W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0010
- Subject:
- Economics and Finance, Microeconomics
This brief note was extracted from notes handwritten in August 1975 to facilitate a project on ’Hedonic Housing’ with Richard Blundell that, in the event, did not proceed. It is included because it ...
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This brief note was extracted from notes handwritten in August 1975 to facilitate a project on ’Hedonic Housing’ with Richard Blundell that, in the event, did not proceed. It is included because it is the culmination of one line of thought about the budgeting problem, and because pseudo‐separability, or ’implicit separability’ as it is sometimes called, has now cropped up in a number of different problems.Less
This brief note was extracted from notes handwritten in August 1975 to facilitate a project on ’Hedonic Housing’ with Richard Blundell that, in the event, did not proceed. It is included because it is the culmination of one line of thought about the budgeting problem, and because pseudo‐separability, or ’implicit separability’ as it is sometimes called, has now cropped up in a number of different problems.
Frank Arntzenius
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199696604
- eISBN:
- 9780191738333
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199696604.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, ...
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Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, some non-standard views about the structure of spacetime and its inhabitants are examined, such as the idea that space and time, literally, are pointless, the idea that quantum mechanics is a completely local and separable theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, metaphysics in particular, plays an important role in this book: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one’s peril!Less
Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, some non-standard views about the structure of spacetime and its inhabitants are examined, such as the idea that space and time, literally, are pointless, the idea that quantum mechanics is a completely local and separable theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, metaphysics in particular, plays an important role in this book: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one’s peril!
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.001.0001
- Subject:
- Economics and Finance, Microeconomics
W. M. (Terence) Gorman has been a major figure in the development of economics during the past 40 years. His publications on separability, aggregation, duality, and the modelling of consumer demand ...
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W. M. (Terence) Gorman has been a major figure in the development of economics during the past 40 years. His publications on separability, aggregation, duality, and the modelling of consumer demand are recognized as fundamental contributions to economic theory. Many of his unpublished papers have achieved similar status as privately circulated classics. This volume brings together, for the first time, all Gorman's important work on aggregation across commodities and agents, including separability, budgeting, representative agents, and the construction of capital and labour aggregates; much of this has never been published before. The 26 chapters are arranged in two parts: I. Separability and budgeting, and II. Aggregation across agents and firms. Each chapter (except the first) is preceded by an editorial introduction describing its origin and place within the literature, as well as the main results themselves. The book is of interest to academic economists interested in the foundations of consumer and producer theory, and in the interface between microeconomics and macroeconomics. A second volume of works, Modelling and Methodology, covers topics on duality, demand, trade, and welfare.Less
W. M. (Terence) Gorman has been a major figure in the development of economics during the past 40 years. His publications on separability, aggregation, duality, and the modelling of consumer demand are recognized as fundamental contributions to economic theory. Many of his unpublished papers have achieved similar status as privately circulated classics. This volume brings together, for the first time, all Gorman's important work on aggregation across commodities and agents, including separability, budgeting, representative agents, and the construction of capital and labour aggregates; much of this has never been published before. The 26 chapters are arranged in two parts: I. Separability and budgeting, and II. Aggregation across agents and firms. Each chapter (except the first) is preceded by an editorial introduction describing its origin and place within the literature, as well as the main results themselves. The book is of interest to academic economists interested in the foundations of consumer and producer theory, and in the interface between microeconomics and macroeconomics. A second volume of works, Modelling and Methodology, covers topics on duality, demand, trade, and welfare.
S. N. Afriat
- Published in print:
- 1987
- Published Online:
- November 2003
- ISBN:
- 9780198284611
- eISBN:
- 9780191595844
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198284616.003.0010
- Subject:
- Economics and Finance, Microeconomics
This is the fourth of six chapters in Part II about demand and utility cost, a typical area for what is understood as choice theory. It discusses separable utility. Its five sections are: models of ...
