in a kinked demand curve

1. Introduction

This set of notes covers the full Cambridge IGCSE/AS‑Level and A‑Level Economics syllabus (9708) with a focus on the kinked‑demand model in oligopoly. It is organised to meet the assessment objectives (AO1‑AO3):

• AO1 – Knowledge: definitions, key formulas and diagrammatic conventions.
• AO2 – Application: worked numerical examples and real‑world illustrations.
• AO3 – Analysis & Evaluation: discussion of implications, policy choices and limitations.

2. AS‑Level Foundations (Syllabus blocks 1‑6)

2.1 Scarcity, Choice & Opportunity Cost

• Resources are limited → societies must decide what to produce, how to produce and for whom to produce.
• Opportunity cost = value of the next best alternative foregone.
• Factors of production: land, labour, capital, entrepreneurship.

2.2 Production Possibility Curve (PPC)

• Shows maximum output combinations of two goods when resources are fully and efficiently employed.
• Key features: efficiency (points on the curve), inefficiency (inside), unattainable (outside), economic growth (outward shift), and opportunity cost (slope).

2.3 Demand and Supply

Concept	Definition / Determinants	Shift Factors
Demand	Quantity of a good that consumers are willing and able to buy at each price.	Income, tastes, price of related goods (substitutes/complements), expectations, number of buyers.
Supply	Quantity that producers are willing and able to sell at each price.	Input prices, technology, expectations, number of sellers, taxes/subsidies.
Equilibrium	Where quantity demanded = quantity supplied; determines market price and output.	Any shift creates a surplus (price falls) or shortage (price rises) moving the market back to equilibrium.
Consumer & Producer Surplus	Area above price but below demand curve (consumer) and area below price but above supply curve (producer).	Used to illustrate welfare gains/losses from policy.

2.4 Elasticities

General formula: \(\displaystyle \varepsilon = \frac{\%\Delta Q}{\%\Delta P}\)

Elasticity	Interpretation	Typical Determinants
PED (price‑elasticity of demand)	|\(\varepsilon\)| > 1 = elastic; |\(\varepsilon\)| < 1 = inelastic; = 1 = unit‑elastic.	Availability of substitutes, proportion of income spent, definition of market, time horizon.
YED (income‑elasticity of demand)	Positive for normal goods, negative for inferior goods.	Nature of the good, proportion of income spent.
XED (cross‑price elasticity of demand)	Positive for substitutes, negative for complements.	Degree of substitutability/complementarity.
PES (price‑elasticity of supply)	More elastic in the long‑run; depends on spare capacity, input mobility.

2.5 Government Micro‑intervention

• Taxes – shift supply curve upward (higher MC). Incidence depends on relative elasticities.
• Subsidies – shift supply curve downward (lower MC). Can create excess supply.
• Price controls – price ceiling (max price) can cause shortages; price floor (min price) can cause surpluses.
• Buffer‑stock schemes – government buys excess (floor) or sells (ceiling) to stabilise price.
• Provision of information – reduces information asymmetry, can shift demand.

2.6 Aggregate Demand (AD) & Aggregate Supply (AS)

• AD = C + I + G + (X‑M). Downward‑sloping because of wealth, interest‑rate and exchange‑rate effects.
• Short‑run AS (SRAS) – upward sloping (price‑wage rigidity).
• Long‑run AS (LRAS) – vertical at potential output (full‑employment).
• Shifts:
  • AD left/right: changes in consumer confidence, fiscal/monetary policy, exchange rates.
  • SRAS left/right: input‑price changes, productivity, expectations.
  • LRAS left/right: changes in resources, technology, institutional factors.

2.7 Macro‑policy Objectives & Tools

Objective	Fiscal Policy	Monetary Policy	Supply‑side Policy
Economic growth	Increase G or cut taxes → shift AD right.	Lower interest rates → increase investment.	Improve infrastructure, education, deregulation → shift LRAS right.
Low unemployment	Expansionary fiscal → higher AD.	Expansionary monetary → lower rates.	Labour‑market reforms, training.
Price stability	Contractionary fiscal (higher taxes, lower G) to shift AD left.	Higher interest rates to curb AD.	Improving productivity to shift LRAS right.
External balance	Adjust G or taxes to affect import demand.	Exchange‑rate interventions, interest‑rate changes.	Export‑promotion, trade‑facilitation.

