Change in Size of Facilities and Social Optimal Allocation of Resources in a Competitive Environment

Abstract

This paper attempts to clarify (i) how the sizes of facilities should be changed and (ii) how they are changed, where competitive facilities are distributed on urban space. (i) Firstly, the optimal allocation of investment, which maximizes social benefit, and optimal redistribution of resources among facilities are found. (ii) Secondly, increase and decrease of social benefit are examined under the circumstances, which the sizes of facilities are changed as a result of seeking profits by each manager of facilities. This paper succeeds to show that the social benefits always increase in accordance with the change of sizes, especially utility is defined as the logarithm of size.