A capacity growth input-output model with forward recursive solution

Abstract

In a previous paper an n- sector input-output model of sector output capacity growth was presented, having a solution through backward recursion from known capacities of a terminal year. Numerical illustration was provided by twelve-sector data including an energy sector, and by two-sector data. The present paper offers a forward recursive uniform growth version of the same open model, with solution by a set of n simultaneous linear equations. It uses any chosen value of k, the uniform one-year capacity growth rate of all sectors. Also examined is the special closed model, implying all capacity being used up by capacity expansion; solutions are found by eigen analysis, giving unique k- values and sector capacity proportions. Numerical illustration is again given for the open and closed versions, using the same twelve-sector data including one sector for energy, and with a simple two-sector illustration. A comparison of uniform growth solutions by forward and backward recursion shows that backward recursion offers a choice of two growth structures, distinct from the growth structure solution of formal forward recursion. The essential component of energy capacity growth is noted for all solutions.