Impact of Risk Aversion on Price and Quality Decisions under Demand Uncertainty via the CARA Utility Function

Abstract

This paper investigates optimal price and quality decisions of a manufacturer-retailer supply chain under demand uncertainty, in which players are both risk-averse decision makers. The manufacturer determines the wholesale price and quality of the product, and the retailer determines the retail price. By means of game theory, we employ the constant absolute risk aversion (CARA) function to analyze two different supply chain structures, that is, manufacturer Stackelberg model (MS) and retailer Stackelberg model (RS). We then analyze the results to explore the effects of risk aversion of the manufacturer and the retailer upon the equilibrium decisions. Our results imply that both the risk aversion of the manufacturer and the retailer play an important role in the price and quality decisions. We find that, in general, in MS and RS models, the optimal wholesale price and quality decrease with the risk aversion of the manufacturer but increase with the risk aversion of the retailer, while the retail price decreases with the risk aversion of the manufacturer as well as the retailer. We also examine the impact of quality cost coefficient on the optimal decisions. Finally, numerical examples are presented to illustrate the different degree of effects of players’ risk aversion on equilibrium results and to compare results in different models considered.