The correct answer is: A. at minimum level
A firm in perfect competition will be in equilibrium when its average cost (AC) is at its minimum level. This is because, in perfect competition, firms are price-takers, meaning that they cannot influence the market price. As a result, they must produce at the level where marginal cost (MC) is equal to price. When MC is equal to price, AC is also at its minimum level.
Option B is incorrect because a firm in perfect competition will not necessarily be in equilibrium when its AR is equal to AC. In fact, a firm in perfect competition may be in equilibrium even if its AR is below its AC. This is because, in perfect competition, firms are price-takers, meaning that they cannot influence the market price. As a result, they must produce at the level where MC is equal to price, regardless of whether or not their AR is equal to AC.
Option C is incorrect because a firm in perfect competition will not necessarily be in equilibrium when it is covering only prime cost of production. Prime cost of production is the cost of production that includes only the variable costs of production. In perfect competition, firms must also cover their fixed costs in order to be in equilibrium.
Option D is incorrect because it is not one of the possible answers.