2.8 International Trade & Exchange Rates

• Comparative advantage – countries specialise where they have lower opportunity cost.
• Terms of trade (TOT) – ratio of export price index to import price index.
• Protectionist measures – tariffs, quotas, subsidies, voluntary export restraints.
• Balance of payments – current account (trade, services, income, transfers) + capital & financial account.
• Exchange‑rate regimes – fixed, floating, managed float; depreciation/appreciation effects on AD.

3. A‑Level Advanced Topics (Syllabus blocks 7‑11)

3.1 Consumer Theory – Utility & Indifference Curves

• Utility – satisfaction from consumption; total vs marginal utility (MU).
• Law of diminishing MU: each additional unit yields less extra satisfaction.
• Indifference curve (IC) – set of bundles giving the same utility; higher IC = higher utility.
• Budget constraint: \(P_x X + P_y Y = I\). Consumer equilibrium where an IC is tangent to the budget line → \(\displaystyle \frac{MU_X}{P_X} = \frac{MU_Y}{P_Y}\).
• Substitution effect vs income effect (Hicksian vs Marshallian decomposition).

3.2 Market Failure & Externalities

• Negative externality – marginal social cost (MSC) > marginal private cost (MPC). Diagram shows welfare loss (dead‑weight loss). Pigouvian tax can internalise the externality (tax = MSC – MPC).
• Positive externality – MSC < MPC; subsidy can correct the under‑consumption.
• Public goods – non‑rival and non‑excludable; market under‑provides; possible solutions: government provision or voluntary contributions.
• Information asymmetry – adverse selection, moral hazard; possible remedies: regulation, warranties, signalling.

3.3 Labour Market – Derived Demand & Wage Determination

• Labour demand derived from the value of marginal product (VMP): \(VMP = MR \times MP_L\).
• In a perfectly competitive product market, \(MR = P\); in monopoly \(MR < P\).
• Monopsony – single buyer of labour; marginal factor cost (MFC) lies above the labour supply curve; wage set where MFC = VMP.
• Trade unions can shift the labour supply curve leftward (higher wage, lower employment).

3.4 Macro‑policy Analysis – Multiplier & Phillips Curve

• Fiscal multiplier (simple): \(\displaystyle k = \frac{1}{1 - MPC(1 - t) + MPI}\). Shows change in equilibrium output from a change in autonomous spending.
• Crowding‑out – higher government borrowing raises interest rates, reducing private investment.
• Phillips curve – short‑run inverse relation between unemployment and inflation; long‑run vertical at the natural rate of unemployment (NAIRU).
• Supply‑side policies aim to shift LRAS right, reducing structural unemployment and inflationary pressure.

3.5 Development Economics

Concept	Key Points
Economic growth vs development	Growth = rise in real GNI per capita; development adds quality of life (health, education, inequality).
Indicators	GNI per capita (PPP), Human Development Index (HDI), Gini coefficient, Poverty headcount ratio.
Sustainable & inclusive growth	Growth that preserves the environment and spreads benefits; policies include green technology, social safety nets.
Aid & debt	Official development assistance (ODA), debt sustainability analysis, conditionality.
Trade & globalization	Export‑led growth, terms of trade, trade‑related aid, impact of WTO rules.

4. Oligopoly – The Kinked‑Demand Model

4.1 Core Assumptions

• Few inter‑dependent firms dominate the market.
• Each firm believes:
  • If it cuts price, rivals will match → the demand it faces becomes relatively elastic.
  • If it raises price, rivals will keep their price → the demand it faces becomes relatively inelastic.
• Result: a demand curve with a “kink’’ at the current market price \(P_k\).

