interactions between demand, supply and price

Roadmap – Where “Demand & Supply” Fits in the Cambridge Business Syllabus

This section (3.1 The Nature of Marketing – Demand and Supply) is the foundation for the rest of the marketing chapter. Understanding how price, demand and supply interact enables you to:

• Analyse market‑research data (3.2)
• Apply the 4 Ps – especially pricing and promotion (3.3‑3.5)
• Use segmentation, targeting and positioning to move demand curves (3.6)
• Assess product‑life‑cycle and portfolio decisions (3.7)
• Calculate elasticities for pricing decisions (A‑Level 8.1‑8.2)

1. Syllabus Checklist – What You Must Know

Syllabus Code	Topic Required	Covered in These Notes?
3.1	Demand, supply and price – equilibrium, shifts and the price mechanism	✓ (expanded)
3.2	Market research – primary/secondary data, sampling, reliability	✗ (see “Link to Other Topics”)
3.3‑3.5	Product, price, promotion, place – marketing mix	✗ (see “Implications for Marketers”)
3.6	Segmentation, targeting, positioning (STP)	✗ (see “Link to Other Topics”)
3.7	Product life‑cycle, portfolio analysis (Boston Matrix, Ansoff)	✗ (see “Link to Other Topics”)
8.1‑8.2 (A‑Level)	Price elasticity, income elasticity, cross‑elasticity; use of elasticity in pricing decisions	✓ (new section 7)

2. Learning Objective

By the end of this unit you should be able to:

• Define demand, supply and market equilibrium.
• Draw and interpret linear (and non‑linear) demand and supply curves.
• Calculate equilibrium price and quantity algebraically.
• Identify and explain all factors that shift demand or supply.
• Use the price‑mechanism to predict how markets self‑adjust.
• Calculate and interpret price, income and cross‑elasticities.
• Apply this analysis to real‑world marketing decisions (pricing, production, promotion, market entry).

3. Core Definitions & Fundamental Laws

• Demand: Quantity of a product that consumers are willing and able to buy at each possible price, ceteris paribus.
• Law of Demand: When price falls, quantity demanded rises; when price rises, quantity demanded falls.
• Supply: Quantity of a product that producers are willing and able to sell at each possible price, ceteris paribus.
• Law of Supply: When price rises, quantity supplied rises; when price falls, quantity supplied falls.
• Market (Equilibrium) Price \(P^{*}\): The price at which quantity demanded equals quantity supplied.
• Equilibrium Quantity \(Q^{*}\): The quantity bought and sold at \(P^{*}\).

4. The Demand Curve

Usually drawn as a downward‑sloping line because of the law of demand.

4.1 Linear Demand Function (simplified)

• \(Q_{d}\) – quantity demanded
• \(P\) – price
• \(a\) – intercept (theoretical maximum demand when price = 0)
• \(b\) – slope (rate at which demand falls as price rises)

4.2 Non‑Linear Forms (A‑Level depth)

• Convex demand curve – reflects diminishing marginal utility more realistically.
• Kinked demand curve – used in oligopoly models where firms expect rivals to match price cuts but not price rises.

5. The Supply Curve

Usually drawn as an upward‑sloping line because of the law of supply.

5.1 Linear Supply Function (simplified)

• \(Q_{s}\) – quantity supplied
• \(c\) – intercept (often zero; quantity supplied when price = 0)
• \(d\) – slope (how quickly supply rises as price rises)

5.2 Alternative Shapes

• S‑shaped supply – reflects capacity constraints at low prices and increasing marginal costs at high output.
• Horizontal supply – typical of perfectly competitive markets in the short run (price takers).

6. Determining Market Equilibrium

Set quantity demanded equal to quantity supplied:

Substituting the linear forms gives:

Solving for the equilibrium price:

Insert \(P^{*}\) into either equation to obtain \(Q^{*}\).

