Module 7.5 – Cost, Revenue & Profit (A‑Level only)
Scope: This hand‑out covers the content required for Topic 7.5 – Costs, Revenue and Profit of the Cambridge International AS & A Level Economics (9708) syllabus. It does not include the other 14 A‑Level sub‑topics (utility, market failure, labour markets, macro‑economics, etc.). Those will be addressed in separate modules.
Learning Objective
Explain how a firm determines the output level that maximises profit, using the relevant cost and revenue concepts in both the short‑run and the long‑run, and describe the implications for market entry, exit and equilibrium.
1. Key Concepts & Formulae
1.1 Cost concepts
- Fixed Cost (FC): does not vary with output (e.g., rent, salaried managers).
- Variable Cost (VC): varies directly with the quantity produced (e.g., raw materials, hourly wages).
- Total Cost (TC):
$$TC = FC + VC$$
- Average Fixed Cost (AFC):
$$AFC = \frac{FC}{Q}$$
- Average Variable Cost (AVC):
$$AVC = \frac{VC}{Q}$$
- Average Total Cost (ATC):
$$ATC = \frac{TC}{Q}=AFC+AVC$$
- Marginal Cost (MC): extra cost of producing one more unit.
$$MC = \frac{\Delta TC}{\Delta Q}$$
- Cost‑output elasticity (EC) (optional, useful for higher‑order analysis):
$$E_C=\frac{\%\Delta Q}{\%\Delta TC}=\frac{MC}{ATC}$$
1.2 Revenue concepts
- Total Revenue (TR):
$$TR = P \times Q$$
- Average Revenue (AR):
$$AR = \frac{TR}{Q}=P$$ (equal to price in perfect competition).
- Marginal Revenue (MR): extra revenue from selling one more unit.
$$MR = \frac{\Delta TR}{\Delta Q}$$
1.3 Profit concepts
- Accounting profit: $$\text{Accounting profit}=TR - TC$$
- Economic profit: $$\text{Economic profit}=TR - (Explicit\;Costs + Implicit\;Costs)$$
- Normal profit: profit that just covers all implicit costs; economic profit = 0.
- Break‑even point: output where $$TR = TC\quad\text{or}\quad P = ATC$$
2. Short‑Run Production (at least one factor fixed)
2.1 Shape of short‑run cost curves
- MC falls at low output (increasing marginal returns) and then rises (diminishing marginal returns) → U‑shaped.
- AVC mirrors MC → U‑shaped, lies below ATC.
- AFC continuously falls as Q rises (spreads the fixed cost).
- ATC = AFC + AVC → U‑shaped: falls while AFC dominates, rises when AVC dominates.
2.2 Profit‑maximisation condition (short run)
- General rule: MR = MC.
- For a price‑taking firm (perfect competition) MR = P, so the rule simplifies to P = MC.
2.3 Short‑run shutdown rule
The firm produces only if price covers average variable cost:
$$\text{If } P \ge AVC \;\; \Rightarrow\;\; \text{produce where } MR = MC$$
$$\text{If } P < AVC \;\; \Rightarrow\;\; \text{shut down (Q = 0)}$$
When the firm stays open but P < ATC it incurs a loss equal to ATC – P per unit, which is smaller than the fixed cost that would be incurred if it shut down.
3. Long‑Run Production (all inputs variable)
3.1 Long‑run cost curves
- Long‑Run Average Cost (LRAC): the envelope of the lowest possible ATC for each output level. It reflects economies and diseconomies of scale.
- Long‑Run Marginal Cost (LRMC): the derivative of the LRAC curve; extra cost of expanding output when the firm can adjust scale.
- Three‑stage LRAC shape:
- Decreasing LRAC – economies of scale (e.g., bulk buying, specialised machinery).
- Flat LRAC – constant returns to scale.
- Increasing LRAC – diseconomies of scale (e.g., managerial overhead, coordination problems).
3.2 Long‑run profit‑maximisation & competitive equilibrium
- Firms still set output where MR = LRMC.
- In a perfectly competitive long‑run equilibrium: P = LRMC = LRAC. Economic profit is zero (normal profit).
- If P > LRAC → economic profit → entry of new firms → LRAC shifts (or output expands) until P = LRAC.
- If P < LRAC → economic loss → exit of firms → LRAC shifts (or output contracts) until P = LRAC.
4. Price‑Taker vs. Price‑Setter
| Feature |
Price‑Taker (Perfect Competition) |
Price‑Setter (Monopoly, Monopolistic Competition, Oligopoly) |
| Demand faced by the firm |
Perfectly elastic (horizontal) at market price |
Downward‑sloping (firm’s own demand curve) |
| Revenue relationship |
MR = P = AR |
MR falls faster than AR; MR < AR |
| Profit‑maximising rule |
P = MC (since MR = P) |
Set output where MR = MC, then read price from the demand curve |
| Short‑run shutdown rule |
Shut down if P < AVC |
Shut down if price on the demand curve < AVC (rare, because price is usually above AVC) |
| Long‑run outcome |
Normal profit (P = LRAC) |
Can sustain economic profit (monopoly) or earn only normal profit (monopolistic competition, long‑run oligopoly) |
5. Decision‑Making Steps
5.1 Short‑run (price‑taker)
- Calculate MC for each feasible output level.
