On Optimal Operation of a Jointly Owned Enterprise.
Abstract
An enterprise is owned jointly by m agents, the i-th agent's share being theta sub i > 0 where the sum of theta sub i's = 1. The enterprise is able to produce some non-negative n-vector x of goods where x lies in some convex production set X. An operation consists of choosing a vector from X and distributing it among the agents. The problem is to find an operation such that the value of the i-th agent's bundle measured in a given price system is proportional to theta sub i and such that operation is (Pareto) optimal with respect to the agent's preferences. It is shown under standard assumptions that operations which are both optimal and proportional always exist. It is conjectured that if preferences are given by separable concave utility functions then such operations are unique. This is proved (a) when there are only two goods; (b) when X is a simplex; and (c) when X represents production of a single good over n time period. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1981
- Accession Number
- ADA104207
Entities
People
- David Gale
- Hilton Machado
Organizations
- University of California, Berkeley