Revenue

Revenue, Cost & Profit – Cambridge A‑Level Economics (9708)

1. Core Concepts & Formulas

Concept Formula Key Interpretation
Total Revenue (TR) TR = P × Q Revenue from selling Q units at market price P.
Average Revenue (AR) AR = TR/Q = P In a perfectly competitive market AR equals the market price; AR is the firm’s demand curve.
Marginal Revenue (MR) MR = ΔTR/ΔQ Additional revenue from selling one more unit.
MR (elasticity form) MR = P · \left(1 + \frac{1}{E_d}\right) E_d = price‑elasticity of demand (negative). When E_d = –∞ (perfectly elastic) MR = P.
Profit (π) π = TR – TC TC = FC + VC. π > 0 = economic profit; π < 0 = loss.
Short‑run Cost Curves
  • TC = FC + VC
  • AVC = VC/Q
  • AFC = FC/Q
  • ATC = TC/Q = AVC + AFC
  • MC = ΔTC/ΔQ
Derived from the underlying cost function; MC cuts ATC at its minimum.
Long‑run Cost Curves
  • LRAC = minimum of all possible short‑run ATC curves
  • LRMC = ΔLRTC/ΔQ (tangent to LRAC at the efficient scale)
Shows the lowest average cost achievable when all inputs are variable; the point of minimum efficient scale (MES) is where LRAC is at its lowest.

2. Cost‑Revenue Diagrams – Key Points to Plot

  • Break‑even point: where TR = TC (π = 0). On a diagram it is the intersection of the TR and TC curves.
  • Shutdown point (very short‑run): where P = AVC (or TR = VC). Below this the firm ceases production and only incurs FC.
  • Normal‑profit point (long‑run equilibrium in perfect competition): P = ATC = MC. Profit is zero but the firm covers all opportunity costs.
  • Minimum Efficient Scale (MES): the output at which LRAC is at its minimum; indicates the most efficient plant size.
Diagram placeholders (to be drawn in the exam):
1. Short‑run TR, TC, ATC, AVC and MC curves showing break‑even and shutdown points.
2. Long‑run LRAC with MES and LRMC tangent.
3. AR & MR for each market structure (perfect competition, monopoly, monopolistic competition, oligopoly).

3. Revenue, Demand & Elasticity

  • AR = Demand: The AR curve is identical to the market demand curve faced by the firm.
  • Deriving MR from the demand curve: Because each extra unit must be sold at the prevailing price (or a lower price), MR is the vertical distance between two points on the TR curve, i.e. the slope of the TR curve.
  • Elasticity link: Using MR = P[1 + 1/E_d] shows that when demand is elastic (|E_d| > 1) MR is positive but less than price; when demand is inelastic (|E_d| < 1) MR can become negative, signalling that raising output reduces total revenue.

4. Revenue & Cost in Different Market Structures

Market Demand Curve (AR) MR Position Price Elasticity of Demand Profit‑maximising Condition Typical Cost‑Curve Features Other Syllabus Points
Perfect Competition Perfectly elastic (horizontal at market price) Coincides with AR (MR = P) Perfectly elastic (|E_d| = ∞) Produce where P = MC (MR = MC) Short‑run MC cuts ATC at its minimum; LRAC is flat at the efficient scale. Zero economic profit in the long run (P = ATC = MC). Entry/exit drives profit to zero.
Monopoly Downward‑sloping (price‑setter) Below AR; for a linear demand MR is twice as steep. Elasticity varies along the curve; MR becomes zero where |E_d| = 1 (unit‑elastic point). Produce where MR = MC; price set from the demand curve at that output. MC may be upward‑sloping; ATC often above MC at the profit‑maximising output, giving a markup. Potential for X‑inefficiency; no entry barriers required for monopoly in the syllabus (e.g., natural monopoly, legal monopoly).
Monopolistic Competition Downward‑sloping but relatively elastic (many close substitutes) Below AR, gap smaller than monopoly. More elastic than monopoly; |E_d| > 1 over a larger range. Short‑run: MR = MC (positive profit possible).
Long‑run: entry drives profit to zero → P = ATC > MC.
Short‑run ATC lies above MC; long‑run LRAC is flatter because firms can adjust plant size. Product differentiation leads to downward‑sloping demand; contestable‑market ideas can be discussed.
Oligopoly (Kinked‑Demand Model) Kinked: relatively elastic above the kink, inelastic below. Discontinuous MR – a “gap” at the kink. Elastic above the kink (price cuts lead to large quantity response); inelastic below (price rises cause small quantity loss). Firms tend to produce where MC intersects the upper MR segment → price rigidity. Cost curves similar to other market forms; often a relatively flat MC at the kinked output.
  • Concentration ratios (CR4, HHI) to measure market power.
  • Game‑theoretic concepts – e.g., Prisoner’s Dilemma, Cournot & Bertrand models.
  • Price leadership (dominant‑firm, bar‑bell, collusive outcomes).
  • Contestable markets – low entry/exit barriers can force competitive outcomes even with few firms.