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This is the fourth of six chapters in Part II about demand and utility cost, a typical area for what is understood as choice theory. It discusses separable utility. Its five sections are: models of separability; separability tests (for classical consistency and the more restrictive classical separable consistency); constructions (the definition of mathematical functions that can be constructed on the basis of the solutions to the conditions of separability presented in the previous section); (the) utility dimension (of the separability of a group of goods); and budget separability.Less
This is the fourth of six chapters in Part II about demand and utility cost, a typical area for what is understood as choice theory. It discusses separable utility. Its five sections are: models of separability; separability tests (for classical consistency and the more restrictive classical separable consistency); constructions (the definition of mathematical functions that can be constructed on the basis of the solutions to the conditions of separability presented in the previous section); (the) utility dimension (of the separability of a group of goods); and budget separability.
Steven French and Décio Krause
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199278244
- eISBN:
- 9780191603952
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199278245.003.0004
- Subject:
- Philosophy, Philosophy of Science
This chapter discusses the concepts of indistinguishability, individuality, and non-individuality in the quantum context. It is argued that the above view of particles as non-individuals is not a ...
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This chapter discusses the concepts of indistinguishability, individuality, and non-individuality in the quantum context. It is argued that the above view of particles as non-individuals is not a necessary consequence of the physics, and that quantum particles can be taken to be individuals, subject to certain constraints. However, the sense of individuality here cannot be understood in terms of the Identity of Indiscernibles, since on a standard interpretation of quantum theory, Leibniz’s Principle is violated by both fermions and bosons. Criticisms of this argument are reviewed, as is Saunders’ recent attempt to defend a Quinean form of the Principle. The consequences of regarding quantum particles as individuals are considered in detail, and Teller’s account of entanglement in terms of non-supervenient relations is developed in this context. The conclusion is reached that quantum physics supports two alternative metaphysical packages of individuality and non-individuality, yielding a stronger form of underdetermination, which can be used to support a form of structuralism.Less
This chapter discusses the concepts of indistinguishability, individuality, and non-individuality in the quantum context. It is argued that the above view of particles as non-individuals is not a necessary consequence of the physics, and that quantum particles can be taken to be individuals, subject to certain constraints. However, the sense of individuality here cannot be understood in terms of the Identity of Indiscernibles, since on a standard interpretation of quantum theory, Leibniz’s Principle is violated by both fermions and bosons. Criticisms of this argument are reviewed, as is Saunders’ recent attempt to defend a Quinean form of the Principle. The consequences of regarding quantum particles as individuals are considered in detail, and Teller’s account of entanglement in terms of non-supervenient relations is developed in this context. The conclusion is reached that quantum physics supports two alternative metaphysical packages of individuality and non-individuality, yielding a stronger form of underdetermination, which can be used to support a form of structuralism.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0013
- Subject:
- Economics and Finance, Microeconomics
This paper is from an unpublished typescript (1970) and is a straightforward elaboration of a referee report on a paper by Robert Pollak that was eventually published in Econometrica (1972). In the ...
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This paper is from an unpublished typescript (1970) and is a straightforward elaboration of a referee report on a paper by Robert Pollak that was eventually published in Econometrica (1972). In the paper, Gorman explores the restrictions on preferences arising from Pollak's notion of generalized additive separability. Pollak essentially defines a generalization of separability as a restriction on the form of the demand curves, shows that it is a true generalization, and, in some special cases, finds the corresponding restrictions on direct and indirect utility functions. This leaves open the question of the general form of preferences implied by the demand‐function restrictions, and it is this question that Gorman addresses. He determines the circumstances in which it would be optimal to make intrasector allocations that depend only upon sector‐specific normalized prices and some function of all normalized prices.Less
This paper is from an unpublished typescript (1970) and is a straightforward elaboration of a referee report on a paper by Robert Pollak that was eventually published in Econometrica (1972). In the paper, Gorman explores the restrictions on preferences arising from Pollak's notion of generalized additive separability. Pollak essentially defines a generalization of separability as a restriction on the form of the demand curves, shows that it is a true generalization, and, in some special cases, finds the corresponding restrictions on direct and indirect utility functions. This leaves open the question of the general form of preferences implied by the demand‐function restrictions, and it is this question that Gorman addresses. He determines the circumstances in which it would be optimal to make intrasector allocations that depend only upon sector‐specific normalized prices and some function of all normalized prices.
