Increasing Returns and Efficiency

By Martine Quinzii | Go to book overview

6
THE CORE

6.1 Why the Core?

Every competitive equilibrium of an economy with convex production sets has the property that agents will voluntarily participate in the production and exchange process. At the simplest level this is true because it is individually rational for each agent to participate, in the sense that all agents are better off in the equilibrium than with their own initial endowment. This property is no longer true for the concept of a marginal cost pricing equilibrium in an economy with increasing returns. For then, as we have seen, marginal cost pricing creates a deficit which must somehow be financed. A particular mode of financing the deficit (i.e., a given income map) may make some agents worse off in the equilibrium than with their own initial endowments. Even if agents are better off in an equilibrium they may object to the allocation if they feel that they are financing too large a component of the deficit of the public sector.

In this chapter we shall adopt a more abstract approach to the problem of finding acceptable ways of financing the deficit. We consider the general problem of finding allocations (i.e., production plans for firms and consumption bundles for agents) which are acceptable to all agents in the economy. We use the framework of cooperative game theory and formulate the problem via the concept of the core as follows. Does there exist an allocation in the core of an economy in which the production sector exhibits increasing returns to scale?

To define the concept of the core the allocations in the economy must be viewed as the result of a cooperative process in which agents accept to exchange goods and to participate in the production of goods through the provision of inputs such as labor. Exchange and production normally generate a surplus of welfare relative to the initial endowment allocation with no production. An allocation for the economy describes a feasible way of creating and distributing the surplus. If an allocation, feasible with the resources of all agents, is worse from the point of view of a particular agent than just consuming his or her initial resources then this allocation

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Increasing Returns and Efficiency
Table of contents

Table of contents

  • Title Page iii
  • Preface v
  • Contents vii
  • 1: Introduction 3
  • Notes 10
  • 2 - Necessary Conditions for Efficiency 13
  • 3 - Marginal Cost Pricing Equilibrium 27
  • 4 - Efficiency 41
  • 5 - Existence 77
  • 6 - The Core 101
  • Notes 152
  • 7 - Conclusion 153
  • References 155
  • Index 161
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