4.1 Game‑Theoretic Illustration (Prisoner’s Dilemma)

Firm A \ Firm BCollude (C)Defect (D)
Collude (C)π = £10 eachπ = £2 (A), £12 (B)
Defect (D)π = £12 (A), £2 (B)π = £4 each

Both firms choosing D is the Nash equilibrium (each earns £4) even though mutual C would give £10 each – demonstrates why oligopolists may end up with price rigidity or tacit collusion.

5. Pricing Policies (Cambridge 7.8)

  • Price discrimination (same product, different prices):
    • First‑degree (perfect) – charge each consumer his maximum willingness to pay; MR = P for every unit.
    • Second‑degree – price varies with quantity or version (bulk discounts, premium‑economy). MR is higher on the first units sold at a higher price and falls on later units.
    • Third‑degree – separate markets (students, seniors, geographic). MR for each segment is calculated using MR = P[1 + 1/E_d] for that segment.
  • Markup (or cost‑plus) pricing – set price = MC + markup (often expressed as a percentage of MC). Implies a constant markup over marginal cost.
  • Target‑return pricing – price = (Average total cost) ÷ (1 – desired rate of return). Used when firms aim for a specific profit rate.
  • Penetration pricing – set a low initial price to gain market share; MR is initially low but rises as demand becomes more elastic.
  • Price‑skimming – start with a high price to capture consumer surplus from less price‑elastic buyers; MR is high at low output and falls sharply.
  • Prestige (or premium) pricing – price set high to signal superior quality; demand is relatively inelastic.
  • Two‑part tariff – fixed fee + per‑unit price (often set at marginal cost). MR from the per‑unit component equals price; the fixed fee captures consumer surplus.
  • Bundling – sell a package of goods at a single price; can raise MR if the combined willingness to pay exceeds the sum of individual prices.

6. Decision Rules – When to Produce, When to Shut Down, and Long‑Run Adjustments

6.1 Short‑Run Rules

  • Profit maximisation: Produce up to the output where MR = MC. If MR > MC increase output; if MR < MC decrease output.
  • Shutdown condition (very short‑run): Continue operating if P ≥ AVC (equivalently TR ≥ VC). If P < AVC shut down and incur only fixed costs.
  • Loss‑minimising rule: If P < ATC but P ≥ AVC, produce to minimise loss (loss = FC + (ATC – P)·Q).

6.2 Long‑Run Rules

  • All factors are variable; firms can enter or exit.
  • Perfect competition: Entry drives economic profit to zero → P = MC = ATC. Firms operate at the minimum of LRAC (MES).
  • Monopoly: No entry; profit can remain > 0 if barriers persist. LRAC may be downward‑sloping (natural monopoly) → price may be set at average cost under regulation.
  • Monopolistic competition: Free entry/exit leads to zero economic profit in the long run → P = ATC > MC. Firms produce at a point where AR is tangent to ATC.
  • Oligopoly: Long‑run outcome depends on strategic interaction:
    • If collusion succeeds → price above MC, positive profit.
    • If competitive pressures dominate (e.g., price leadership, contestable markets) → price may approach MC.

