Explanation:
The two concepts represent theories about how a modern society works, and there are some fundamental relationships between them. But at bottom they are separate social factors that allow for independent forms of social causation. The first is fundamentally concerned with the economic structure of a society, the systems through which wealth is created and distributed, and the second is concerned with the expressions of politics within a society.
Both class and power can be placed into the dichotomies of structure and agency. The class system sets some of the parameters of "structure" within which individuals act, but it also creates some of the motivations and features of consciousness that constitute the agency of class actors. The forms of power present in a given society define some of the features of agency on the basis of which individuals and groups pursue their goals; but it is also fair to say that the institutions and social relations that define social power are also a part of the structured environment of action that is present in the social world. So both power and class are simultaneously features of structure and agency within a complex society; and the configurations created by class and power are causally inter-related without being isomorphic.
A class system can be defined as a system for producing social wealth in which productive resources and the results of production are unevenly divided across different groups. The producing class is "exploited" by the ascendant class: wealth is transferred from producers to owners. Serfs and lords, slaves and masters, workers and owners represent the primary classes of feudalism, ancient slavery, and nineteenth century capitalism. Within any society there are groups that fall outside the primary classes -- small traders, artisans, small farmers, intellectuals. But it is central to Marx's theory of class, that there is a primary cleavage between owners of the means of production and the direct producers, and that this cleavage embodies a fundamental conflict of interest between the two groups.
First, a class system constitutes a set of social inequalities within which there are deep conflicts of interest. So a class system sets the stage for the exercise of power; various groups have an interest in wielding power over others within a class system. Ascendant groups have an interest in sustaining the productive economic activities of subordinates whom they exploit, and they have an interest in squelching acts of resistance. But likewise, subordinate groups have an interest in using instruments of power to reduce or overturn the exploitative social relations within which they function.
Second, a class system assigns resources and positions to different groups and individuals that greatly influence the nature and weight of the instruments and tactics of power available to them. Owners have economic assets, alliances, and the state in their column. Producers have their numbers and their key locations in the economic process. A strike of rail workers is a substantial exercise of power, given the centrality of transport in a complex economy. So the particulars of a class system provide key determinants of the distribution of power within society.
Third, a class system also creates a subjectivity of power, powerlessness, and resistance that may iterate into new forms of the exercise of power. It may be an effective instrument of social control to cultivate a subjectivity of powerlessness in subordinate groups. And likewise, it may be materially empowering to subordinate groups to cultivate a culture of resistance -- by making collective action and solidarity more attainable, for example.
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