A spatial economic model under network externalities: symmetric equilibrium and efficiency

Abstract

This paper studies a spatial economic model under network externalities, assuming a quadratic transport cost function. A classical circular model is applied where the consumers, each with a fixed demand, are uniformly distributed along the circumference of a circle. Assuming symmetric locations of profit-maximizing suppliers, a unique symmetric price equilibrium is derived under both positive and negative network externalities. The price equilibrium is obtained using the tridiagonality property of the demand system. The equilibrium price is higher with negative network externalities than the price without externalities whereas the converse is true with positive network externalities. The efficiency loss of the free entry equilibrium is studied in terms of the price of anarchy. Numerical experiments suggest that the price of anarchy is robust to weak externalities but can be significant under strong network externalities.