7. Worked Examples

Example 1 – Perfectly Competitive Firm (Short‑Run)

Given: P = £5, Q = 300, FC = £200, VC per unit = £2, MC is constant at £2.

  1. Total Revenue: TR = 5 × 300 = £1 500
  2. Total Variable Cost: VC = 2 × 300 = £600
  3. Total Cost: TC = FC + VC = 200 + 600 = £800
  4. Profit: π = TR – TC = £700 (positive – entry likely).
  5. Check shutdown: P = £5 > AVC = £2 ⇒ firm stays open.
  6. MR = P = £5; MC = £2 ⇒ MR > MC, so the firm could increase output in the very short‑run (if capacity allows).

Example 2 – Monopoly with Linear Demand

Demand: P = 30 – 0.5Q  MC = 4 (constant)

  1. Derive MR: MR = 30 – Q (twice the slope of demand).
  2. Set MR = MC: 30 – Q = 4 → Q* = 26 units.
  3. Price from demand: P* = 30 – 0.5(26) = £17.
  4. Total Revenue: TR = 17 × 26 = £442.
  5. Assume FC = £50. Total Cost: TC = 50 + 4 × 26 = £154.
  6. Profit: π = £442 – £154 = £288.
  7. Elasticity at Q*: E_d = (dP/dQ)·(Q/P) = (‑0.5)·(26/17) ≈ ‑0.76 (inelastic). MR is still positive because the monopoly is operating left of the unit‑elastic point.

Example 3 – Oligopoly – Prisoner’s Dilemma (Cournot‑type)

Two firms decide output simultaneously. Market price: P = 100 – 0.5(Q₁ + Q₂). MC = 20 for each.

  1. Firm 1’s profit: π₁ = (P – MC)·Q₁ = [100 – 0.5(Q₁ + Q₂) – 20]·Q₁.
  2. Best‑response function (first‑order condition): 80 – Q₁ – 0.5Q₂ = 0 → Q₁ = 80 – 0.5Q₂.
  3. Symmetry gives Q₁ = Q₂ = Q. Substitute: Q = 80 – 0.5Q → 1.5Q = 80 → Q ≈ 53.3.
  4. Total market output ≈ 106.6, price ≈ 100 – 0.5·106.6 = £46.7.
  5. Each firm’s profit: π = (46.7 – 20)·53.3 ≈ £1 420.
  6. If firms colluded and acted as a monopoly, Q = 80 (from MR = MC) and price = £60, giving total profit ≈ £3 200 – higher than the Cournot outcome, illustrating the incentive to cheat.

8. Summary Checklist (Exam‑Ready)

  • Know the definitions and formulas for TR, AR, MR (including the elasticity form), profit, and all short‑run/long‑run cost curves.
  • Be able to draw and label:
    • Short‑run TR, TC, ATC, AVC, AFC, MC with break‑even and shutdown points.
    • Long‑run LRAC showing MES and LRMC.
    • AR & MR for perfect competition, monopoly, monopolistic competition, and oligopoly (kinked demand).
  • Explain why AR equals the demand curve and why MR lies below AR when demand slopes downwards.
  • State and apply the short‑run decision rules (MR = MC, P ≥ AVC) and the long‑run equilibrium conditions for each market structure.
  • Discuss price elasticity of demand in each market and its impact on MR (use MR = P[1 + 1/E_d]).
  • Identify additional oligopoly concepts required by the syllabus:
    • Concentration ratios & HHI.
    • Game‑theoretic outcomes (Prisoner’s Dilemma, Cournot, Bertrand).
    • Price leadership, X‑inefficiency, contestable markets.
  • Recall the three degrees of price discrimination and the other pricing policies (markup, target‑return, penetration, skim, prestige, two‑part tariff, bundling) and how each affects MR and profit.
  • Practice numerical questions that require calculation of TR, TC, profit, AR, MR, and the application of the appropriate decision rule.

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