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Online Resource
Handbook of mathematical economics : volume 2 (1982)
Amsterdam : North-Holland Pub. Co
Details
UID:
gbv_1659177626
Format: Online Ressource (xii, 381-1070 pages) , illustrations.
Edition: Online-Ausg.
ISBN: 0444861270 , 9780444861276
Series Statement: Handbooks in economics bk. 1
Content: The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field. Volume 2 elaborates on Mathematical Approaches to Microeconomic Theory, including consumer, producer, oligopoly, and duality theory, as well as Mathematical Approaches to Competitive Equilibrium including such aspects of competitive equilibrium as existence, stability, uncertainty, the computation of equilibrium prices, and the core of an economy
Content: The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field. Volume 2 elaborates on Mathematical Approaches to Microeconomic Theory, including consumer, producer, oligopoly, and duality theory, as well as Mathematical Approaches to Competitive Equilibrium including such aspects of competitive equilibrium as existence, stability, uncertainty, the computation of equilibrium prices, and the core of an economy
Note: Includes bibliographical references and index , Mathematical Approaches to Microeconomic Theory. Consumer theory (A.P. Barten, V. Buhm). Producers theory (M.I. Nadiri). Oligopoly theory (J.W. Friedman). Duality approaches to microeconomic theory (W.E. Diewert). On the microeconomic theory of investment under uncertainty (R.C. Merton). Market demand and excess demand functions (W. Shafer, H. Sonnenschein). Mathematical Approaches to Competitive Equilibrium. Existence of competitive equilibrium (G. Debreu). Stability (F. Hahn). Regular economies (E. Dierker). Core of an economy (W. Hildenbrand). Temporary general equilibrium theory (J.-M. Grandmont). Equilibrium under uncertainty (R. Radner). The computation of equilibrium prices: An exposition (H.E. Scarf).
Language: English
Subjects: Economics , Mathematics
RVK:
SK 980
RVK:
QH 100
Keywords: Wirtschaftsmathematik ; Ökonometrie ; Electronic books
URL: Volltext  (Deutschlandweit zugänglich)
URL: lizenzpflichtig
URL: Volltext
Author information: Arrow, Kenneth Joseph 1921-2017
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  • 2
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    Chapter 10 Producers theory (1982)
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    UID:
    gbv_1831647974
    ISBN: 0444861270
    Content: The producers theory is concerned with the behavior of firms in hiring and combining productive inputs to supply commodities at appropriate prices. Two sets of issues are involved in this process: one is the technical constraints, which limit the range of feasible productive processes, while the other is the institutional context such as the characteristics of the market where commodities and inputs are purchased and sold. The chapter describes the set of axiomatic approaches to production technology and the neoclassical theory of the multi-product and multi-input firm. It is an attempt to set forth the general framework of analysis that underlies neoclassical producer decision theory. The chapter discusses the properties of the production function, its various forms, and applications of the duality principles and also provides a brief discussion of the CambridgeCambridge controversy insofar as it pertains to the existence and usefulness of production functions. The chapter also presents three special cases of the theory of the firm in which new research has appeared, specifically dynamic input disequilibrium models, response to regulatory constraints, and optimal price and output decisions in multi-product firms.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 431-490, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:431-490
    Language: English
    DOI: 10.1016/S1573-4382(82)02005-0
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  • 3
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    Chapter 11 Oligopoly theory (1982)
    Details
    UID:
    gbv_1831647966
    ISBN: 0444861270
    Content: The oligopoly theory usually refers to the partial equilibrium study of markets in which the demand side is competitive, while the supply side is neither monopolized nor competitive. It is exclusively concerned with single period models. The two models that are mainly discussed are Cournot's and a model based on Chamberlin. In Cournot's model, it is assumed that the products of the firms are perfect substitutes and each firm decides the output levels with price being determined in the market. The Chamberlinian model allows for imperfect substitutability among the outputs of the firms, and each firm is assumed to name prices for their products. The chapter also presents some of the basic structure for the models of multi-period oligopoly. The time structure of none of these models is explicit; however, none of them makes sense when interpreted as strictly single-period models. Thus, for the best understanding of them, it is necessary to augment them by making the time relations explicit and by making an appropriate reformulation of the firm's objective functions. The chapter also examines various models in which the time structure is explicit and the firms seek to maximize discounted profit streams. The chapter also discusses models with entry and exit of firms.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 491-534, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:491-534
    Language: English
    DOI: 10.1016/S1573-4382(82)02006-2
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  • 4
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    Chapter 12 Duality approaches to microeconomic theory (1982)
    Details
    UID:
    gbv_1831647958
    ISBN: 0444861270