Tim Maudlin
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780199218219
- eISBN:
- 9780191711596
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199218219.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology
In some contemporary metaphysics theories, there is an explicit preference or desire, or in some cases demand, for‘Humean’ theories. Humean, or ‘empiricist’ theories of law and of chance are sought; ...
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In some contemporary metaphysics theories, there is an explicit preference or desire, or in some cases demand, for‘Humean’ theories. Humean, or ‘empiricist’ theories of law and of chance are sought; theories that posit irreducible nomic, modal, dispositional, or causal facts are dismissed as un-Humean. David Lewis has characterized a central motivation for some of his theories as a desire to ‘uphold not so much the truth of Humean supervenience but the tenability of it’, a somewhat modest but still mysterious ambition. Why, to put it bluntly, should one want to be Humean? What is the appeal of ‘Humean Supervenience’ such that metaphysical accounts should aspire to it? Although Lewis and others issue calls to rally to Hume's banner, no strategic justification for this campaign is offered. The reason for this reticence is that the motivations will not withstand close scrutiny in the light of day. The aim of this essay is to unshutter the windows.Less
In some contemporary metaphysics theories, there is an explicit preference or desire, or in some cases demand, for‘Humean’ theories. Humean, or ‘empiricist’ theories of law and of chance are sought; theories that posit irreducible nomic, modal, dispositional, or causal facts are dismissed as un-Humean. David Lewis has characterized a central motivation for some of his theories as a desire to ‘uphold not so much the truth of Humean supervenience but the tenability of it’, a somewhat modest but still mysterious ambition. Why, to put it bluntly, should one want to be Humean? What is the appeal of ‘Humean Supervenience’ such that metaphysical accounts should aspire to it? Although Lewis and others issue calls to rally to Hume's banner, no strategic justification for this campaign is offered. The reason for this reticence is that the motivations will not withstand close scrutiny in the light of day. The aim of this essay is to unshutter the windows.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0011
- Subject:
- Economics and Finance, Microeconomics
Suppose that an agent has preferences over a finite time horizon, and that, in addition, marginal rates of substitution between adjacent time periods are independent of the level of consumption in ...
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Suppose that an agent has preferences over a finite time horizon, and that, in addition, marginal rates of substitution between adjacent time periods are independent of the level of consumption in other time periods. This means, for example, that marginal rates of substitution between commodities in periods one and two are independent of consumption in period three, and that marginal rates of substitution between commodities in periods two and three are independent of consumption in period one. Then, by the overlapping theorem, the utility function must be additive in the consumption of the three periods. A proof along these lines is presented in Sect. 4 of ’The structure of utility functions’ (Ch. 12); this paper presents an alternative proof of the same theorem. John Whitaker at the Oxford Mathematical Economics Seminar posed the problem in 1964, and Gorman submitted the paper to Econometrica in July 1965 and it was published in Econometrica 36 (1968).Less
Suppose that an agent has preferences over a finite time horizon, and that, in addition, marginal rates of substitution between adjacent time periods are independent of the level of consumption in other time periods. This means, for example, that marginal rates of substitution between commodities in periods one and two are independent of consumption in period three, and that marginal rates of substitution between commodities in periods two and three are independent of consumption in period one. Then, by the overlapping theorem, the utility function must be additive in the consumption of the three periods. A proof along these lines is presented in Sect. 4 of ’The structure of utility functions’ (Ch. 12); this paper presents an alternative proof of the same theorem. John Whitaker at the Oxford Mathematical Economics Seminar posed the problem in 1964, and Gorman submitted the paper to Econometrica in July 1965 and it was published in Econometrica 36 (1968).
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0009
- Subject:
- Economics and Finance, Microeconomics
This paper is from an unpublished typescript from the University of North Carolina (1970). When confronted with additivity, it is far more convenient to use profit functions than cost functions or ...