- Find the output where MC = P. If MC never exactly equals P, choose the highest output for which MC ≤ P (the next unit would make MC > P).
- Apply the shutdown test:
- If P ≥ AVC → produce the output from step 2.
- If P < AVC → shut down (Q = 0).
- Compare TR and TC at the chosen output to identify profit, normal profit or loss.
5.2 Long‑run (price‑taker)
- Identify the LRMC curve that corresponds to the scale of production.
- Set output where LRMC = P.
- Check the long‑run condition:
- If P = LRAC → normal profit (long‑run equilibrium).
- If P > LRAC → economic profit → entry → LRAC shifts until P = LRAC.
- If P < LRAC → economic loss → exit → LRAC shifts until P = LRAC.
6. Diagram Checklist (Exam‑style drawing)
- Axes: Price / Cost (vertical) and Quantity (horizontal).
- Short‑run curves: MC, AVC, ATC (label each). Show the point where MC intersects P (or MR) – this is the profit‑maximising output (Q*).
- Shut‑down point: label the intersection of P with AVC. Shade the area where P < AVC (firm would shut down).
- Long‑run curves: LRAC (envelope) and LRMC. In competitive equilibrium, label the point where P = LRMC = LRAC.
- For price‑setters, include the firm’s downward‑sloping demand curve, the MR curve (twice as steep), and the MC curve. Mark the profit‑maximising output (where MR = MC) and the corresponding price on the demand curve.
- Indicate profit (or loss) area: rectangle between P and ATC (or LRAC) over Q*.
- All curves and points must be clearly labelled (e.g., “Q*”, “P”, “AVC”, “ATC”, “LRAC”).
7. Worked Examples
Example 1 – Perfect Competition (short‑run)
Market price = £20 per unit. Cost data are shown below.
| Q | TC (£) | TR (£) (P=20) | Profit (£) |
|---|
| 0 | 100 | 0 | -100 |
| 1 | 110 | 20 | -90 |
| 2 | 130 | 40 | -90 |
| 3 | 165 | 60 | -105 |
| 4 | 215 | 80 | -135 |
- Calculate MC: 10, 20, 35, 50.
- Compare with price (£20): MC < P at Q=1, MC = P at Q=2, MC > P at Q=3 → profit‑maximising output is **Q = 2**.
- Shutdown test: AVC at Q=2 = (TC‑FC)/Q = (130‑100)/2 = £15. Since P = £20 ≥ AVC, the firm produces.
- Profit assessment: Profit = –£90 (a loss). The loss is smaller than the fixed cost (£100), so the firm prefers to produce in the short run.
- Break‑even: Solve P = ATC. ATC at Q=2 = £130/2 = £65 → P < ATC, so the firm is not breaking even.
Example 2 – Long‑run competitive equilibrium
Suppose the LRAC curve is U‑shaped with a minimum of £15 at Q = 100. The market price is £15.
- Because P = LRAC = £15, the firm earns normal profit. LRMC at Q = 100 also equals £15, satisfying the condition P = LRMC = LRAC.
- If the market price rose to £18, firms would earn an economic profit of £3 per unit. This would attract entry, shifting the LRAC envelope leftward (or expanding plant size) until the new minimum LRAC rises to £18, restoring P = LRAC.
- If the price fell to £12, firms would incur a loss of £3 per unit and would exit. The exit reduces industry output, causing the LRAC envelope to shift rightward (or encouraging remaining firms to adopt a larger scale) until the new minimum LRAC falls to £12.
8. Summary Table
| Concept | Short‑Run | Long‑Run |
|---|
| Fixed Cost (FC) |
Positive (plant size fixed) |
Zero – all inputs variable |
| Variable Cost (VC) |
Changes with output |
Changes with output and with scale of production |
| Average Cost curves |
U‑shaped ATC; AFC falls, AVC U‑shaped |
U‑shaped LRAC (economies → constant → diseconomies of scale) |
| Profit‑maximising condition |
MR = MC (or P = MC for price‑takers) |
MR = LRMC; in competitive equilibrium P = LRMC = LRAC |
| Shutdown / Exit rule |
Shut down if P < AVC |
Exit if P < LRAC |
| Break‑even point |
TR = TC or P = ATC |
TR = TC or P = LRAC (minimum of LRAC) |
| Entry / Exit dynamics |
Not applicable (fixed plant size) |
Entry when P > LRAC, exit when P < LRAC → long‑run equilibrium at P = LRAC |
9. Key Take‑aways
- Profit maximisation occurs where MR = MC. For a price‑taking firm this reduces to P = MC.
- In the short run the firm stays open as long as P ≥ AVC; otherwise it shuts down.
- All costs become variable in the long run; competitive equilibrium is reached when P = LRMC = LRAC, yielding normal profit.
- Entry and exit adjust the industry’s LRAC until the long‑run equilibrium condition is satisfied.
- Understanding the shape and interaction of MC, AVC, ATC, LRAC, MR and the relevant demand curves is essential for analysing a firm’s production decisions, market‑entry choices and the likely outcome in different market structures.
- When drawing exam diagrams, label every curve, axis, intersection point and the relevant profit or loss area to demonstrate full command of the syllabus requirements.