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This paper investigates the difference in bullwhip effects in online and offline retail supply chains, offering insights into how frequent price discounts in e-commerce influence the bullwhip effect in the online retail supply chain. We consider a two-level online retail supply chain with a manufacturer and an online retailer in which the demand faced by the retailer is price sensitive and based on the price discount. Assuming that the online retailer employs an optimal order-up-to inventory policy with an optimal minimum mean-squared error forecasting technique, we derive the expression of the bullwhip effect in the online retail supply chain and make analysis and comparison. Finally, we develop a dual-channel supply chain model to directly observe the impact of price discounts in e-commerce on the bullwhip effect. The results suggest that price discounts in the online retail market generally amplify the bullwhip effect in the online retail supply chain, but in certain conditions, the bullwhip in the online supply chain may be smaller than that in the offline supply chain. We also find that the relationship between the lead time and the bullwhip effect in the online supply chain presents a distinctive feature contrary to the conclusions of previous studies. Based on the analysis, we develop important managerial insights regarding online retail supply chains. [ABSTRACT FROM AUTHOR]