4.2 Demand and Marginal‑Revenue (MR) Functions

\[ \text{Demand:}\quad P= \begin{cases} a_1-b_1Q & \text{if } P>P_k\;(elastic\;segment)\\[4pt] a_2-b_2Q & \text{if } Pb_2) \] \[ \text{MR:}\quad MR= \begin{cases} a_1-2b_1Q & \text{if } P>P_k\\[4pt] a_2-2b_2Q & \text{if } P4.3 Why a “gap’’ Appears in the MR Curve

• When price falls below \(P_k\) the demand curve flattens (lower elasticity), so the MR slope becomes flatter.
• The two MR segments do not meet at the kink; a vertical discontinuity (the “gap’’) is created at quantity \(Q_k\).
• Any marginal‑cost (MC) curve that lies within this vertical gap intersects MR at the same price \(P_k\). Hence a range of MC values can change output without moving price – price is “sticky’’.

4.4 Worked Numerical Example

Assume the following demand segments:

\[ P= \begin{cases} 120-2Q & \text{(elastic)}\\ 80-0.5Q & \text{(inelastic)} \end{cases} \]

Corresponding MR curves:

\[ MR= \begin{cases} 120-4Q & \text{(elastic)}\\ 80-Q & \text{(inelastic)} \end{cases} \]

Find the kink:

\[ 120-2Q_k = 80-0.5Q_k \;\Rightarrow\; Q_k = 26.7,\qquad P_k = 66.7 \]

MR values at the kink:

\[ MR_{\text{elastic}} = 120-4(26.7)=13.3,\qquad MR_{\text{inelastic}} = 80-26.7=53.3 \]

The vertical gap = \(53.3-13.3 = 40.0\).

If the firm’s marginal cost lies anywhere between 13.3 and 53.3, the profit‑maximising price stays at \(P_k = 66.7\). Only when MC moves outside this interval will the firm adjust price.

4.5 Implications for Price Rigidity

• Firms can change output (and thus profit) by moving along the MC curve inside the gap, but the market price remains unchanged.
• The model explains why many oligopolistic markets (e.g., petrol, mobile‑phone contracts) exhibit “sticky’’ prices even when costs fluctuate.
• Because rivals are expected to match price cuts, firms avoid price competition and turn to non‑price tactics.

5. Firm Objectives (Syllabus 7.8) in the Context of a Kinked‑Demand Curve

Objective	Definition (AO1)	Implication under a Kinked‑Demand Curve (AO2)	Typical Policy Response (AO3)
Traditional profit‑maximisation	Produce where MR = MC (short‑run).	If MC lies inside the MR gap, output can change without changing price.	Keep price at \(P_k\); adjust output to keep MC within the gap; monitor cost changes.
Survival (avoid price wars)	Stay in business; profit not necessarily maximised.	Sticky price prevents a destructive cut‑and‑match spiral.	Maintain the prevailing price; focus on cost control, product differentiation, advertising.
Profit‑satisficing	Target a “good enough’’ profit rather than the absolute maximum.	Since profit does not rise by moving inside the gap, any MC within the gap is acceptable.	Accept modest margins; reinvest surplus in R&D or brand equity.
Sales‑maximisation (volume focus)	Maximise total quantity sold, even if profit per unit falls.	Price stays at \(P_k\); sales are increased via advertising, product variety, bundling.	Boost marketing spend; introduce new models or services while keeping price unchanged.
Revenue‑maximisation	Maximise total revenue \(TR = P \times Q\).	Revenue rises on the elastic segment if price is cut, but rivals’ matching cuts erode the gain.	Prefer non‑price tactics; cut price only when a substantial market‑share gain is realistic.
Long‑run growth	Expand capacity, market share or product range.	Stable price environment encourages investment rather than price competition.	Allocate profits to capacity expansion, strategic alliances, or innovation.

6. Pricing Policies in Oligopoly

6.1 Price Discrimination

• First‑degree (perfect) discrimination – charge each consumer his/her maximum willingness to pay. Rare in oligopoly because detailed information is costly and rivals may copy the price cuts.
• Second‑degree discrimination – price varies with the quantity purchased (e.g., bulk discounts, versioning). Viable if the firm can segment the market without prompting a rival price match.
• Third‑degree discrimination – different prices for identifiable groups (students, seniors, geographic regions). Feasible when groups are small enough that rivals cannot easily duplicate the price break.

