Competition In Two-Tier Serial And Assembly Supply Chains With General Consumer Utility Functions

We consider two-tier serial supply chains with multiple entrants at each tier and investigate the existence of an equilibrium under a general consumer utility function corresponding to a general inverse price-demand function. In the case of a polynomial inverse price-demand function, we obtain closed-form expressions for the equilibrium prices, the production quantities and the profits of the supply chain entrants. We conclude that the quantity of finished goods supplied to the market, the maximum total operating profit accrued by all supply chain entrants, and the elasticity of the (imputed) demand are all sensitive to the elasticity of slope of the polynomial inverse price-demand function. We then extend our analysis to two-tier assembly supply chains and conclude that most of our results extend to them as well.