1. How much of its income should a nation save? This problem of optimum savings has been discussed by Ramsey on the assumption of a constant population and later by a number of economists on the more general assumption that the labour force expands at a constant rate exogenously fixed. Different rates of population growth lead to different solutions; that is to say, the path of optimum capital accumulation is relative to the population growth.
On the other hand, Meade and others have been concerned with the problem of optimum population, assuming among other things that at any given time the economy is provided with a given rate of savings as well as a given stock of capital equipment to be used. 1 It follows that the path of optimum population is relative to capital accumulation. In fact a population growth that is optimal in some circumstances would be too fast in other circumstances—say, when capital is accumulated at a very low rate.
It is evident that these two partial optimizations procedures should be synthesized so as to give a genuine supreme path which is an optimum with respect to both capital and population. We devote this final chapter to a generalization of the Ramsey-Meade problem in that direction and show that two kinds of long-run paths—efficient and optimum paths—will under some conditions converge to the Golden Growth path when the time-horizon of the paths becomes infinite. Efficiency is defined in terms of the 'final' outcomes of paths, while optimality takes into account not only the final states but also intermediate states en route. Two long-run tendencies we shall derive may be regarded as extensions of those discussed in the chapters entitled First and Second Turnpike Theorems.
2. In the previous chapter, the Silvery or Golden Equilibrium has been compared, for efficiency and Pareto Optimality, with feasible paths starting from an initial position from which the economy can grow in equilibrium without discarding any labour but possibly discarding some goods. 2 It is