Worked Example (Linear Model)

Demand: \(Q_{d}=500-5P\) Supply: \(Q_{s}=100+3P\)

1. Set \(Q_{d}=Q_{s}\): \(500-5P = 100+3P\)
2. Solve for \(P\):
   \(500-100 = 5P+3P\)
   \(400 = 8P\)
   \(P^{*}=50\)
3. Find \(Q^{*}\):
   \(Q^{*}=500-5(50)=250\)

Result: equilibrium price £50, equilibrium quantity 250 units.

7. Elasticities – Measuring Responsiveness (A‑Level)

Elasticity Type	Formula	Interpretation	Typical Use for Marketers
Price Elasticity of Demand (PED)	\(\displaystyle \varepsilon_{p}= \frac{\%\Delta Q_{d}}{\%\Delta P}= \frac{\Delta Q_{d}}{\Delta P}\times\frac{P}{Q_{d}}\)	‑ |ε| > 1 = elastic; |ε| < 1 = inelastic; |ε| = 1 = unit‑elastic	Set optimal price, decide on price‑skimming vs. penetration
Income Elasticity of Demand (YED)	\(\displaystyle \varepsilon_{y}= \frac{\%\Delta Q_{d}}{\%\Delta Y}= \frac{\Delta Q_{d}}{\Delta Y}\times\frac{Y}{Q_{d}}\)	Positive → normal good; negative → inferior good	Forecast demand when consumer incomes change (e.g., recession)
Cross‑Price Elasticity (XED)	\(\displaystyle \varepsilon_{xy}= \frac{\%\Delta Q_{x}}{\%\Delta P_{y}}= \frac{\Delta Q_{x}}{\Delta P_{y}}\times\frac{P_{y}}{Q_{x}}\)	Positive → substitutes; negative → complements	Assess impact of competitor price changes or bundling decisions

Sample Calculation – Price Elasticity

Suppose a 10 % fall in price leads to a 25 % rise in quantity demanded.

Because |‑2.5| > 1, demand is elastic – a price cut will increase total revenue.

8. Factors That Shift the Curves

8.1 Demand‑Shifting Factors

Factor	Effect on Demand Curve	Short‑run / Long‑run
Consumer income – normal good	Rightward shift (increase)	Both
Consumer income – inferior good	Leftward shift (decrease)	Both
Price of substitutes	Right if substitute price rises; left if it falls	Both
Price of complements	Left if complement price rises; right if it falls	Both
Consumer tastes & preferences	Right for favourable trends; left for unfavourable	Both (especially long‑run)
Expectations of future price or income	Right if higher future price/income expected; left otherwise	Short‑run (affects current buying)
Number of buyers (population, market size)	Right with growth; left with decline	Both

8.2 Supply‑Shifting Factors

Factor	Effect on Supply Curve	Short‑run / Long‑run
Technology (improvements)	Rightward shift (increase)	Long‑run
Input costs (wages, raw materials)	Left if costs rise; right if they fall	Both
Number of sellers (entry/exit)	Right with more firms; left with fewer	Both
Government policy – taxes, subsidies, regulation	Tax/strict regulation → left; subsidy/deregulation → right	Both
Expectations of future price	Right if higher future price expected (producers hold back output); left if lower price expected	Short‑run
Prices of related products (output substitutes)	Right if alternative product price falls (switch production); left if it rises	Both
Natural conditions (weather, disease, seasonality)	Left if adverse; right if favourable	Short‑run (agriculture)

9. The Price Mechanism – How Markets Self‑Adjust

1. Initial imbalance: A rightward shift in demand (or leftward shift in supply) creates a shortage at the original price.
2. Price response: Sellers raise the price to capture higher marginal profit.
3. Quantity response:
   • Higher price → movement up the demand curve (quantity demanded falls).
   • Higher price → movement up the supply curve (quantity supplied rises).
4. New equilibrium: The market settles where the new demand and supply curves intersect, eliminating the shortage.
5. Surplus case: A leftward demand shift or rightward supply shift creates a surplus; price falls, prompting the opposite adjustments until a new equilibrium is reached.

