one to three decades. It is, moreover, not concerned with the cyclical variations of the variables nor with problems of a really secular character such as those studied by Haavelmo.' Furthermore, the implications of disequilibria due to a disproportionate development as between sectors of the economy will be ignored.2 The main problem to be dealt with is therefore the question of equilibrium for the macro variables in the medium-long run. As compared with economic statics the equilibrium concept should obviously be widened so as to allow for the dynamics of long-run development. In the following equilibrium will be defined as a development that is compatible with the equality of demand and supply for each of the factors of production. Neither stable values of the endogenous variables nor constancy of the policy parameters is required. Defined in this way, long-term equilibrium does not necessarily imply optimal development. Unless only one development-equilibrium is possible, restrictions other than that