Core and Equilibria of a Large Economy. (PSME-5)

Core and Equilibria of a Large Economy. (PSME-5)

WERNER HILDENBRAND
Copyright Date: 1974
Pages: 260
https://www.jstor.org/stable/j.ctt13x0tjf
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  • Book Info
    Core and Equilibria of a Large Economy. (PSME-5)
    Book Description:

    Can every allocation in the core of an economy be decentralized by a suitably chosen price system? Werner Hildenbrand shows that the answer is yes if the economy has "many" participating agents and if the influence of every individual agent on collective actions is "negligible." To give a general and precise definition of economics with this property he considers both economies with a continuum of agents, and a sequence of economies with an increasing number of participants. In both cases this leads to a measure theoretic formulation of economic equilibrium analysis.

    In the first part of the book the relevant mathematics is developed. In the second part the continuity and convexity properties of the total demand of a consumption sector are investigated. An important result is the equivalence between the core and the set of Walras equilibria for an exchange economy with a continuum of agents. The author then deals with limit theorems on the core for purely competitive sequences of exchange economies. In the last chapter the core and the set of Walras equilibria for a coalition production economy and the relation between these two equilibrium concepts are studied.

    Originally published in 1974.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6947-3
    Subjects: Economics

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. PREFACE
    (pp. vii-viii)
    W. H.
  4. PART I MATHEMATICS
    (pp. 1-80)

    The notion of asetis taken here as a primitive concept. The objects constituting a set are calledelementsof the set.

    $x \in S$meansxis an element of the setS(xbelongs toS).

    $x \notin S$meansxis not an element of the setS.

    $T \subset S$means every element of the setTis also an element of the setS(Tis asubsetofS,orTiscontainedinS).

    T=Smeans and$T \subset S$and$S \subset T$(SandTare equal).

    $\phi $denotes the set without any element (empty set).

    {x,y,z, ...}...

  5. PART II ECONOMICS
    • CHAPTER 1 DEMAND
      (pp. 83-122)

      Acommodityis a good or a service. It is characterized by its physical characteristics (properties) and the date and the location at which it will be available. Thus, given physical characteristics (e.g. wheat of a specified type) made available at different dates and / or different locations will be treated as different commodities. Typical examples of commodities are consumption goods related to food, housing, and clothing. A typical example of a service is labor. The physical characteristic of labor is the task performed.

      Thequantityof a commodity can be expressed by a number. The physical characteristics, which define...

    • CHAPTER 2 EXCHANGE
      (pp. 123-176)

      In this chapter we study a simple form of economic activity: the exchange of commodities. Thus, we consider a set of individuals, each of whom is described by his consumption set, his preference relation, and his initial endowment. Hence by an element in the space (ρ X R¹, the space of agents’ characteristics.

      An exchange economy then is defined by a mapping of a finite setA, the set of agents, into the space (ρ X R¹ of agents’ characteristics. For reasons which will become clear later, we shall also consider setsAof agents which are infinite. In the...

    • CHAPTER 3 LIMIT THEOREMS ON THE CORE
      (pp. 177-208)

      In Theorem 1 of the last chapter we showed that every allocationfin the core of an atomless exchange economy ε can be “decentralized” by a suitably chosen price vectorp, that is to say, the commodity vectorf(a) which is allocated to agentain the core-allocationfbelongs to the demand set φ(a,p). Thus, if the price systempprevails, then any other commodity vector preferred tof(a) by agentawould exceed his incomepe(a).

      In this chapter we want to show that in asimpleexchange economy with “sufficiently many” participants, every allocation in the...

    • CHAPTER 4 ECONOMIES WITH PRODUCTION
      (pp. 209-233)

      The last chapters were confined to pure exchange economies: the only activity the agents of a coalition could carry out was to re distribute their initial endowments. Now we extend this model by considering for every coalition of agents its productive capabilities as well. There are noa priorigiven firms or producers. The productive capabilities of every coalition S of economic agents is described by a set of input-output combinations, theproduction possibility set Ysfor the coalitionS.The production possibility setYscan be described by a subset in the commodity space R¹ if we use the...

  6. SUMMARY OF NOTATION
    (pp. 234-235)
  7. BIBLIOGRAPHY
    (pp. 236-246)
  8. NAME INDEX
    (pp. 247-248)
  9. SUBJECT INDEX
    (pp. 249-251)
  10. Back Matter
    (pp. 252-252)