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This paper is from an unpublished typescript from the University of North Carolina (1970). When confronted with additivity, it is far more convenient to use profit functions than cost functions or indirect utility functions. The reason for this is that if the objective function is additive then the resulting profit function is also additive, so one does not lose all of the explicit original structure in moving to the dual. To be able to do this, however, each of the functions in question must be concave. However, concavity is typically not an easy assumption to accept in utility theory. The question addressed in this paper is whether concavity is more plausible in the case of additive separability.Less
This paper is from an unpublished typescript from the University of North Carolina (1970). When confronted with additivity, it is far more convenient to use profit functions than cost functions or indirect utility functions. The reason for this is that if the objective function is additive then the resulting profit function is also additive, so one does not lose all of the explicit original structure in moving to the dual. To be able to do this, however, each of the functions in question must be concave. However, concavity is typically not an easy assumption to accept in utility theory. The question addressed in this paper is whether concavity is more plausible in the case of additive separability.
Andy Clark
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195333213
- eISBN:
- 9780199868858
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195333213.003.0009
- Subject:
- Philosophy, Philosophy of Mind
Embodiment appears to matter for mind and cognition in three ways: spreading the load, self-structuring information, and supporting extended cognition. The three threads are joined by the supporting ...
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Embodiment appears to matter for mind and cognition in three ways: spreading the load, self-structuring information, and supporting extended cognition. The three threads are joined by the supporting hypothesis of cognitive impartiality: Our problem-solving performances take shape according to some cost function or functions that, in the typical course of events, accord no special status or privilege to specific types of operation (motoric, perceptual, introspective) or modes of encoding (in the head or in the world). This chapter argues that these appeals to embodiment, action, and cognitive extension are best understood as fully continuous with computational, representational, and information-theoretic approaches to understanding mind and cognition. In so doing, it attempts to display at least something of the likely shape of a mature science of the embodied mind.Less
Embodiment appears to matter for mind and cognition in three ways: spreading the load, self-structuring information, and supporting extended cognition. The three threads are joined by the supporting hypothesis of cognitive impartiality: Our problem-solving performances take shape according to some cost function or functions that, in the typical course of events, accord no special status or privilege to specific types of operation (motoric, perceptual, introspective) or modes of encoding (in the head or in the world). This chapter argues that these appeals to embodiment, action, and cognitive extension are best understood as fully continuous with computational, representational, and information-theoretic approaches to understanding mind and cognition. In so doing, it attempts to display at least something of the likely shape of a mature science of the embodied mind.
John Broome
- Published in print:
- 2004
- Published Online:
- October 2005
- ISBN:
- 9780199243761
- eISBN:
- 9780191602900
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019924376X.003.0008
- Subject:
- Philosophy, Moral Philosophy
This chapter distinguishes a notion of separability of lives from a stronger notion of separability of people, which takes into account the possibility of a person’s nonexistence. It defends ...
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This chapter distinguishes a notion of separability of lives from a stronger notion of separability of people, which takes into account the possibility of a person’s nonexistence. It defends separability of lives on the basis of the principle of personal good. It thereby opens up the people route to aggregation when the population of the world is constant. It assesses the principle of personal good, particularly considering its relation to the value of equality and its conflict with discounting for time.Less
This chapter distinguishes a notion of separability of lives from a stronger notion of separability of people, which takes into account the possibility of a person’s nonexistence. It defends separability of lives on the basis of the principle of personal good. It thereby opens up the people route to aggregation when the population of the world is constant. It assesses the principle of personal good, particularly considering its relation to the value of equality and its conflict with discounting for time.
Ekkehart Schlicht
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198292241
- eISBN:
- 9780191596865
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198292244.003.0015
- Subject:
- Economics and Finance, Microeconomics, History of Economic Thought
Smith's theorem—that the division of labour is limited by the extent of the market—is explained. But there exists another limitation to the division of labour that relates to the nature of the task. ...
