In the short run, which of the following condition is mandatory for a firm for its profit maximization at q₀?

Option 1 -> Ensures economic profit but not mandatory for profit maximization; a firm can maximize profit even when operating at a loss in the short run.

Option 2 -> At profit maximization, Price equals Marginal Cost (P=MC), not greater than it; if P>MC, the firm should increase production.

Option 3 -> For profit maximization, Marginal Cost must be increasing (not decreasing) at q₀ to satisfy the second-order condition.

Option 4 -> This represents the shutdown condition; if P<AVC, the firm minimizes loss by shutting down, so P>AVC is mandatory for any production to occur.

Hence, Option 4: Price must be greater than the average variable cost -> In the short run, a firm will produce at q₀ only if price covers average variable cost (P≥AVC). This is the shutdown rule: if P<AVC, the firm loses less by producing zero. Even if the firm makes losses (P<AC), it should continue operating as long as P>AVC because it covers variable costs and contributes something toward fixed costs. This condition is mandatory for production at any positive quantity q₀. -> correct