The Degree of Monopoly and Multivariable Sales Policies

  • Klaus Spremann

Summary

The degree of monopoly for multivariable sales policies and multipart tariffs, where these output decisions may be corner solutions of the admissible set, and where there may be kinks in the demand or cost functions is analyzed within a general model. A monopoly is understood as a situation where an agent (the firm) affects the aggregate welfare of the economy by his output decisions via external effects. These external effects and the marginal loss of welfare due to the selfishness of the agent can be measured by two real numbers ω+, ω-, which have the meaning of indices of aggression against and consideration of the society’s objective. Hence the degree of monopoly is defined as a function, which assigns to every situation a pair (ω+, ω-). The determination of this pair (ω+, ω-) for a given situation requires a special linearization technique for sets and functional s which is termed homogeneous approximation of the situation under consideration. The main result states the failure of efficiency of situations, which reveal (ω+ > ω-); and examples illustrate that almost all situations with multivariable sales policies are non-efficient in the following sense : There is a slight modification of the agent’s policy which is admissible and increases both his own utility (profit) and the society’s welfare. Conditions for such a “non-tangency” of iso-profit and iso-welfare loci are derived in real Banach spaces and expressed in terms of (the value of) the degree of monopoly (ω+, ω-).

Keywords

Propen Income Dition Exter Rote 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Klaus Spremann

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