Numerical illustration (third‑degree)

Two market segments:

\[ P_1 = 100 - Q_1,\qquad P_2 = 80 - 0.5Q_2 \]

MR curves:

\[ MR_1 = 100 - 2Q_1,\qquad MR_2 = 80 - Q_2 \]

If MC = 30, profit‑maximising quantities are:

\[ Q_1^{*}=35,\; P_1^{*}=65;\qquad Q_2^{*}=50,\; P_2^{*}=55 \]

Both prices are below the common market price that would result from a single‑price strategy, showing how third‑degree discrimination can raise total profit – provided rivals do not immediately copy the lower price in either segment.

6.2 Other Oligopolistic Pricing Strategies

• Limit pricing – set price low enough to deter entry. In a kinked‑demand market the price is already sticky, so limit pricing is only effective if the firm can credibly sustain the low price for a long period.
• Predatory pricing – price below cost to drive rivals out. The MR gap makes this risky; rivals are likely to match the cut, forcing the predator into losses.
• Price leadership – a dominant firm (the “leader”) sets the price; followers accept it as the kink point. This explains coordinated price stability without explicit collusion.

7. Relationship Between Elasticity and Total Revenue

For any demand curve:

\[ \% \Delta TR = \% \Delta Q + \% \Delta P \]

Elasticity range	Effect of a price change on TR
Elastic (\(|\varepsilon|>1\))	Price cut → proportionally larger increase in Q → TR rises. Price rise → TR falls.
Inelastic (\(|\varepsilon|<1\))	Price cut → TR falls. Price rise → proportionally smaller fall in Q → TR rises.
Unit‑elastic (\(|\varepsilon|=1\))	Any price change leaves TR unchanged.

In the kinked‑demand model the upper segment is elastic and the lower segment inelastic, so both a price cut and a price rise could, in theory, raise revenue. In practice, rival reactions neutralise the gain, reinforcing price rigidity.

Worked revenue example (elastic segment)

Demand: \(P = 120 - 2Q\) → at \(Q=20\), \(P=80\) and \(\varepsilon = -2\).

If price falls to 70 (ΔP = –12.5 %), quantity rises to 25 (ΔQ = +25 %).

\[ \% \Delta TR = 25\% - 12.5\% = +12.5\% \]

Revenue rises, but a matching price cut by rivals shifts the whole demand curve leftward, eroding the increase.

8. Diagrammatic Representation

Figure: Kinked‑demand curve with MR gap and a range of MC curves

• Kink point \((Q_k , P_k)\).
• Upper (elastic) demand segment – flatter slope.
• Lower (inelastic) demand segment – steeper slope.
• Two MR segments (MR₁, MR₂) with a vertical gap at \(Q_k\).
• Several MC curves lying inside the gap illustrate price rigidity.
• Equilibrium: any MC inside the gap → price remains at \(P_k\), output adjusts to the MC curve.

9. Non‑Price Competition in an Oligopoly

• Advertising & promotion – shifts the firm’s demand outward without changing price.
• Product differentiation – quality, design, branding creates “micro‑kinks’’ that let a firm capture a larger share of the elastic segment.
• Research & Development (R&D) – new features or technologies increase marginal profit while price stays sticky.
• Loyalty programmes & bundling – raise repeat purchases, effectively moving the demand curve rightward.
• Cost leadership – economies of scale lower MC; profit rises even though price does not change.
• Strategic alliances & joint ventures – share technology or distribution, reducing costs and enhancing market power.

10. Summary

The kinked‑demand model explains the characteristic price rigidity of oligopolistic markets. Because the marginal‑revenue curve contains a vertical gap, a firm’s marginal cost can vary within a wide range without forcing a price change. This “sticky‑price’’ environment influences the choice of firm objectives (profit‑maximisation, survival, satisficing, sales‑maximisation, growth) and encourages a shift toward non‑price competition, selective price discrimination, and strategic pricing policies such as price leadership. Mastery of the underlying micro‑foundations (demand, elasticity, MR) and the broader macro‑context (government policy, international trade, development) equips students to analyse real‑world oligopolies and to evaluate the effectiveness of different objectives and policies.