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Optimal price and marketing policies with stock demand

This paper presents a model of optimal pricing and marketing policies in “stock demand” markets, such as the financial services industries, cell phones and mandatory “privatized” social security. In these markets the clientele with contracts evolves slowly. It is shown that in a perfect equilibrium, the unique optimal price path leads to a steady state where the effective price elasticity depends on the rate of depreciation of the clientele through exit, on the discount rate, and on the elasticity of both entry and exit flows to prices. A perfect symmetric equilibrium does not exist always, however. Under some parameter conditions there can be multiple asymmetric Nash equilibrium in marketing investment, which are more reasonable than the symmetric equilibrium because the latter does not meet a refinement we propose. The asymmetric equilibria lead to a war of attrittion and to mergers that concentrate the industry. It is shown that in the case of mandatory demand, for an important region of parameter values, only concentrated industry structures allow a perfect symmetric equilibrium to exist, while excessively atomistic structures encourage marketing wars and mergers.