    Content: This chapter develops the duality between cost and production functions. The chapter derives the regularity conditions that a cost function C must have and shows how a production function is constructed from a given cost function. The chapter considers the duality between a (direct) production function F and the corresponding indirect production function G. Under certain regularity conditions, G can also completely describe the technology, and thus there is a duality between direct and indirect production functions. The duality theorems have two interpretations: one in the producer context and the other in the consumer context. The chapter discusses a variety of other duality theoremsthat is, other methods for equivalently describing tastes or technology, either locally or globally, in the one-output, N-inputs context. The mathematical theorems presented in the chapter appear to be only theoretical results devoid of practical applications. However, this is not the case. The chapter also surveys some of the applications of the duality theorems developed earlier. These applications fall in two main categories: (1) the measurement of technology or preferences and (2) the derivation of comparative statics results.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 535-599, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:535-599
    Language: English
    DOI: 10.1016/S1573-4382(82)02007-4
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  • 5
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    Chapter 13 On the microeconomic theory of investment under uncertainty (1982)
    Details
    UID:
    gbv_183164794X
    ISBN: 0444861270
    Content: This chapter describes investment theory as the study of the individual behavior of households and economic organizations in the allocation of their resources to the available investment opportunities. For the purposes of investment theory, economic organizations are characterized as being members of one of two groups: business firms that hold as assets the physical means of production for the economy and finance their production decisions by issuing financial claims or securities and financial intermediaries that hold financial claims as assets and finance these assets by issuing securities. Individuals or households are assumed to invest primarily in securities and, therefore, invest only indirectly in physical assets. The markets in which these securities are traded are called the capital markets. The natural starting point for the development of investment theory is to derive the investment behavior of individuals. It is traditional in economic theory to take the existence of households and their tastes as exogenous to the theory. However, this tradition does not extend to economic organizations and institutions. They are regarded as existing primarily because of the functions they serve instead of functioning primarily because they exist.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 601-669, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:601-669
    Language: English
    DOI: 10.1016/S1573-4382(82)02008-6
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  • 6
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    Chapter 14 Market demand and excess demand functions (1982)
    Details
    UID:
    gbv_1831647931
    ISBN: 0444861270
    Content: Market demand and market excess demand functions are defined by summing the preference-maximizing actions of consumers. These functions are central to most treatments of value theory. It discusses that the demand theory of the individual consumer has been well developed. Just as consumer demand theory is the study of properties common to demand functions that are generated by the preference-maximization of an individual consumer, market demand theory investigates properties that are shared by market demand functions. As market demand is often the observable and relevant variable for analysis, it is important to see how it is restricted by the utility hypothesis. When preferences are homothetic and the distribution of income is independent of prices, the market demand function has all the properties of a consumer demand function. The chapter discusses conditions under which market demand and market excess demand functions are consumer demand functions. It also provides an overview of Debreu's theorem, which explains that for every continuous function F that satisfies homogeneity and Walra's Law and for every compact set of positive prices K, there exists an economy with market excess demand function F on K.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 671-693, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:671-693
    Language: English
    DOI: 10.1016/S1573-4382(82)02009-8
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  • 7
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    Chapter 15 Existence of competitive equilibrium (1982)
    Details
    UID:
    gbv_1831647923
    ISBN: 0444861270
    Content: This chapter discusses that the mathematical model of a competitive economy conceived as an attempt to explain the state of equilibrium reached by a large number of small agents interacting through markets. Four distinct, but closely related, approaches to the existence problem are recognized. At first, proofs of existence of an economic equilibrium were uniformly obtained by application of a fixed-point theorem of the Brouwer type or Kakutani type or by analogous arguments. This approach, which has remained of central importance to the present, is the subject of the chapter. Second, in the past decade, efficient algorithms of a combinatorial nature for the computation of an approximate economic equilibrium were developed. Third, recently, the theory of the fixed-point index of a map and the degree theory of maps were used to establish the existence of an economic equilibrium, and finally a differential process was proposed whose generic convergence to an economic equilibrium provides an alternative constructive solution of the existence problem.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 697-743, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:697-743
