Definitions of total revenue (TR) and average revenue (AR)

Firms’ Costs, Revenue and Objectives (Cambridge IGCSE Economics 0455 – Topic 3.6)

Learning Objective

Define the main cost and revenue concepts, calculate them correctly, and explain how they guide a firm’s profit‑maximising decisions and other objectives.

1. Cost Concepts – Definitions, Formulas & Economic Meaning

Short‑run vs Long‑run Cost Behaviour

• Short‑run: At least one factor (e.g., plant size) is fixed → AFC > 0, MC may rise after a certain output because of diminishing marginal returns.
• Long‑run: All factors are variable → no fixed cost, AFC = 0. The Long‑run ATC (LRATC) shows the lowest possible ATC for each output level and indicates economies of scale.

2. Revenue Concepts – Definitions, Formulas & Market‑Structure Implications

Behaviour of TR, AR & MR in Different Market Structures

• Perfect competition: AR and MR are horizontal at the market price; TR is a straight line through the origin with slope = P.
• Monopoly: AR is the downward‑sloping demand curve; MR lies below AR (steeper) because each extra unit reduces the price on all previous units.
• Monopolistic competition & oligopoly: Similar to monopoly for a single firm’s demand, but the market price is influenced by the actions of rivals.

3. Linking Revenue, Cost and Profit

• Profit (π): $$\pi = TR - TC$$
• Profit is maximised where MR = MC.
  • In perfect competition this reduces to P = MC because MR = P.
  • In monopoly the firm produces where its MR curve intersects MC.
• Break‑even point: Output at which TR = TC (or equivalently AR = ATC). Below this level the firm makes a loss; above it a profit.

4. Firm Objectives (Cambridge Syllabus 3.6.5)

• Profit maximisation – achieve the highest possible profit (or minimise loss in the short‑run).
• Growth – increase size, market share or output over time.
• Survival – continue operating in the short‑run, especially when making a loss.
• Social welfare / sustainability – consider wider societal goals such as environmental protection, employee welfare or ethical production.

Evaluating Trade‑offs (AO3)

For example, a firm may sacrifice short‑run profit to invest in greener technology (social welfare) which could support long‑run growth and survival. Discussing these trade‑offs demonstrates higher‑order thinking.

5. Worked Example – Full Set of Calculations

Data for a small firm (short‑run):

1. Total Revenue: $$TR = P \times Q = 5 \times 200 = £1{,}000$$
2. Total Cost: $$TC = FC + VC = 300 + 600 = £900$$
3. Profit: $$\pi = TR - TC = 1{,}000 - 900 = £100$$
4. Average Costs:
   • $$ATC = \frac{TC}{Q} = \frac{900}{200}= £4.50$$
   • $$AFC = \frac{FC}{Q} = \frac{300}{200}= £1.50$$
   • $$AVC = \frac{VC}{Q} = \frac{600}{200}= £3.00$$
5. Average Revenue: $$AR = \frac{TR}{Q}= \frac{1{,}000}{200}= £5.00$$ (equal to P)
6. Marginal Cost (approx.):

   Assume that increasing output from 200 to 210 units raises VC to £630. Then

   $$MC = \frac{\Delta VC}{\Delta Q}= \frac{630-600}{210-200}= \frac{30}{10}= £3.00$$
7. Marginal Revenue: Since the market is perfectly competitive, $$MR = P = £5.00$$
8. Break‑even check: AR (£5) > ATC (£4.50) → the firm is above the break‑even point.

Extension – Changing Output

If the firm raises output to 300 units, keeping FC = £300 and VC rising to £1 050:

• $$TR = 5 \times 300 = £1{,}500$$
• $$TC = 300 + 1{,}050 = £1{,}350$$
• $$\pi = 1{,}500 - 1{,}350 = £150$$ (higher profit)
• $$ATC = \frac{1{,}350}{300}= £4.50$$ (unchanged)
• $$AFC = \frac{300}{300}= £1.00$$ (falls)
• $$AVC = \frac{1{,}050}{300}= £3.50$$ (rises)

Profit rises because the extra output adds more revenue (£5 per unit) than the extra marginal cost (£3–£3.5 per unit).

6. Diagrammatic Summary (for note‑taking)

• ATC, AVC & AFC curves: Downward‑sloping AFC; AVC falls then rises; ATC lies above AVC and is U‑shaped, touching its minimum where MC = ATC.
• MC curve: Typically falls, reaches a minimum, then rises; cuts the ATC curve at its lowest point.
• TR, AR & MR (perfect competition): Horizontal AR = MR = P; TR is a straight line through the origin with slope = P.
• TR, AR & MR (monopoly): AR is the market demand curve (downward); MR lies below AR; both are curved.

Suggested sketch: Quantity (Q) on the horizontal axis; price/revenue on the vertical axis. Plot ATC (U‑shaped), MC (∩‑shaped), and a horizontal line for AR = MR = P. Mark the profit‑maximising output where MC = MR and indicate the break‑even point where AR = ATC.

7. Data‑Interpretation & Analysis Tasks (AO2 & AO3)

1. Using the original data, calculate TR, TC, ATC, AFC, AVC, MC (approx.) and profit. Show each step.
2. Re‑calculate the figures for the 300‑unit scenario. Explain why profit changes, referring to the relationship between MR and MC.
3. On a sketch of the ATC curve, indicate the output at which ATC is lowest. Explain why producing at this “most efficient scale” helps achieve profit maximisation.
4. Suppose the firm makes a loss of £50 at 200 units. Discuss which of the four objectives (profit maximisation, growth, survival, social welfare) would dominate the firm’s short‑run decision and why.
5. Evaluate a situation where a firm chooses to invest in environmentally‑friendly equipment that raises FC. Discuss the trade‑off between short‑run profit and the long‑run objective of social welfare/sustainability.

8. Key Points to Remember (Quick Revision)

• TR = P × Q; AR = TR/Q = P (perfect competition).
• MR = ΔTR/ΔQ; in perfect competition MR = AR = P, in monopoly MR < AR.
• Cost per unit: ATC = TC/Q, AFC = FC/Q, AVC = VC/Q.
• MC = ΔTC/ΔQ = ΔVC/ΔQ; profit maximised where MR = MC.
• Break‑even occurs where AR = ATC (or TR = TC).
• Four firm objectives: profit maximisation, growth, survival, social welfare – often involve trade‑offs.