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Smith's theorem—that the division of labour is limited by the extent of the market—is explained. But there exists another limitation to the division of labour that relates to the nature of the task. Further, the division of labour can be coordinated alternatively by markets or by the coordination mechanisms available within firms that rely heavily on custom. It is argued that coordination within firms entails productivity advantages at the expense of inflexibility in certain dimensions, whereas the market requires standardization of some sort, but is more flexible in other ways.Less
Smith's theorem—that the division of labour is limited by the extent of the market—is explained. But there exists another limitation to the division of labour that relates to the nature of the task. Further, the division of labour can be coordinated alternatively by markets or by the coordination mechanisms available within firms that rely heavily on custom. It is argued that coordination within firms entails productivity advantages at the expense of inflexibility in certain dimensions, whereas the market requires standardization of some sort, but is more flexible in other ways.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0014
- Subject:
- Economics and Finance, Microeconomics
This paper, which was published as Technical Report No. 359 from the Institute of Mathematical Studies in the Social Sciences, Stanford University (1982), analyses uncertainty in an intertemporal ...
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This paper, which was published as Technical Report No. 359 from the Institute of Mathematical Studies in the Social Sciences, Stanford University (1982), analyses uncertainty in an intertemporal context, and is designed to use to the fullest extent possible the overlapping theorem presented in ’The structure of utility functions’ (Ch. 12). At each point of time, a set of states of the world is possible, presenting the agent with a utility tree; the agent has a complete set of preferences over all possible states of the world at all periods of time; one of these states occurs, and in the next period, he or she faces some smaller portion of the tree. Assumption 2 requires the states that follow any branch of the tree to be separable from those events that can no longer happen––conditional on the actual history followed; Gorman calls this the ’very weak independence axiom’; the only other assumption used here is that the agent only examines the future closely for the next two periods, and, for the rest of the future, is content with a summary statistic. Hence Assumption 3 requires the future from t + 2 to the horizon to be separable from its complement at each t. These two assumptions are enough to generate ’Bentham and Bernoulli at a stroke’.Less
This paper, which was published as Technical Report No. 359 from the Institute of Mathematical Studies in the Social Sciences, Stanford University (1982), analyses uncertainty in an intertemporal context, and is designed to use to the fullest extent possible the overlapping theorem presented in ’The structure of utility functions’ (Ch. 12). At each point of time, a set of states of the world is possible, presenting the agent with a utility tree; the agent has a complete set of preferences over all possible states of the world at all periods of time; one of these states occurs, and in the next period, he or she faces some smaller portion of the tree. Assumption 2 requires the states that follow any branch of the tree to be separable from those events that can no longer happen––conditional on the actual history followed; Gorman calls this the ’very weak independence axiom’; the only other assumption used here is that the agent only examines the future closely for the next two periods, and, for the rest of the future, is content with a summary statistic. Hence Assumption 3 requires the future from t + 2 to the horizon to be separable from its complement at each t. These two assumptions are enough to generate ’Bentham and Bernoulli at a stroke’.
Amartya Sen
- Published in print:
- 1973
- Published Online:
- November 2003
- ISBN:
- 9780198281931
- eISBN:
- 9780191715815
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198281935.003.0002
- Subject:
- Economics and Finance, Public and Welfare
Various measures of inequality that have been proposed in the literature are discussed. These fall into two categories: those that measure in some objective sense—positive measures that make no ...
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Various measures of inequality that have been proposed in the literature are discussed. These fall into two categories: those that measure in some objective sense—positive measures that make no explicit use of any concept of social welfare and those that measure in terms of a normative notion of social welfare and the loss incurred from unequal distribution. The characteristics of positive measures are described in respect of range, relative mean deviation, variance and the coefficient of variation, the standard deviation of logarithms, the Gini coefficient, and Theil's entropy measure. Normative measures are described in terms of Dalton's measure, Atkinson's measure, axioms for additive separability, and a more general measure.Less
Various measures of inequality that have been proposed in the literature are discussed. These fall into two categories: those that measure in some objective sense—positive measures that make no explicit use of any concept of social welfare and those that measure in terms of a normative notion of social welfare and the loss incurred from unequal distribution. The characteristics of positive measures are described in respect of range, relative mean deviation, variance and the coefficient of variation, the standard deviation of logarithms, the Gini coefficient, and Theil's entropy measure. Normative measures are described in terms of Dalton's measure, Atkinson's measure, axioms for additive separability, and a more general measure.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0001
- Subject:
- Economics and Finance, Microeconomics
This chapter is Gorman's contribution to The New Palgrave: A Dictionary of Economics (London: MacMillan Press, 1987), and represents his own summary of many of the issues of functional ...
