Monotonicity Properties of Wholesale Price Contracts
Mathematical Social Sciences 56(1): 127-143 (2008)
Posted: 20 Sep 2007 Last revised: 17 Jul 2012
Date Written: December 6, 2006
This paper contributes to the supply chain contracts literature in economics and operations by performing qualitative sensitivity analysis on a wholesale price contract in a two-echelon supply chain setting. It is assumed that the upstream supplier has complete information about the costs and revenue function of the downstream retailer and that the supplier acts as a Stackelberg leader.
Monotone statics analysis is particularly useful in gaining insight when closed form solutions are not available. It is shown that an equilibrium wholesale price weakly increases with an increase in the supplier production cost rate, but it may increase or decrease with an increase in the retailer cost rate. As either the supplier production cost or the retailer cost increases, the supplier profit decreases weakly. Additional sensitivity analysis is performed assuming certain properties of the retailer revenue function.
Monotonicity results are applied to the analysis of a newsvendor problem examined in (Lariviere and Porteus 2001). This paper extends their work, by establishing properties of the newsvendor demand distribution that guarantee monotonicity of the contract parameters, without requiring a unique contract solution.
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