This paper presents an analysis of the bullwhip effect and net-stock amplification in a three-echelon supply chain considering step-changes in the production rates during a product's life-cycle demand. The analysis is focused around highly complex and engineered products (e.g., automobiles), that have relatively long production life-cycles and require significant capital investment in manufacturing. Using a simulation approach, we analyze three stages of the product life-cycle including low volumes during product introduction, peak demand, and eventual decline toward the end of the life-cycle. Parts of the simulation model have been adopted by a major North-American automotive OEM as part of a scenario analysis tool for strategic supply network design and analysis. The simulation results show that performance of a system as a whole deteriorates when there is a step-change in the life-cycle demand. While restriction in production capacity does not significantly impact the bullwhip effect, it increases the net stock amplification significantly for the supply chain setting under consideration. Furthermore, a number of important managerial insights are presented based on sensitivity analysis of interaction effect of capacity constraints with other supply chain parameters.