This paper studies the impact of supply chain power structure on firms' profitability in an assembly system with one assembler and two suppliers. Two power regimes are investigated—in a Single Power Regime, a more powerful firm acts as the Stackelberg leader to decide the wholesale price but not the quantity whereas in a Dual Power Regime, both the price and quantity decisions are granted to the more powerful firm. Tallying the power positions of the three firms, for each power regime we study three power structures and investigate the system's as well as the firms' preference of power. We find that when the assembler is the most powerful firm among the three, the system-wide profit is the highest and so is the assembler's profit. The more interesting finding is that, if the assembler is not the most powerful player in the system, more power does not necessarily guarantee her a higher profit. Similarly, a supplier's profit can also decrease with the power he has. These results contrast with the conclusion for serial systems, where a firm always prefers more power. We also find that when both suppliers are more (less) powerful than the assembler, it can be beneficial (indifferent) for everyone if the two suppliers merge into a mega supplier to make decisions jointly. When the assembler is more powerful than one supplier and less so than the other, it is always better for the system to have the two suppliers merge, and for each individual firm, merging is preferred if the firm becomes the more powerful party after merging.