 Since the path of the capital-labor ratio determines the path of the interest and wage rate, which determine both the annual supply of and demand for the two factors of production, the problem boils down to finding the precise path of the capital-labor ratio that will draw forth from extant households each year aggregate supplies of capital and labor that exactly match each year's respective aggregate demands for capital and labor by firms.There are no mathematical techniques for calculating the exact solution of high order non-linear difference equations.