Profit maximisation: the three conditions

Detail

1. What profit maximisation means

• Profit (π) is the money left after paying all costs.
• Formula: π = TR − TC.
• TR (total revenue) = price × quantity sold = p × q.
• TC (total cost) = TFC + TVC.

• TFC (total fixed cost) is a cost that does not change with output, such as rent. TVC (total variable cost) changes with output, such as raw material or wages.

• Profit maximisation means the firm chooses the output at which TR − TC is as large as possible.

• Perfect competition is a market with many small firms that all sell the same product. No single firm can change the price, so each firm is a price-taker: it can sell any quantity at the market price p.

2. NCERT's assumptions and the alternative views

• NCERT treats the firm as a "ruthless profit maximiser".
• The firm sells everything it produces.

• So output = quantity sold in this chapter.

• NCERT itself calls this assumption critical, if somewhat unreasonable.

• Baumol's sales (revenue) maximisation (beyond NCERT):
• The firm tries to make its sales revenue as large as possible, not its profit.
• It still has to earn a minimum profit, enough to keep shareholders satisfied.

• The logic: managers' pay and prestige depend more on the size of the firm than on its profit.

• Simon's satisficing (beyond NCERT):

• Satisficing means aiming for a "good enough" result, not the best possible one.
• Simon described it as reaching acceptable economic targets while keeping complications and risks low. He set this against the traditional focus on maximising profit [4].
• It rests on bounded rationality: people have incomplete information and limited thinking capacity. So they do not check every option. They often pick the first one that is good enough [5].
• Herbert A. Simon won the 1978 Nobel Prize in Economics for this work [4].

3. Condition 1 — MR = MC, i.e. p = MC

• Marginal revenue (MR) is the extra revenue from selling one more unit: MR = ΔTR / Δq.
• Marginal cost (MC) is the extra cost of producing one more unit: MC = ΔTC / Δq.
• The MR = MC rule: profit is highest where MR = MC.
• While MR > MC: each extra unit adds more to TR than to TC → profit rises → produce more.
• While MR < MC: each extra unit adds more to cost than to revenue → profit falls → produce less.

• Britannica gives the same rule. Profits keep rising as long as MR > MC and fall once MR < MC [2].

• For a price-taker, MR = p. Every extra unit sells at the same market price.

• So the condition becomes p = MC [3].

• At any given price, the profit-maximising firm supplies the quantity where MC equals that price [3].

• Small example: p = ₹10. The 5th unit costs ₹7 extra (MC = 7 < 10), so it adds ₹3 to profit. The 6th unit costs ₹11 extra (MC = 11 > 10), so it cuts profit by ₹1. The firm stops at 5 units.

4. Condition 2 — MC must not be falling (non-decreasing MC)

• The rule p = MC alone is not enough. The MC curve is U-shaped, so it can meet the price line twice.
• At q₀, MC must be rising or flat, not falling. In other words, MC must cut the price line from below.
• Reading NCERT Fig 4.3 (p = MC at both q₁ and q₄):
• At q₁, MC is falling.
  • Just to the left of q₁, p < MC, so those units lose money. Producing a little less raises profit.
  • Just to the right of q₁, p > MC, so producing more also raises profit.
  • So q₁ is a profit minimum, not a maximum.
• At q₂ and q₃: p > MC → expanding output raises profit.
• At q₅ and q₆: MC > p → cutting output raises profit.

• Only q₄, where MC is rising, is the profit maximum.

• Exam logic: the "second-order" check is that MC slopes upward at the chosen output.

5. Condition 3 — price must cover the relevant average cost

• AVC (average variable cost) = TVC / q. SAC (short-run average cost) = TC / q. LRAC (long-run average cost) = cost per unit when all inputs can be changed.

(a) Short run: p ≥ AVC

• In the short run, fixed costs (TFC) must be paid even if the firm produces nothing.
• If the firm shuts down: TR = 0 and TVC = 0, so profit = −TFC.
• If it produces at q₁ with p < AVC (Fig 4.4):
• TR = area OpAq₁. TVC = area OEBq₁, and TVC > TR.
• Profit = TR − TVC − TFC = −(area pEBA) − TFC.
• So producing loses more than TFC. The extra loss is the rectangle pEBA.

• So the firm shuts down.

• Worked example: TFC = ₹300, p = ₹10, and at q = 100, AVC = ₹12.

• Produce: TR = 1,000, TVC = 1,200 → profit = 1,000 − 1,200 − 300 = −₹500.
• Shut down: profit = −₹300.

• Shutting down loses ₹200 less, so the firm stops.

• Shut-down point: the lowest point of the AVC curve.

• Short-run supply curve of a firm: the rising part of the SMC curve that lies above minimum AVC. Below that price, supply is zero.
• The industry's short-run supply is the sum of these firm supply curves [3][2].

