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

WERNER HILDENBRAND
Pages: 260
https://www.jstor.org/stable/j.ctt13x0tjf

1. Front Matter
(pp. i-iv)
(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)