*Michio Morishima*

- Published in print:
- 1969
- Published Online:
- November 2003
- ISBN:
- 9780198281641
- eISBN:
- 9780191596667
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198281641.003.0013
- Subject:
- Economics and Finance, Development, Growth, and Environmental

Chapter 10 was concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to ...
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Chapter 10 was concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to maximize the stocks of goods that they can bestow, at the horizon, upon the future citizens; this chapter looks at a Second Turnpike Theorem. The partial optimization for the sake of the future should more properly be superseded by a general mutual optimization, so that the benefits from the properties initially available are shared between the people living in the planning period and those after that; this would inevitably cause confrontation with one of the hardest problems of economics—the interpersonal and intertemporal comparisons of utilities. In this chapter, attempts to solve the crux of the problem are abandoned and the other extreme is addressed: the conditions are derived for Ramsey optimality as distinct from DOSSO efficiency, i.e. optimization is in favour of the people in the planning period, and the satisfaction of the future residents is pegged at a certain level, of which the present residents approve. Among all feasible programmes that leave, at the end of the planning period, necessary amounts of goods for the future residents, the question is whether the people living choose a single one that is most preferable from their own point of view, i.e. there is a switch over of ideology from abstinence for the future to satisfaction in the transient life. The different sections of the chapter include discussion of: two norms of optimum growth—the Golden Balanced Growth path and the Consumption Turnpike; the existence of the Consumption Turnpike; the Silvery Rule of Accumulation’ the singular case where there is no discrimination between the living and the coming people; the Consumption Turnpike Theorem—the cases of the subjective time‐preference factor not being greater than the growth factor of the population, and of the former being greater than the latter; and an example of a cyclic Ramsey‐optimum growth.Less

Chapter 10 was concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to maximize the stocks of goods that they can bestow, at the horizon, upon the future citizens; this chapter looks at a Second Turnpike Theorem. The partial optimization for the sake of the future should more properly be superseded by a general mutual optimization, so that the benefits from the properties initially available are shared between the people living in the planning period and those after that; this would inevitably cause confrontation with one of the hardest problems of economics—the interpersonal and intertemporal comparisons of utilities. In this chapter, attempts to solve the crux of the problem are abandoned and the other extreme is addressed: the conditions are derived for Ramsey optimality as distinct from DOSSO efficiency, i.e. optimization is in favour of the people in the planning period, and the satisfaction of the future residents is pegged at a certain level, of which the present residents approve. Among all feasible programmes that leave, at the end of the planning period, necessary amounts of goods for the future residents, the question is whether the people living choose a single one that is most preferable from their own point of view, i.e. there is a switch over of ideology from abstinence for the future to satisfaction in the transient life. The different sections of the chapter include discussion of: two norms of optimum growth—the Golden Balanced Growth path and the Consumption Turnpike; the existence of the Consumption Turnpike; the Silvery Rule of Accumulation’ the singular case where there is no discrimination between the living and the coming people; the Consumption Turnpike Theorem—the cases of the subjective time‐preference factor not being greater than the growth factor of the population, and of the former being greater than the latter; and an example of a cyclic Ramsey‐optimum growth.

*Michio Morishima*

- Published in print:
- 1969
- Published Online:
- November 2003
- ISBN:
- 9780198281641
- eISBN:
- 9780191596667
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198281641.003.0016
- Subject:
- Economics and Finance, Development, Growth, and Environmental

The 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 ...
More

The 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 exogenously fixed rate; different rates of population growth lead to different solutions; i.e. the path of optimum capital accumulation is relative to the population growth. In contrast, 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; it follows that the path of optimum population is relative to capital accumulation. It is evident that these two partial optimization procedures should be synthesized so as to give a genuine supreme path, which is optimum with respect to both capital and population. This final chapter generalizes the Ramsey–Meade problem in that direction and shows 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; the two long‐run tendencies that are derived may be regarded as extensions of those discussed in the chapters entitled First and Second Turnpike Theorems. The different sections of the chapter discuss: the generalized Ramsey–Meade problem; the finding that the Golden Equilibrium rate of growth is greater than the Silvery Equilibrium rate; the Average Final State Turnpike Theorem; the strong superadditivity of processes—a sufficient condition for strong convergence; the tendency towards the ‘top facet’ as the general rule; cyclic phenomena; the Average Consumption Turnpike Theorem and its proof; and aversion to fluctuation in consumption.Less

The 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 exogenously fixed rate; different rates of population growth lead to different solutions; i.e. the path of optimum capital accumulation is relative to the population growth. In contrast, 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; it follows that the path of optimum population is relative to capital accumulation. It is evident that these two partial optimization procedures should be synthesized so as to give a genuine supreme path, which is optimum with respect to both capital and population. This final chapter generalizes the Ramsey–Meade problem in that direction and shows 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; the two long‐run tendencies that are derived may be regarded as extensions of those discussed in the chapters entitled First and Second Turnpike Theorems. The different sections of the chapter discuss: the generalized Ramsey–Meade problem; the finding that the Golden Equilibrium rate of growth is greater than the Silvery Equilibrium rate; the Average Final State Turnpike Theorem; the strong superadditivity of processes—a sufficient condition for strong convergence; the tendency towards the ‘top facet’ as the general rule; cyclic phenomena; the Average Consumption Turnpike Theorem and its proof; and aversion to fluctuation in consumption.