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This chapter is Gorman's contribution to The New Palgrave: A Dictionary of Economics (London: MacMillan Press, 1987), and represents his own summary of many of the issues of functional separability––or separable utility functions––in the theory of demand.Less
This chapter is Gorman's contribution to The New Palgrave: A Dictionary of Economics (London: MacMillan Press, 1987), and represents his own summary of many of the issues of functional separability––or separable utility functions––in the theory of demand.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0002
- Subject:
- Economics and Finance, Microeconomics
This paper is from an unpublished typescript (University of North Carolina, 1970), and is the first of a series of papers in Part I of the book on the general subject of budgeting––the rather vague ...
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This paper is from an unpublished typescript (University of North Carolina, 1970), and is the first of a series of papers in Part I of the book on the general subject of budgeting––the rather vague notion that households, organizations, or governments first allocate a given total expenditure to various subsets of commodities, such as ’food’, ’recreation’, or 'saving’. Only after the allocations to these broad sectors have been specified, does the agent or organization decide how to split each sectoral expenditure among its component parts, such as the particular food commodities. The set of papers assumes that the agent or organization has a well‐defined preference ordering over all relevant commodities, and hence the problems are cast in the context of consumer theory (purely for expositional purposes). Reinterpreting the results in terms of a firm presents no special difficulties, and allows a variety of problems to be discussed. ’Two‐stage budgeting’ supposes that the correct intersector allocations have been made, and then shows that separability of that sector is necessary and sufficient for the resulting intrasector allocations to be optimal.Less
This paper is from an unpublished typescript (University of North Carolina, 1970), and is the first of a series of papers in Part I of the book on the general subject of budgeting––the rather vague notion that households, organizations, or governments first allocate a given total expenditure to various subsets of commodities, such as ’food’, ’recreation’, or 'saving’. Only after the allocations to these broad sectors have been specified, does the agent or organization decide how to split each sectoral expenditure among its component parts, such as the particular food commodities. The set of papers assumes that the agent or organization has a well‐defined preference ordering over all relevant commodities, and hence the problems are cast in the context of consumer theory (purely for expositional purposes). Reinterpreting the results in terms of a firm presents no special difficulties, and allows a variety of problems to be discussed. ’Two‐stage budgeting’ supposes that the correct intersector allocations have been made, and then shows that separability of that sector is necessary and sufficient for the resulting intrasector allocations to be optimal.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0003
- Subject:
- Economics and Finance, Microeconomics
Separability is a maintained hypothesis throughout this paper, which was published in Econometrica 27 (1959). Hence, the results of the previous paper are applicable: that is, it begins with the ...
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Separability is a maintained hypothesis throughout this paper, which was published in Econometrica 27 (1959). Hence, the results of the previous paper are applicable: that is, it begins with the assumption that two‐stage budgeting is possible, but that no restrictions are imposed on the information used to discover the optimal expenditure on each group. The paper considers the implications of reducing the information available to make the intergroup allocation decision, and begins by investigating the conditions in which a consumer with a well‐behaved separable utility function can find the optimal income allocation for a group, given only the price indices for each group. In Sect. 1, Gorman posits the existence of differential price indices, and his Proposition I provides the necessary and sufficient conditions for local price aggregation, maintaining separability of the direct utility function. Section 2 of the paper considers the case of perfect price aggregates, and the conclusion makes specific remarks about an earlier paper written for the same journal by R. H. Strotz, of which this paper of Gorman's is essentially an elaboration of Gorman's referee's report.Less
Separability is a maintained hypothesis throughout this paper, which was published in Econometrica 27 (1959). Hence, the results of the previous paper are applicable: that is, it begins with the assumption that two‐stage budgeting is possible, but that no restrictions are imposed on the information used to discover the optimal expenditure on each group. The paper considers the implications of reducing the information available to make the intergroup allocation decision, and begins by investigating the conditions in which a consumer with a well‐behaved separable utility function can find the optimal income allocation for a group, given only the price indices for each group. In Sect. 1, Gorman posits the existence of differential price indices, and his Proposition I provides the necessary and sufficient conditions for local price aggregation, maintaining separability of the direct utility function. Section 2 of the paper considers the case of perfect price aggregates, and the conclusion makes specific remarks about an earlier paper written for the same journal by R. H. Strotz, of which this paper of Gorman's is essentially an elaboration of Gorman's referee's report.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0005
- Subject:
- Economics and Finance, Microeconomics
This is the most ambitious of the papers in Part I of the book that are explicitly concerned with budgeting; it is from an unpublished typescript dated 1965. Here, Gorman discards the previously ...
