in the the longrun, a firm must shut down if its average revenue is?

Analyze the question: It asks when a firm must shut down in the long run. This is about the relationship between average revenue (AR, which is the price) and costs.

Concept:

• Short run: a firm has fixed costs it must pay whether or not it produces. It keeps operating as long as AR (price) covers average variable cost (AVC). It shuts down only if AR < AVC.
• Long run: all costs are variable, so there are no fixed costs. The firm must cover all of its costs, meaning average cost (AC). If AR < AC, the firm makes a loss and exits the industry.

Checking each option:

• A. AR greater than AC: the firm makes supernormal profit, so it stays and others are attracted in. Not a shutdown.
• B. AR less than AVC: this is the classic shutdown condition. It is strictly the short-run rule, but if AR is below AVC, AR is certainly below the long-run AC as well, so the firm cannot survive in either period. The firm cannot even cover its variable costs.
• C. AR equal to minimum AC: this is the long-run equilibrium of a perfectly competitive firm (normal profit). The firm stays.
• D. AR equal to AC: the firm earns normal profit, covers all its costs, and stays.

Reasoning on the key: Strictly speaking, the long-run exit condition is AR < AC. That exact option is not offered. Of the choices given, only B describes a situation where the firm definitely has to shut down, since A, C and D all describe a firm that covers its costs.

Answer: B. The firm shuts down when AR falls below average variable cost.

Exam tip: Remember it as "Short run: AR < AVC → shut down. Long run: AR < AC → exit." If the exam does not list the long-run version, pick the option where revenue fails to cover costs. Options where AR ≥ AC mean the firm stays.