*Michio Morishima*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198281641.003.0010
- Subject:
- Economics and Finance, Development, Growth, and Environmental

The conditions for the Golden Equilibrium have been established earlier in the book and this chapter turns to an examination of the economy for stability; it asks whether a Hicks–Malinvaud ...
More

The conditions for the Golden Equilibrium have been established earlier in the book and this chapter turns to an examination of the economy for stability; it asks whether a Hicks–Malinvaud competitive equilibrium trajectory starting from the historically given initial point approaches nearer and nearer to the state of Golden Equilibrium when the order of the path gets larger. This problem, which amounts to asking whether an economy obeying the principle of competition can attain a Golden Age, is discussed repeatedly in this chapter and the following one. Convergence of this sort will be compared with another kind of convergence recently dealt with by many writers under the common heading of Turnpike Theorems, particular applications of which may occur in more or less planned economies but not in purely competitive economies. In this chapter, the simple case of ‘L‐shaped’ indifference curves is examined. The different sections of the chapter compare the Hicks–Malinvaud equilibrium trajectory (Hicks–Malinvaud equilibrium growth path) with the DOSSO‐efficient path, discuss the Final State Turnpike Theorem, offer a proof of the theorem by the jyoseki (a formula in the game of go), present a lemma by Gale, discuss the convergence to the Turnpike, discuss yosses (the final part of a game of go) of the proof and cyclic exceptions, and look at the tendency towards the Golden Equilibrium of a competitive economy with no planning authorities.Less

The conditions for the Golden Equilibrium have been established earlier in the book and this chapter turns to an examination of the economy for stability; it asks whether a Hicks–Malinvaud competitive equilibrium trajectory starting from the historically given initial point approaches nearer and nearer to the state of Golden Equilibrium when the order of the path gets larger. This problem, which amounts to asking whether an economy obeying the principle of competition can attain a Golden Age, is discussed repeatedly in this chapter and the following one. Convergence of this sort will be compared with another kind of convergence recently dealt with by many writers under the common heading of Turnpike Theorems, particular applications of which may occur in more or less planned economies but not in purely competitive economies. In this chapter, the simple case of ‘L‐shaped’ indifference curves is examined. The different sections of the chapter compare the Hicks–Malinvaud equilibrium trajectory (Hicks–Malinvaud equilibrium growth path) with the DOSSO‐efficient path, discuss the Final State Turnpike Theorem, offer a proof of the theorem by the *jyoseki* (a formula in the game of *go*), present a lemma by Gale, discuss the convergence to the Turnpike, discuss *yosses* (the final part of a game of *go*) of the proof and cyclic exceptions, and look at the tendency towards the Golden Equilibrium of a competitive economy with no planning authorities.

*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.

*Michio Morishima*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198281641.003.0011
- Subject:
- Economics and Finance, Development, Growth, and Environmental

Earlier chapters in the book have: introduced consumer's choice into the conventional framework of economic growth originated by J. von Neumann, and assumed that consumers are classified into two ...
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Earlier chapters in the book have: introduced consumer's choice into the conventional framework of economic growth originated by J. von Neumann, and assumed that consumers are classified into two broad groups of persons—the worker and the capitalist (Ch. 6 ); observed that a balanced growth equilibrium obtained when only the worker consumes and only the capitalist saves is distinguished as the ‘best’ one from all other possible states of balanced growth and is, therefore, referred to as the Golden Equilibrium (Ch. 10); and concentrated on a particular economy where the capitalist is thrifty enough to carry out no consumption of goods at all while the worker is well paid so that he/she can buy goods in the Golden Equilibrium amounts, thus enabling the establishment of convergence to the Turnpike (Ch. 10). The following question is then naturally asked: Is the Golden Equilibrium still stable when the assumption of rigid consumption is replaced by the more realistic one that the worker's demand for consumption goods depends on prices and the wage income? In association with the assumption of rigid consumption, Ch. 10 made another powerful assumption that there is no shortage at all in the supply of labour; an economy was considered where the labour force grows at a constant rate, which is exogenously determined, and it was found that a state of balanced growth is compatible with such a flexible demand schedule. Therefore, it is suspected that the flexible demand for consumption goods is an additional cause of the cyclic behaviour of the Hicks–Malinvaud competitive equilibrium path and the DOSSO‐efficient growth path. The different sections of this chapter look at the possibility that flexible demand for consumption goods may cause cycles, the possibility of a Hicks–Malinvaud path in this case (and a numerical example), the DOSSO efficiency in the case of flexible consumption, and a DOSSO zigzag.Less

Earlier chapters in the book have: introduced consumer's choice into the conventional framework of economic growth originated by J. von Neumann, and assumed that consumers are classified into two broad groups of persons—the worker and the capitalist (Ch. 6 ); observed that a balanced growth equilibrium obtained when only the worker consumes and only the capitalist saves is distinguished as the ‘best’ one from all other possible states of balanced growth and is, therefore, referred to as the Golden Equilibrium (Ch. 10); and concentrated on a particular economy where the capitalist is thrifty enough to carry out no consumption of goods at all while the worker is well paid so that he/she can buy goods in the Golden Equilibrium amounts, thus enabling the establishment of convergence to the Turnpike (Ch. 10). The following question is then naturally asked: Is the Golden Equilibrium still stable when the assumption of rigid consumption is replaced by the more realistic one that the worker's demand for consumption goods depends on prices and the wage income? In association with the assumption of rigid consumption, Ch. 10 made another powerful assumption that there is no shortage at all in the supply of labour; an economy was considered where the labour force grows at a constant rate, which is exogenously determined, and it was found that a state of balanced growth is compatible with such a flexible demand schedule. Therefore, it is suspected that the flexible demand for consumption goods is an additional cause of the cyclic behaviour of the Hicks–Malinvaud competitive equilibrium path and the DOSSO‐efficient growth path. The different sections of this chapter look at the possibility that flexible demand for consumption goods may cause cycles, the possibility of a Hicks–Malinvaud path in this case (and a numerical example), the DOSSO efficiency in the case of flexible consumption, and a DOSSO zigzag.