Drawing and interpretation of the demand diagram

Allocation of Resources – Demand (2.2)

1. Learning Objective (AO1‑AO3)

By the end of this unit students will be able to:

• Define demand and distinguish it from quantity demanded (AO1).
• Draw and label a correct demand diagram for an individual and for a market (AO1).
• Explain the law of demand and the two effects that give the curve its downward slope (AO1).
• Identify and evaluate the difference between a movement along a demand curve and a shift of the curve (AO2).
• Analyse the five determinants of demand and predict the direction of the shift (AO2).
• Calculate price elasticity of demand (PED) using the midpoint method and the point‑elasticity formula; interpret the result (AO2‑AO3).
• Link demand‑side concepts to market‑failure ideas such as merit and demerit goods and suggest appropriate government interventions (AO3).

2. Syllabus Coding (Cambridge 9709/9700)

1. Definition of demand & market demand (2.2.1)
2. Law of demand (2.2.2)
3. Movement along the demand curve (2.2.3)
4. Shift of the demand curve (2.2.4)
5. Determinants of demand (2.2.5)
6. Interpretation of slope & price elasticity of demand (2.2.6)

3. Definition of Demand

• Demand (individual): the relationship, ceteris paribus, between the price of a good and the quantity of that good a single consumer is willing and able to buy at each price.
• Market demand: the horizontal summation of all individual demand curves in a particular market.

Diagram (placeholder): individual demand curves D₁, D₂, … Dₙ summed to give the market demand curve D_m.

4. The Law of Demand

All else being equal, when the price of a good rises the quantity demanded falls, and when the price falls the quantity demanded rises. The downward slope is caused by two underlying effects:

• Substitution effect: a higher price makes the good relatively more expensive than its substitutes, so consumers replace it with cheaper alternatives.
• Income effect: a higher price reduces real purchasing power, so consumers can afford less of the good (and vice‑versa).

5. Drawing a Demand Diagram

1. Label the vertical axis Price (P) and the horizontal axis Quantity demanded (Q).
2. Draw a downward‑sloping straight line from left to right and label it D (individual or market demand as required).
3. Mark a specific price‑quantity pair on the curve, e.g. (P₁, Q₁).
4. Movement along the curve: choose a second point (P₂, Q₂) on the same curve with P₂ < P₁ and Q₂ > Q₁. Add an arrow from (P₁,Q₁) to (P₂,Q₂) to show the direction of change.
5. Shift of the curve:
   • Right‑hand shift (increase in demand) – draw a new curve parallel to the original and label it D′.
   • Left‑hand shift (decrease in demand) – draw a new curve labelled D″.
   • Annotate the diagram with the determinant that causes the shift (e.g., “higher consumer income”).

Diagram (placeholder): original curve D, points (P₁,Q₁) → (P₂,Q₂) with arrow, and shift arrow from D to D′.

6. Movement Along vs. Shift of the Demand Curve

Feature	Movement Along the Curve	Shift of the Curve
What changes?	The good’s own price (P)	Any other determinant (income, tastes, prices of related goods, expectations, number of buyers)
Result on the diagram	A new point on the same curve (arrow shown)	The whole curve moves right (increase) or left (decrease)
Typical AO	AO2 – explain cause and effect	AO2 & AO3 – analyse reasons and evaluate likely impact

7. Determinants of Demand (2.2.5)

Determinant	Effect on the Demand Curve	Typical Reason for a Shift
Consumer income	Rightward for normal goods; leftward for inferior goods	Higher disposable income raises demand for normal goods (e.g., restaurant meals); lower income raises demand for inferior goods (e.g., instant noodles).
Prices of related goods	Rightward if the price of a substitute rises; leftward if the price of a complement rises	Tea price ↑ → coffee demand ↑ (substitutes); petrol price ↑ → car demand ↓ (complement).
Tastes and preferences	Rightward when the good becomes more popular; leftward when it becomes less popular	Advertising campaign for smartphones → demand ↑; health warnings about sugary drinks → demand ↓.
Expectations of future price	Rightward if consumers expect higher future prices; leftward if they expect lower future prices	Anticipated rise in house prices → current demand for houses ↑.
Number of buyers (population)	Rightward if the market size grows; leftward if it shrinks	Population growth in a city → demand for public transport ↑.

8. Price Elasticity of Demand (PED) (2.2.6)

8.1 Definition (AO1)

PED measures the responsiveness of the quantity demanded to a change in the price of the good, holding all other determinants constant.

