We consider the exercise of power in competitive markets for goods, labour and credit. We offer a definition of power and show that if contracts are incomplete it may be exercised either in Pareto-improving ways or to the disadvantage of those without power. Contrasting conceptions of power including bargaining power, market power, and consumer sovereignty are considered. Because the exercise of power may alter prices and other aspects of exchanges, abstracting from power may miss essential aspects of an economy. The political aspect of private exchanges challenges conventional ideas about the appropriate roles of market and political competition in ensuring the efficiency and accountability of economic decisions.