Extant supply chain coordination research has largely focused on additive linear demand functions. However, in many markets such as consumer electronics, e-commerce, and luxury products, demand is better represented as a multiplicative function of price. This study develops a three-echelon decentralized supply chain model consist of one supplier, one manufacturer, one retailer under multiplicative price-dependent demand. This study analyses the contract sequence choices involving wholesale price (WP) and linear two-part tariff (LTT) contracts using a Stackelberg game of full information. Further, closed form solutions of all the optimal parameters are derived. Finally, study also examines how demand elasticity influences profit distribution among agents of supply chain. Numerical analysis demonstrates that multiplicative demand magnifies the sensitivity of channel profits to price elasticity, strengthening the incentive for long-term contracts. Managerial implications are provided for suppliers and manufacturers operating in elastic markets.