出版社: Cambridge University Press
出版年: 19850830
页数: 764
定价: USD 85.00
装帧: Paperback
ISBN: 9780521314985
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This book provides a systematic exposition of mathematical economics, presenting and surveying existing theories and showing ways in which they can be extended. One of its strongest features is that it emphasises the unifying structure of economic theory in such a way as to provide the reader with the technical tools and methodological approaches necessary for undertaking origi...
This book provides a systematic exposition of mathematical economics, presenting and surveying existing theories and showing ways in which they can be extended. One of its strongest features is that it emphasises the unifying structure of economic theory in such a way as to provide the reader with the technical tools and methodological approaches necessary for undertaking original research. The author offers explanations and discussion at an accessible and intuitive level providing illustrative examples. He begins the work at an elementary level and progessively takes the reader to the frontier of current research. This second edition brings the reader fully up to date with recent research in the field.
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小鸥 (小和尚)
People have very different interpretations of the notion of an equilibrium, reflected in different formulations of the problem. Some consider it as rather a dynamic process, so formulated it as fixed point, which is more common in growth problems (also in the taxation dynamics). It is not clear yet how this is related to using duality in linear programming. According to Takayama, Arrow formulated ...20120308 15:15
People have very different interpretations of the notion of an equilibrium, reflected in different formulations of the problem. Some consider it as rather a dynamic process, so formulated it as fixed point, which is more common in growth problems (also in the taxation dynamics). It is not clear yet how this is related to using duality in linear programming. According to Takayama, Arrow formulated it as games. Takayama's advocated formulation is actually by recognizing a resemblance between Pareto Optimum and the vector maximization in nonlinear programming, and as a result, the use of nonlinear programming to solve for competitive equilibrium ensures direct satisfaction of Pareto Optimum, and the existence conditions of such an equilibrium is already implicit in the requirements of nonlinear programming (such as concavity, local nonsatiation, etc).It seems that to understand the equilibrium problem is somewhat equivalent to understanding the relationship between the following few concepts:fixedpointduality (envelope)nonlinear programming (saddle point)intermediate value theorem (related to taylor expansion and asymptotic properties)convergence of sequencesmean value theoremcentral limit theorem回应 20120308 15:15 
小鸥 (小和尚)
Takayama arrived at the substitution properties of demand in Section 2.D directly from properties of the preference orderings (probably without transitivity). He also covered the other approach of using duality, which he derived in Section 1.F with nonlinear programming and separation theory (while MWG could only provide some intuitions of it with normal calculus). Takayama's advocated approach wa...20120302 19:45
Takayama arrived at the substitution properties of demand in Section 2.D directly from properties of the preference orderings (probably without transitivity). He also covered the other approach of using duality, which he derived in Section 1.F with nonlinear programming and separation theory (while MWG could only provide some intuitions of it with normal calculus). Takayama's advocated approach was centered around a 'minimum expenditure funcion', which can be just another way of expressing the supporting hyperplane or support function. Also convexity is included in the conditions of the stated demand properties, which resonate what I have wrote in the other note about the connection between linearity and convexity which supports the approach of solving optimization problems with its dual form.回应 20120302 19:45 
小鸥 (小和尚)
This is about the properties of the 'envelope' of optimization problems (solved readily with nonlinear programming), a correspondence between the solutions of optimization processes and its conditions, i.e. properties of a projection from others behavior to an individual's reactions which is determined by properties of another correspondence confined within one individual, under the optimizing pri...20120228 15:03
This is about the properties of the 'envelope' of optimization problems (solved readily with nonlinear programming), a correspondence between the solutions of optimization processes and its conditions, i.e. properties of a projection from others behavior to an individual's reactions which is determined by properties of another correspondence confined within one individual, under the optimizing principle. The behavior of this 'envelope' correspondence under some principles like equilibrium is what people want to know, and the behavior is determined by properties such as continuity, elasticities, and as related to its differentials.These properties are traditionally derived with the preference ordering representation of behavior, elaborated in Takayama's book. Yet as emphasized in the more recent Microeconomic Theory, they can also be derived from the choice representation. This connection is essentially due to the fact that the axiom of transitivity of the preference orderings is generally irrelevant to properties of the demand function, thus can be relaxed in investigating demand, reducing the behavioral representation to something more or less equivalent to the choice approach.About the detailed results from demand theory. All properties are derived directly from the preference representations, and the internal optimization process inside the envelop is taken as already finished (leading to equivalence with choice approach, as pointed out in Takayama's footnote 4 on Page248).The compensated demand function is a function from the desired demand to the demand that a rational consumer adjust to so that one can still enjoy the same utility but achieved within one's budget. In a very strong sense, it is an envelope closing at an indifference curve. In this perspective, an envelope is just a tangent line that is not tangent at any specific point. Such an concept enabled the description of a tangent or sloping relationship without being restricted to one point, i.e. envelope is the tangent line of a set, and all the efforts with separation theories or minimum expenditure function are just to mathematically express an envelope. Then under certain conditions, the envelopes form a dual relationship with the demand function, and substitution properties of the demand function which is an implicit function involving optimization can be conveniently transferred to the substitution properties of its envelope.回应 20120228 15:03 
