A monopolist's two best quantities

Profit is largest where marginal revenue equals marginal cost. Up to that point each unit adds more to revenue than to cost; past it the reverse holds. On the graph the MR line crosses the MC curve directly above Q1 (at the height of P1). So Q1 is the profit-maximizing quantity. The monopolist would then charge the price read off the demand curve above Q1, which is P6.

Total revenue is largest where MR = 0. Before that point each unit still raises revenue; after it, MR is negative and selling more lowers revenue. The MR line hits the quantity axis at Q3, so Q3 is the revenue-maximizing quantity.

Notice that Q3 is larger than Q1. A firm chasing revenue ignores cost, so it produces more than the profit-maximizing amount.

Each choice

• A. Q5 is where demand meets ATC, the zero-profit output a regulator might aim for with a fair-return price. Q2 is where MC crosses ATC at its lowest point. Neither answers either half of the question.
• B. Q4 is where MC crosses demand on the way up, which is the allocatively efficient quantity, not the monopolist's profit choice. The revenue half, Q3, is right.
• C. The revenue half is right, but profit is not maximized where MR is zero. At Q3 the cost of the last units is positive while they add nothing to revenue, so profit is lower than at Q1.
• D. The profit half is right. Q4 is where MC crosses demand, not where MR reaches zero; the MR line hits the axis at Q3.
• E (correct). Profit peaks where MR = MC; total revenue peaks where MR = 0.