Profit maximisation: total and marginal approaches
Profit is highest where the gap between TR and TC is widest. That is where MR = MC and marginal cost is rising.
Revenue and profit
Total revenue (TR) = price × quantity. Average revenue (AR) = TR ÷ Q, which equals price. Marginal revenue (MR) = ΔTR ÷ ΔQ, the extra revenue from one more unit. Profit = TR − TC. Because economic costs include the owner's opportunity cost, zero economic profit means the firm earns normal profit: just enough to stay in the business. Anything above that is supernormal (economic) profit. Traditional theory assumes firms aim to maximise profit, and there are two ways to find the best output.
Worked example 1: the total approach
The bakery (TC for 0-6 batches: Rs. 10,000; 14,000; 17,000; 19,000; 22,000; 27,000; 34,000) can sell any number of batches at Rs. 6,000 each. Find the profit-maximising output using TR and TC.
- TR = 6,000 × Q: 0; 6,000; 12,000; 18,000; 24,000; 30,000; 36,000.
- Profit = TR − TC: Q0: −10,000; Q1: −8,000; Q2: −5,000; Q3: −1,000.
- Q4: 24,000 − 22,000 = 2,000. Q5: 30,000 − 27,000 = 3,000. Q6: 36,000 − 34,000 = 2,000.
- The largest profit is Rs. 3,000 at 5 batches.
Produce 5 batches a day; maximum profit is Rs. 3,000.
Worked example 2: the marginal approach
Same bakery: price (and so MR) is Rs. 6,000 per batch. MC of batches 1-6 is Rs. 4,000; 3,000; 2,000; 3,000; 5,000; 7,000. Find the best output by comparing MR and MC.
- Rule: produce a unit if it adds at least as much to revenue as to cost (MR ≥ MC).
- Batches 1 to 5: MR = 6,000 is greater than MC (4,000, 3,000, 2,000, 3,000, 5,000), so each adds to profit.
- Batch 5 adds 6,000 − 5,000 = Rs. 1,000 to profit.
- Batch 6: MC = 7,000 > MR = 6,000, so it would reduce profit by Rs. 1,000 (3,000 → 2,000).
- Stop at 5 batches: MC is rising, and the next batch's MC (7,000) would exceed MR.
Both approaches give 5 batches and a profit of Rs. 3,000. The marginal approach reaches it without computing every profit.
Reading the two approaches on diagrams
The marginal decision rule
If MR < MC for the last unit, cut output: that unit loses money.
Other business objectives
- Sales revenue maximisation (Baumol): managers may push sales to the point where MR = 0, subject to a minimum profit.
- Growth maximisation: bigger market share, new branches and acquisitions.
- Satisficing (Simon): aim for 'good enough' profit that keeps shareholders content.
- Social and environmental goals: corporate social responsibility, community programmes.
- Survival: in a crisis, covering costs and keeping staff matters more than maximum profit.
A bakery or hotel deciding whether to stay open an extra hour is applying MR = MC: if the extra sales cover the extra wages, power and materials, the hour adds profit. Sri Lankan listed firms report profit to shareholders under SLFRS, but managers decide output at the margin.
Structured question: “Given price Rs. 6,000 and a TC schedule, find the profit-maximising output using both the total and marginal approaches.” Profit = TR − TC is largest (Rs. 3,000) at Q = 5; MR (6,000) ≥ MC up to the 5th unit, and MC of the 6th (7,000) exceeds MR.
Essay: “Explain profit maximisation using the total revenue-total cost approach and the marginal revenue-marginal cost approach.” Define TR, MR, TC, MC and profit; draw TR-TC with the widest gap; draw MR-MC with MC cutting MR from below; work a numerical example; mention other objectives.
Short answer: “State the two conditions for profit maximisation.” MR = MC (first-order) and MC must be rising, cutting MR from below (second-order).
Keep going while MR beats MC; stop when they meet. And check MC is rising, or you have found the worst point, not the best.