(b) Long run: p ≥ LRAC

• In the long run all costs are variable, so there is no TFC.
• Shutting down (exiting the industry) gives zero profit.
• If p < LRAC, every unit makes a loss → the firm exits.
• Example: p = ₹8 and minimum LRAC = ₹10 → loss of ₹2 on every unit → exit is better, since it gives a profit of 0.

6. NCERT error: "> " vs "≥"

• The chapter's list of conditions says "p > AVC" and "p > AC".
• The chapter summary says p ≥ AVC (short run) and p ≥ LRAC (long run).
• ≥ is correct. When p = AVC (or p = LRAC), producing and shutting down give the same profit. The firm is indifferent between the two.

7. Geometry of profit (NCERT Fig 4.6, short run)

• At price p, the firm picks q₀ where p = SMC on the rising part of SMC (SMC = short-run marginal cost).
• TR = area OpAq₀ (price × quantity).
• TC = area OEBq₀ (SAC × quantity).
• Profit = rectangle EpAB = (p − SAC) × q₀.
• Worked example: p = ₹20, q₀ = 50, SAC at q₀ = ₹16 → profit = (20 − 16) × 50 = ₹200.
• If SAC > p but p ≥ AVC, the same rectangle shows a loss. The firm still produces in the short run, because that loss is smaller than TFC.

8. Exercise 21 drill (p = ₹10)

q	0	1	2	3	4	5	6	7	8	9	10
TC	5	15	22	27	31	38	49	63	81	101	123
TR	0	10	20	30	40	50	60	70	80	90	100
π	−5	−5	−2	3	9	12	11	7	−1	−11	−23
MC	–	10	7	5	4	7	11	14	18	20	22

• TFC = ₹5 (the TC at q = 0).
• Profit is highest at 5 units (₹12).

• MC rises from 7 (q = 5) to 11 (q = 6). So it crosses ₹10 from below between q = 5 and q = 6. This is conditions 1 and 2 together.

• p = MC also holds at q = 1 (MC = 10), but MC is falling there (10 → 7 → 5). Profit there is only −₹5. This is the condition 2 trap.

• Condition 3 check at q = 5: AVC = (38 − 5) / 5 = ₹6.6 < p = ₹10, so producing is better than shutting down.
• Exercise 20: TR/q gives p = ₹5. Profits are −5, −2, 0, 3, 5, 2, −3, −5, so the maximum is at 4 units.
• The shapes of SMC, AVC, SAC and LRAC are covered in the production-and-costs note.

Prelims Hooks

• The general profit-maximising rule is MR = MC. Under perfect competition MR = p, so the rule becomes p = MC [3].
• p = MC is necessary but not sufficient. MC must also be non-decreasing, i.e. it must cut the price line from below.
• A point where p = MC on a falling MC curve is a profit minimum. Trap: in NCERT Exercise 21, p = MC at q = 1, but the profit maximum is at q = 5.
• Short-run shut-down rule: produce only if p ≥ AVC. If the firm shuts down, its loss equals TFC.
• Long-run exit rule: p ≥ LRAC. Exit gives zero profit, because there are no fixed costs in the long run.
• A firm's short-run supply curve = the rising SMC above minimum AVC [3].
• In Fig 4.6, profit = rectangle EpAB = (p − SAC) × q₀.
• Satisficing is linked to Herbert Simon (Nobel 1978) and bounded rationality [4][5]. Sales-revenue maximisation subject to a minimum-profit constraint is linked to Baumol.
• Trap: NCERT's condition list says "p > AVC", but the correct condition is p ≥ AVC. At equality the firm is indifferent.

Mains Points

• Why loss-making firms keep running (GS-III, industry and MSMEs):
• In the short run a firm keeps producing as long as p ≥ AVC, even with an accounting loss, because fixed costs have to be paid anyway.
• This explains why power plants, airlines or MSMEs run at a loss in a downturn instead of closing.

• It also shows why working-capital support (which helps cover variable costs) can keep firms alive during a crisis.

• Why firms exit and why that can be efficient:

• In the long run, if p stays below LRAC, the firm should exit.

• A quick, low-cost exit system (for example insolvency resolution) lets capital move out of unviable firms. Propping them up with subsidies ties up resources that could be used better.

• The limits of the profit-maximising model:

• Real firms may chase sales and market share (Baumol).
• They may also settle for "good enough" targets because of bounded rationality (Simon) [4][5].

• So policy that assumes firms respond only to price signals, such as tax incentives or price caps, may produce weaker results than the model predicts.

• Linking p = MC to efficiency and pricing policy:

• Under perfect competition, price equals marginal cost. So the value consumers place on the last unit equals what it costs society to make it. This is the basis for allocative efficiency.
• The same principle guides marginal-cost pricing of public utilities.