    Language: English
    DOI: 10.1016/S1573-4382(82)02010-4
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  • 8
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    Chapter 16 Stability (1982)
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    UID:
    gbv_1831647915
    ISBN: 0444861270
    Content: The chapter is concerned with endogenous processes operating in an economy that brings equilibrium; the most famous and most discussed is the law of demand and supply. If, at prevailing market signals, there is a positive excess demand in a market price, it will rise; if there is a negative excess demand, it will fall. In a partial equilibrium framework when all other prices are held fixed, it seemed that this process would bring about equilibrium provided only that the excess demand in this market was a diminishing function of its price. The chapter discusses that there is a large class of economies that have unstable equilibria under the most popular form of the price mechanism. The chapter discusses the ArrowDebreu specifications in which goods are distinguished by physical characteristics, location, date of delivery, and state of nature. It is a commonplace that many of these goods lack markets in actual economies. It is also clear that many planned excess demands are not public knowledge and that one cannot sensibly retain the traditional price adjustment schema. An alternative is to study a sequence of short period equilibriaa procedure familiar from the theory of growth. The aim is to study convergence to long-run equilibrium whether in a deterministic or in a stochastic setting. Expectations and their formation are central to this kind of approach once durable goods and production lags are included. One is then concerned with convergence to rational expectation equilibrium.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 745-793, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:745-793
    Language: English
    DOI: 10.1016/S1573-4382(82)02011-6
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  • 9
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    Chapter 17 Regular economies (1982)
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    UID:
    gbv_1831647907
    ISBN: 0444861270
    Content: The theory of regular economies is useful for the studies of the local uniqueness of equilibria, continuity of the equilibrium price correspondence, and possibility of comparative statics. The theory of regular economies also helps give a better understanding of the core correspondence, because core allocations in a large economy is approximately decentralized through prices. There is an intimate relationship between the theory of regular economies and the new methods of computing economic equilibria. The chapter discusses that regularity studies play a role in fields related to economic equilibrium theory. For instance, the general complementarity problem in mathematical programming has been investigated by regularity methods. Another field where regularity methods are applied is game theory. The chapter also focuses on the ArrowDebreu equilibrium theory. The chapter discusses other problems arising in this context, such as the basic problem of existence of price equilibria or the problem of how equilibrium prices are reached. The investigation of regular equilibria has led to a revival of calculus methods in equilibrium theory. A valuable comprehensive study of many important questions of equilibrium theory is presented in the chapter in a differentiable framework.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 795-830, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:795-830
    Language: English
    DOI: 10.1016/S1573-4382(82)02012-8
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  • 10
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    Chapter 18 Core of an economy (1982)
    Details
    UID:
    gbv_1831647893
    ISBN: 0444861270
    Content: The core of an economy consists of those states of the economy that no group of agents can improve upon. A group of agents can improve upon a state of the economy if the group, by using the means available to it, can make each member of that group better off, regardless of the actions of the agents outside that group. This chapter explains that the core of an economy might be empty. But if an allocation in the core exists at all, there are, in general, many such allocations. The core is a rather theoretical equilibrium concept. It is used to provide a theoretical foundation of a more operational equilibrium conceptthe competitive equilibriumwhich, in fact, is a very different notion of equilibrium. The allocation process is organized through markets; there is a price for every commodity. All economic agents take the price system as given and make their decisions independent of each other. The equilibrium price system coordinates these independent decisions in such a way that all markets are simultaneously balanced. A state of the economy that is decentralized by an equilibrium price system cannot be improved upon by cooperation. This proposition strengthens the well-known proposition of welfare economics to the case where ownership in initial endowments is not collective but individual. For economies with a finite number of participants, the influence of every agent is not strictly negligible, and the core is larger than the set of competitive equilibria.
    In: Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 831-877, 0444861270
    In: 9780444861276
    In: year:1982
    In: pages:831-877
    Language: English
    DOI: 10.1016/S1573-4382(82)02013-X
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