More
This is the most ambitious of the papers in Part I of the book that are explicitly concerned with budgeting; it is from an unpublished typescript dated 1965. Here, Gorman discards the previously maintained hypothesis of separability and attempts to discover the implications of perfect price aggregation itself. Specifically, in the notation of this paper, he looks for the conditions under which a consumer with a well‐behaved utility function can determine the optimal intersector allocations. Sect. 2 of the paper solves this problem by deriving the necessary and sufficient conditions on the indirect utility function and develops this in various ways. The remaining sections add an assumption on price aggregation, and a requirement that the demand functions are derived from conditional subutility functions.Less
This is the most ambitious of the papers in Part I of the book that are explicitly concerned with budgeting; it is from an unpublished typescript dated 1965. Here, Gorman discards the previously maintained hypothesis of separability and attempts to discover the implications of perfect price aggregation itself. Specifically, in the notation of this paper, he looks for the conditions under which a consumer with a well‐behaved utility function can determine the optimal intersector allocations. Sect. 2 of the paper solves this problem by deriving the necessary and sufficient conditions on the indirect utility function and develops this in various ways. The remaining sections add an assumption on price aggregation, and a requirement that the demand functions are derived from conditional subutility functions.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0008
- Subject:
- Economics and Finance, Microeconomics
This chapter comprises three notes from unpublished typescripts on the relationship between separability and the linearity of Engel curves, which have been put together into one paper with three ...
More
This chapter comprises three notes from unpublished typescripts on the relationship between separability and the linearity of Engel curves, which have been put together into one paper with three sections. They were apparently all written about the same time, and one of them is dated March 1971. Engel curves are curves showing the relationship between income level and spending on the consumption of some good, at a given price. Preferences with linear Engel curves are a natural generalization of homotheticity, which yields straight‐line Engel curves passing through the origin. The subject has appeared tangentially in some of the budgeting papers in Part I of the book, and reappears in the discussion of representative consumers and firms in Part II.Less
This chapter comprises three notes from unpublished typescripts on the relationship between separability and the linearity of Engel curves, which have been put together into one paper with three sections. They were apparently all written about the same time, and one of them is dated March 1971. Engel curves are curves showing the relationship between income level and spending on the consumption of some good, at a given price. Preferences with linear Engel curves are a natural generalization of homotheticity, which yields straight‐line Engel curves passing through the origin. The subject has appeared tangentially in some of the budgeting papers in Part I of the book, and reappears in the discussion of representative consumers and firms in Part II.
James Davidson
- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0005
- Subject:
- Economics and Finance, Econometrics
This chapter introduces and illustrates the concept of a metric (distance measure), and the definition of a metric space. Open, closed, and compact sets are discussed in a general context, and the ...
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This chapter introduces and illustrates the concept of a metric (distance measure), and the definition of a metric space. Open, closed, and compact sets are discussed in a general context, and the concepts of separability and completeness introduced. It goes on to look at mappings on metric spaces, and then examines the important case of function spaces, and treats the Arzelà‐Ascoli theorem.Less
This chapter introduces and illustrates the concept of a metric (distance measure), and the definition of a metric space. Open, closed, and compact sets are discussed in a general context, and the concepts of separability and completeness introduced. It goes on to look at mappings on metric spaces, and then examines the important case of function spaces, and treats the Arzelà‐Ascoli theorem.