小鸥 (小和尚)
This terminology is referring to the other note on Subgame Optimization. I compared Pareto optimum to Nash equilibrium there, and here there are more things to say about the Pareto optimum. First there is still something more about the comparison. Both are about decisions. In games the individual decisions are connected and converged with each individual playing both as herself and as every oth...20120213 21:57
This terminology is referring to the other note on Subgame Optimization. I compared Pareto optimum to Nash equilibrium there, and here there are more things to say about the Pareto optimum.First there is still something more about the comparison. Both are about decisions. In games the individual decisions are connected and converged with each individual playing both as herself and as every other players, so that she knows where the equilibrium is and act accordingly. In competitive markets, this thinking process is replaced by simply following the price, knowing that the price contains information about the others' actions. This pricetaking behavior can actually be interpreted as a solution to the game of market, where the condition of Nash equilibrium is interpreted as Pareto Optimum. From reading Fei's lecture notes, it became clear that the Pareto Optimum (pareto efficient allocation) is nothing but a further level of constrained utility / profit maximization, which in this sense is just a pareto efficient allocation of the individual's constrained wealth / production set (?) which maximizes individual preference (utility) / production pareto efficiently. On the market exchange level, this constrained maximization becomes pareto efficient allocation of constrained total resource that maximizes group preference (utility) pareto efficiently.pareto optimum = vector maximumdecision theory = vector maximizationAs such, the existence question of an equilibrium should be the same as the existence question of a maximum which is solved for in utility maximization with nonlinear programming conditions, e.g. KTCQ.回应 20120213 21:57

小鸥 (小和尚)
(topology) Examples of continuous functions, with which topological properties such as compactness and therefore extremums can be preserved. This is important because it enables the search for optimal solutions without requiring a continuity of possibilities, which is required when approaching the problem with calculus thus differentiation, so that in addition to requiring the continuity of fun...20120213 16:25
(topology)Examples of continuous functions, with which topological properties such as compactness and therefore extremums can be preserved.This is important because it enables the search for optimal solutions without requiring a continuity of possibilities, which is required when approaching the problem with calculus thus differentiation, so that in addition to requiring the continuity of functions, continuity of the set on which the function is defined (set of possibilities) is also required to ensure differentiability, which is not necessary, as a noncontinuous set can as well achieve optimality, and as long as such properties can be transferred consistently in between possibilities (e.g. production sets/function or consumption bundle) and welfare measures (e.g. profit or utility), answering questions such as how to allocate resource (possibilities) to achieve an optimum social welfare state would become possible.回应 20120213 16:25 
小鸥 (小和尚)
People have very different interpretations of the notion of an equilibrium, reflected in different formulations of the problem. Some consider it as rather a dynamic process, so formulated it as fixed point, which is more common in growth problems (also in the taxation dynamics). It is not clear yet how this is related to using duality in linear programming. According to Takayama, Arrow formulated ...20120308 15:15
People have very different interpretations of the notion of an equilibrium, reflected in different formulations of the problem. Some consider it as rather a dynamic process, so formulated it as fixed point, which is more common in growth problems (also in the taxation dynamics). It is not clear yet how this is related to using duality in linear programming. According to Takayama, Arrow formulated it as games. Takayama's advocated formulation is actually by recognizing a resemblance between Pareto Optimum and the vector maximization in nonlinear programming, and as a result, the use of nonlinear programming to solve for competitive equilibrium ensures direct satisfaction of Pareto Optimum, and the existence conditions of such an equilibrium is already implicit in the requirements of nonlinear programming (such as concavity, local nonsatiation, etc).It seems that to understand the equilibrium problem is somewhat equivalent to understanding the relationship between the following few concepts:fixedpointduality (envelope)nonlinear programming (saddle point)intermediate value theorem (related to taylor expansion and asymptotic properties)convergence of sequencesmean value theoremcentral limit theorem回应 20120308 15:15 
小鸥 (小和尚)
Takayama arrived at the substitution properties of demand in Section 2.D directly from properties of the preference orderings (probably without transitivity). He also covered the other approach of using duality, which he derived in Section 1.F with nonlinear programming and separation theory (while MWG could only provide some intuitions of it with normal calculus). Takayama's advocated approach wa...20120302 19:45