10. Limitations of the Simple Linear Model

• Assumes ceteris paribus – in reality many variables change simultaneously.
• Linear curves ignore diminishing marginal utility at very low prices (convex demand) and capacity constraints at high output (S‑shaped supply).
• Does not capture market failures (externalities, public goods) where equilibrium is not socially optimal.
• In oligopolistic or monopolistic markets, price may be set above equilibrium (price‑setter) – the “price mechanism” works differently.

11. Case Study – Tax on Sugary Drinks (Real‑World Application)

Context: The UK government introduces a £0.24 per litre excise tax on drinks containing more than 5 g of sugar per 100 ml.

Step 1 – Identify the immediate effect

• Tax raises the marginal cost for producers.
• Supply curve shifts leftward (higher price for any given quantity).

Step 2 – Predict the new equilibrium

Assume original linear supply: \(Q_{s}=200+4P\). Tax adds £0.24 per litre, effectively raising price by 0.24 for producers. New supply: \(Q_{s}^{\prime}=200+4(P-0.24)\).

Demand (unchanged) might be \(Q_{d}=800-5P\).

Set \(Q_{d}=Q_{s}^{\prime}\):

Equilibrium price rises from the pre‑tax level (≈ £62) to about £66.8, while equilibrium quantity falls (from 190 units to ≈ 166 units). The tax therefore reduces consumption – a policy goal.

Step 3 – Marketing implications

• Companies may reformulate drinks to avoid the tax → shifts demand rightward for “low‑sugar” variants.
• Price‑elasticity analysis helps decide whether to absorb part of the tax or pass it fully to consumers.
• Promotional campaigns can be targeted at health‑conscious consumers to increase demand for untaxed alternatives.

12. Implications for Marketers – Linking Theory to the 4 Ps

13. Diagram – Right‑ward Shift in Demand (with Labels)

• D₁ – original demand curve
• S – supply curve (unchanged)
• E₁ – original equilibrium (price \(P_{1}\), quantity \(Q_{1}\))
• D₂ – new demand curve after shift
• E₂ – new equilibrium (higher price \(P_{2}\), higher quantity \(Q_{2}\))
• Shortage at \(P_{1}\) shown by the gap between D₂ and S

14. Quick Revision Table – Key Points to Remember

Concept	Key Formula / Rule	Typical Exam Question
Equilibrium price (linear)	\(P^{*}= \dfrac{a-c}{b+d}\)	Calculate \(P^{*}\) and \(Q^{*}\) given demand \(Q_{d}=a-bP\) and supply \(Q_{s}=c+dP\).
Price elasticity of demand	\(\varepsilon_{p}= \dfrac{\Delta Q_{d}}{\Delta P}\times\dfrac{P}{Q_{d}}\)	Determine whether a price cut will increase total revenue.
Shift in demand	Rightward shift → higher \(P^{*}\) & higher \(Q^{*}\) (if supply unchanged)	Explain the impact of a rise in consumer income on equilibrium.
Shift in supply	Leftward shift → higher \(P^{*}\) & lower \(Q^{*}\) (if demand unchanged)	Analyse the effect of a new tax on production costs.
Cross‑price elasticity	\(\varepsilon_{xy}= \dfrac{\Delta Q_{x}}{\Delta P_{y}}\times\dfrac{P_{y}}{Q_{x}}\)	Classify two goods as substitutes or complements.

15. Further Reading & Practice

• Cambridge International AS & A Level Business (9609) – Chapter 3: The Nature of Marketing.
• Past paper questions on equilibrium, elasticities and the price mechanism (June 2024, May 2023).
• Online simulation: “MarketSim” – lets you manipulate demand‑shifting factors and observe new equilibria.