If a firm under a particular market structure has zero costs or only fixed cost, and its equilibrium output is determined where marginal revenue is zero, this firm is operating under which market structure?

Introduction / Context:
This question digs deeper into the idea of profit maximisation when a firm faces no variable cost and only fixed cost. Under such conditions, total cost does not change with output, so the firm behaves like a revenue maximiser. The question connects this to the condition that equilibrium is reached where marginal revenue is zero and asks which market structure matches this description.

Given Data / Assumptions:

• The firm's cost structure consists of zero variable cost or only fixed cost.
• Profit equals total revenue minus a constant total cost.
• Profit maximisation therefore coincides with total revenue maximisation.
• Equilibrium is said to occur at the point where marginal revenue is zero.
• Standard textbook models of perfect competition and monopoly are assumed.

Concept / Approach:
A monopoly faces a downward sloping demand curve and therefore a downward sloping marginal revenue curve that can cross zero. The revenue maximising output is where marginal revenue becomes zero, because beyond that point extra units add no revenue and may reduce it. A perfectly competitive firm, in contrast, faces a perfectly elastic demand curve at the market price and has marginal revenue equal to price, which does not fall to zero within the normal range of operation. Hence, the combination of zero cost and equilibrium at marginal revenue equal to zero points clearly to monopoly.

Step-by-Step Solution:
1. With zero variable cost, total cost is fixed and independent of output.2. Profit maximisation under constant total cost is equivalent to maximising total revenue.3. Total revenue is maximised where marginal revenue, the change in revenue from selling one more unit, becomes zero.4. For marginal revenue to decline to zero, the firm must face a downward sloping demand curve, so that price falls as quantity increases.5. In basic theory, a single seller facing the whole market demand curve is a monopolist; this is where we typically draw a downward sloping marginal revenue curve crossing the quantity axis.6. Therefore, the market structure described is monopoly.

Verification / Alternative check:
Using a simple linear demand curve P = a - bQ, total revenue is TR = aQ - bQ^2 and marginal revenue is a - 2bQ. At marginal revenue equal to zero, Q = a/(2b), which is the revenue maximising output. If cost is zero, this is also the profit maximising output. This is the standard monopoly revenue maximisation result. In perfect competition, marginal revenue equals the constant market price, so it does not fall to zero as output increases, which shows that the described condition cannot apply to a competitive firm.

Why Other Options Are Wrong:
Option A: Perfect competition involves many small firms that are price takers, and their marginal revenue equals the market price. It does not fall to zero while the price remains positive.
Option C: Oligopoly has a few firms whose outcomes depend on strategic interaction. The simple rule marginal revenue equal to zero for a firm with full market control is not a standard description of equilibrium here.
Option D: Monopolistic competition features many firms with differentiated products, but the textbook marginal revenue equal to zero when cost is zero is usually presented in the context of a pure monopoly.
Option E: Duopoly is a special case of oligopoly with two firms, again involving strategic interaction rather than a single firm controlling the entire market.

Common Pitfalls:
Students sometimes treat monopoly and monopolistic competition as almost the same. A simple cue is that questions referring to a single firm that controls the market and sets price using the entire demand curve typically point to monopoly. Another pitfall is forgetting that marginal revenue equal to zero is a revenue maximisation condition, not the usual profit maximisation condition. Only when marginal cost is zero over the relevant range does profit maximisation coincide with this condition.

Final Answer:
When a zero cost firm chooses equilibrium output where marginal revenue is zero, it is operating as a monopoly.