Takayama arrived at the substitution properties of demand in Section 2.D directly from properties of the preference orderings (probably without transitivity). He also covered the other approach of using duality, which he derived in Section 1.F with nonlinear programming and separation theory (while MWG could only provide some intuitions of it with normal calculus). Takayama's advocated approach was centered around a 'minimum expenditure funcion', which can be just another way of expressing the supporting hyperplane or support function. Also convexity is included in the conditions of the stated demand properties, which resonate what I have wrote in the other note about the connection between linearity and convexity which supports the approach of solving optimization problems with its dual form.回应 20120302 19:45 
小鸥 (小和尚)
This is about the properties of the 'envelope' of optimization problems (solved readily with nonlinear programming), a correspondence between the solutions of optimization processes and its conditions, i.e. properties of a projection from others behavior to an individual's reactions which is determined by properties of another correspondence confined within one individual, under the optimizing pri...20120228 15:03
This is about the properties of the 'envelope' of optimization problems (solved readily with nonlinear programming), a correspondence between the solutions of optimization processes and its conditions, i.e. properties of a projection from others behavior to an individual's reactions which is determined by properties of another correspondence confined within one individual, under the optimizing principle. The behavior of this 'envelope' correspondence under some principles like equilibrium is what people want to know, and the behavior is determined by properties such as continuity, elasticities, and as related to its differentials.These properties are traditionally derived with the preference ordering representation of behavior, elaborated in Takayama's book. Yet as emphasized in the more recent Microeconomic Theory, they can also be derived from the choice representation. This connection is essentially due to the fact that the axiom of transitivity of the preference orderings is generally irrelevant to properties of the demand function, thus can be relaxed in investigating demand, reducing the behavioral representation to something more or less equivalent to the choice approach.About the detailed results from demand theory. All properties are derived directly from the preference representations, and the internal optimization process inside the envelop is taken as already finished (leading to equivalence with choice approach, as pointed out in Takayama's footnote 4 on Page248).The compensated demand function is a function from the desired demand to the demand that a rational consumer adjust to so that one can still enjoy the same utility but achieved within one's budget. In a very strong sense, it is an envelope closing at an indifference curve. In this perspective, an envelope is just a tangent line that is not tangent at any specific point. Such an concept enabled the description of a tangent or sloping relationship without being restricted to one point, i.e. envelope is the tangent line of a set, and all the efforts with separation theories or minimum expenditure function are just to mathematically express an envelope. Then under certain conditions, the envelopes form a dual relationship with the demand function, and substitution properties of the demand function which is an implicit function involving optimization can be conveniently transferred to the substitution properties of its envelope.回应 20120228 15:03

小鸥 (小和尚)
People have very different interpretations of the notion of an equilibrium, reflected in different formulations of the problem. Some consider it as rather a dynamic process, so formulated it as fixed point, which is more common in growth problems (also in the taxation dynamics). It is not clear yet how this is related to using duality in linear programming. According to Takayama, Arrow formulated ...20120308 15:15
People have very different interpretations of the notion of an equilibrium, reflected in different formulations of the problem. Some consider it as rather a dynamic process, so formulated it as fixed point, which is more common in growth problems (also in the taxation dynamics). It is not clear yet how this is related to using duality in linear programming. According to Takayama, Arrow formulated it as games. Takayama's advocated formulation is actually by recognizing a resemblance between Pareto Optimum and the vector maximization in nonlinear programming, and as a result, the use of nonlinear programming to solve for competitive equilibrium ensures direct satisfaction of Pareto Optimum, and the existence conditions of such an equilibrium is already implicit in the requirements of nonlinear programming (such as concavity, local nonsatiation, etc).It seems that to understand the equilibrium problem is somewhat equivalent to understanding the relationship between the following few concepts:fixedpointduality (envelope)nonlinear programming (saddle point)intermediate value theorem (related to taylor expansion and asymptotic properties)convergence of sequencesmean value theoremcentral limit theorem回应 20120308 15:15 
小鸥 (小和尚)
Takayama arrived at the substitution properties of demand in Section 2.D directly from properties of the preference orderings (probably without transitivity). He also covered the other approach of using duality, which he derived in Section 1.F with nonlinear programming and separation theory (while MWG could only provide some intuitions of it with normal calculus). Takayama's advocated approach wa...20120302 19:45
