Pareto and Kaldor–Hicks improvements with revenue-sharing and wholesale-price contracts under manufacturer rebate policy

Abstract

Rebate policies are widely used by manufacturers to stimulate sales. This paper analyzes a supply chain with revenue sharing and wholesale price contracts under manufacturer rebate policy, where the stochastic multiplicative demand function depends on both retail price and manufacturer rebate. We identify Stackelberg equilibrium for the supply chain under each contract. It is our finding that under the manufacturer’s respective optimal decisions for revenue sharing and wholesale price contracts with rebates, the retailer’s optimal retail prices are the same. We recognize sufficient conditions under which a revenue sharing contract and a wholesale price contract with rebate can achieve Pareto improvement, i.e., both the manufacturer and the retailer obtain a greater expected profit, compared with the cases without rebate. A sufficient condition is found, under which a revenue sharing contract with rebate policy can achieve Kaldor–Hicks improvement, i.e., yielding a greater expected profit for the manufacturer, a lower expected profit for the retailer, and a greater expected total profit, over pure revenue sharing contract without rebate. Further, it is shown that with rebate, a revenue sharing contract can achieve Kaldor–Hicks improvement over a wholesale price contract. Finally, our findings are demonstrated using numerical studies.