8.2 Formulas (AO2)

Percentage‑change (mid‑point) formula (recommended for exam questions):

\[ \varepsilon_{d}= \frac{\displaystyle\frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}}{\displaystyle\frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}} \]

Point‑elasticity formula (useful for linear demand curves):

\[ \varepsilon_{d}= \frac{1}{\text{slope}} \times \frac{P}{Q} \qquad\text{where }\text{slope}= \frac{\Delta P}{\Delta Q} \]

8.3 Interpretation – Elasticity Categories (Cambridge terminology)

• Perfectly inelastic (|ε| = 0) – vertical demand curve; quantity does not change with price.
• Inelastic (0 < |ε| < 1) – quantity changes proportionally less than price.
• Unit‑elastic (|ε| = 1) – percentage change in quantity equals percentage change in price.
• Elastic (|ε| > 1) – quantity changes proportionally more than price.
• Perfectly elastic (|ε| → ∞) – horizontal demand curve; any price increase drives quantity to zero.

8.4 Determinants of PED (Why some goods are more elastic than others)

Determinant	Effect on Elasticity
Availability of close substitutes	More substitutes → higher |ε| (more elastic).
Proportion of income spent on the good	Higher proportion → higher |ε| (more elastic).
Necessity vs. luxury	Necessities tend to be inelastic; luxuries more elastic.
Time‑period considered	Demand is more elastic in the long run as consumers can adjust habits and find alternatives.

8.5 Worked Example (mid‑point method)

Demand function: Q = 200 – 5P

1. Calculate quantities at two prices:
   • P₁ = £20 → Q₁ = 200 – 5(20) = 100
   • P₂ = £15 → Q₂ = 200 – 5(15) = 125
2. Mid‑point percentage changes: \[ \% \Delta Q = \frac{125-100}{(100+125)/2}\times100 = \frac{25}{112.5}\times100 \approx 22.2\% \] \[ \% \Delta P = \frac{15-20}{(20+15)/2}\times100 = \frac{-5}{17.5}\times100 \approx -28.6\% \]
3. Elasticity: \[ \varepsilon_{d}= \frac{22.2\%}{-28.6\%}\approx -0.78 \]
   Absolute value |ε| = 0.78 < 1 → demand is inelastic between £20 and £15.
4. Interpretation (AO3): A 1 % fall in price raises quantity demanded by only 0.78 %; the firm could raise total revenue by increasing price, but must consider other factors (costs, market share, long‑run elasticity).

9. Interpreting the Demand Diagram

• Movement along the curve – caused solely by a change in the good’s own price.
• Shift of the curve – caused by any of the five determinants listed above.
• Slope – the steeper the curve, the less responsive (more inelastic) the quantity is to price changes; a flatter curve indicates higher responsiveness (more elastic).
• PED – quantifies the responsiveness shown by the slope; the sign is negative by convention, but the absolute value determines the elasticity category.

10. Link to Market Failure (Merit & Demerit Goods)

11. Optional Extension – Consumer Surplus

Consumer surplus = area under the demand curve and above the market price. It measures the net benefit to consumers and is useful when evaluating the welfare impact of price changes, taxes, or subsidies.

12. Suggested Diagram (placeholder)

13. Practice Questions (with AO tags)

1. Explain why a fall in the price of coffee leads to a movement along the demand curve for coffee, but a rise in consumers’ income leads to a shift of the demand curve.
   AO1, AO2
2. Given the demand function Q = 200 – 5P:
   1. Calculate the quantity demanded when the price is £20 and plot the point on a diagram.
      AO1
   2. Using the same function, compute the price elasticity of demand between £20 and £15. State whether demand is elastic, inelastic or unit‑elastic and explain what this tells a firm about revenue.
      AO2, AO3
3. Identify two factors that could cause the demand curve for smartphones to shift to the right and explain the economic reasoning behind each.
   AO2
4. Briefly discuss how a right‑hand shift in the demand curve for a de‑merit good could lead to market failure. Suggest one policy response and evaluate its likely effectiveness.
   AO3
5. Using the midpoint method, calculate the PED for a good whose price falls from £8 to £6 and quantity rises from 40 to 55 units. Classify the elasticity and comment on the implication for a firm considering a price cut.
   AO2, AO3

14. Mark‑scheme Hints (for teacher use)

• Q1 – mention ceteris paribus, price as the only variable that moves along the curve; income as a non‑price determinant causing a shift.
• Q2a – show calculation (Q = 200 – 5×20 = 100) and label point (20, 100) on the diagram.
• Q2b – work the midpoint calculation, give |ε| ≈ 0.78, state “inelastic”, explain that a price rise would increase total revenue.
• Q3 – examples: (i) rise in consumer income, (ii) launch of a popular new app that makes smartphones more fashionable; link each to right‑hand shift.
• Q4 – describe over‑consumption, negative externalities, government tax; evaluate (e.g., tax reduces quantity but may be regressive).
• Q5 – ΔQ = 15, ΔP = –2; %ΔQ = 15/47.5×100 ≈ 31.6 %; %ΔP = –2/7×100 ≈ –28.6 %; ε ≈ –1.10 → elastic; a price cut would increase total revenue, but consider cost‑structure.