Takayama arrived at the substitution properties of demand in Section 2.D directly from properties of the preference orderings (probably without transitivity). He also covered the other approach of using duality, which he derived in Section 1.F with nonlinear programming and separation theory (while MWG could only provide some intuitions of it with normal calculus). Takayama's advocated approach was centered around a 'minimum expenditure funcion', which can be just another way of expressing the supporting hyperplane or support function. Also convexity is included in the conditions of the stated demand properties, which resonate what I have wrote in the other note about the connection between linearity and convexity which supports the approach of solving optimization problems with its dual form.回应 20120302 19:45 
小鸥 (小和尚)
This is about the properties of the 'envelope' of optimization problems (solved readily with nonlinear programming), a correspondence between the solutions of optimization processes and its conditions, i.e. properties of a projection from others behavior to an individual's reactions which is determined by properties of another correspondence confined within one individual, under the optimizing pri...20120228 15:03
This is about the properties of the 'envelope' of optimization problems (solved readily with nonlinear programming), a correspondence between the solutions of optimization processes and its conditions, i.e. properties of a projection from others behavior to an individual's reactions which is determined by properties of another correspondence confined within one individual, under the optimizing principle. The behavior of this 'envelope' correspondence under some principles like equilibrium is what people want to know, and the behavior is determined by properties such as continuity, elasticities, and as related to its differentials.These properties are traditionally derived with the preference ordering representation of behavior, elaborated in Takayama's book. Yet as emphasized in the more recent Microeconomic Theory, they can also be derived from the choice representation. This connection is essentially due to the fact that the axiom of transitivity of the preference orderings is generally irrelevant to properties of the demand function, thus can be relaxed in investigating demand, reducing the behavioral representation to something more or less equivalent to the choice approach.About the detailed results from demand theory. All properties are derived directly from the preference representations, and the internal optimization process inside the envelop is taken as already finished (leading to equivalence with choice approach, as pointed out in Takayama's footnote 4 on Page248).The compensated demand function is a function from the desired demand to the demand that a rational consumer adjust to so that one can still enjoy the same utility but achieved within one's budget. In a very strong sense, it is an envelope closing at an indifference curve. In this perspective, an envelope is just a tangent line that is not tangent at any specific point. Such an concept enabled the description of a tangent or sloping relationship without being restricted to one point, i.e. envelope is the tangent line of a set, and all the efforts with separation theories or minimum expenditure function are just to mathematically express an envelope. Then under certain conditions, the envelopes form a dual relationship with the demand function, and substitution properties of the demand function which is an implicit function involving optimization can be conveniently transferred to the substitution properties of its envelope.回应 20120228 15:03 
小鸥 (小和尚)
This terminology is referring to the other note on Subgame Optimization. I compared Pareto optimum to Nash equilibrium there, and here there are more things to say about the Pareto optimum. First there is still something more about the comparison. Both are about decisions. In games the individual decisions are connected and converged with each individual playing both as herself and as every oth...20120213 21:57
This terminology is referring to the other note on Subgame Optimization. I compared Pareto optimum to Nash equilibrium there, and here there are more things to say about the Pareto optimum.First there is still something more about the comparison. Both are about decisions. In games the individual decisions are connected and converged with each individual playing both as herself and as every other players, so that she knows where the equilibrium is and act accordingly. In competitive markets, this thinking process is replaced by simply following the price, knowing that the price contains information about the others' actions. This pricetaking behavior can actually be interpreted as a solution to the game of market, where the condition of Nash equilibrium is interpreted as Pareto Optimum. From reading Fei's lecture notes, it became clear that the Pareto Optimum (pareto efficient allocation) is nothing but a further level of constrained utility / profit maximization, which in this sense is just a pareto efficient allocation of the individual's constrained wealth / production set (?) which maximizes individual preference (utility) / production pareto efficiently. On the market exchange level, this constrained maximization becomes pareto efficient allocation of constrained total resource that maximizes group preference (utility) pareto efficiently.pareto optimum = vector maximumdecision theory = vector maximizationAs such, the existence question of an equilibrium should be the same as the existence question of a maximum which is solved for in utility maximization with nonlinear programming conditions, e.g. KTCQ.回应 20120213 21:57
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0 有用 小鸥 20120415
really cannot find a substitute for it so far. Varian is too conclusive. MWG is a modern extension to Takayama's, but very often too extended to retain focus. However it helps a lot if one read Takayama's first and catch up with the current state with MWG
0 有用 许跑焦 20091228
真他妈绕
0 有用 小鸥 20120415
really cannot find a substitute for it so far. Varian is too conclusive. MWG is a modern extension to Takayama's, but very often too extended to retain focus. However it helps a lot if one read Takayama's first and catch up with the current state with MWG
0 有用 许跑焦 20091228
真他妈绕