Derivation of optimal spatial prices

Abstract

The price of a good prevailing at some local market point may or may not be identical to the price of that same good at another market point. Price differentials over regions depend in part upon the number and locations of firms which sell to these regions, and on the demand curves of buyers. The present paper evaluates the price policy of a firm selling over a set of linearly extended buying points. It derives the optimal spatial prices under alternative assumptions of consumer behavior and demand. It demonstrates mathematically as well as graphically that a spatial monopolist maximizes profits by subdividing his market into economic submarkets, utilizing fob mill prices for some submarkets, and optimal discriminatory prices for the remaining ones. Thus it explains the use of fob pricing over selected distances in a firm's market area notwithstanding the apparently greater profitability of a discriminatory price policy throughout a firm's market space.