A Multi-Sector Model of Balanced Growth

Abstract

HIS paper presents a model of T which is an extension to n sectors of the original one-sector equilibrium paths developed by R. F. Harrod and E. D. Domar.1 Following Harrod, we employ discrete periods of time and hence a (first-order) difference equation technique. However, in order to give the model a prescriptive rather than a predictive overtone, the first differences refer to the immediate future instead of the immediate past. In addition, an allowance for depreciation is included in the model. By balanced growth we simply mean the existence of equilibrium (the equality of supply and demand) in every market in every time period. Equiproportionate of each market is a special case of as used in this paper. Prices do not explicitly enter the model. Supply in each market is an increasing linear function of the existing capital stock in that sector or industry, and hence the model refers to a one-factor economy. However, capital is not transferable from one sector to another. The single factor of production (capital) is produced by a single industry, the investment-goods industry, the input into which is also capital. Demand for the output of each industry, with the exception of the investment-goods sector, is an increasing linear function of net real income. By definition, these industries are producers of consumption goods, all of which are non-inferior from the point of view of the income-demand relation. The demand for investment goods is a mixed accelerator-multiplier relation. The solution of the system expresses net aggregate output as a function of integral values of time. The output of each sector at any time can then be determined from the structural equations of the model.