Worked Solutions
Topic 3: Markets — Worked Solutions (Preliminary Economics)
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Worked examples for Topic 3 of Preliminary Economics. Each shows where the marks are awarded, the key idea, and the full solution explained by your choice of tutor — Stella, Ella or Cassie.
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Try each question first, then check your working. Use the tutor tabs to read the full solution in the style that suits you: Stella is direct and challenging, Ella is warm and explains the why, and Cassie is concise and analytical.
Example 1 — Price elasticity of demand
Question
When the price of a product rises from \$20 to \$24, the quantity demanded falls from 1 000 units to 850 units per week.
(a) Calculate the price elasticity of demand using the simple percentage-change method. (2 marks)
(b) State whether demand is elastic or inelastic, and explain what would happen to the firm's total revenue if it raised the price. (2 marks)
Solution
(a) Use $E_d = \dfrac{\%\Delta Q}{\%\Delta P}$.
- %ΔQ $= \dfrac{850 - 1000}{1000} = \dfrac{-150}{1000} = -15\%$
- %ΔP $= \dfrac{24 - 20}{20} = \dfrac{4}{20} = +20\%$
- $E_d = \dfrac{-15}{20} = -0.75$, or 0.75 in magnitude.
(b) Since $|E_d| < 1$, demand is inelastic — quantity responds proportionally less than price. With inelastic demand, raising price increases total revenue, because the percentage fall in quantity (15%) is smaller than the percentage rise in price (20%). Check it: revenue goes from $20 × 1000 = \$20\,000$ to $24 × 850 = \$20\,400$. It rises, exactly as the elasticity predicts.
(a) Price elasticity of demand measures how responsive quantity demanded is to a price change — we compare the percentage change in quantity with the percentage change in price.
- Quantity: $\dfrac{850 - 1000}{1000} = -15\%$
- Price: $\dfrac{24 - 20}{20} = +20\%$
- $E_d = \dfrac{-15\%}{+20\%} = -0.75$. We usually quote the size, so 0.75.
(b) Because the value is less than 1 (ignoring the sign), demand is inelastic — buyers don't cut back much when price rises. Here's why total revenue matters: revenue is price × quantity. When demand is inelastic, a price rise loses only a small amount of quantity, so the higher price more than makes up for it. Let's confirm: revenue starts at $\$20 × 1000 = \$20\,000$ and ends at $\$24 × 850 = \$20\,400$. So raising the price actually increases total revenue — which is the general rule whenever demand is inelastic.
(a)
- %ΔQ $= \dfrac{850 - 1000}{1000} = -15\%$
- %ΔP $= \dfrac{24 - 20}{20} = +20\%$
- $E_d = \dfrac{-15}{20} = \mathbf{-0.75}$ (magnitude 0.75).
(b)
- $|E_d| < 1$ → inelastic.
- Inelastic + price rise → total revenue rises.
- Check: $20 × 1000 = 20\,000$ → $24 × 850 = 20\,400$. ✓
Where the marks go
- 1 mark: Correctly calculates the percentage changes in quantity (−15%) and price (+20%)
- 1 mark: Correctly calculates elasticity as −0.75 (magnitude 0.75)
- 1 mark: Identifies demand as inelastic because |Ed| < 1
- 1 mark: Explains that total revenue rises when price increases under inelastic demand
Key idea
Price elasticity is %ΔQ ÷ %ΔP; when demand is inelastic (|Ed| < 1) a price rise increases total revenue.
Example 2 — Market equilibrium and market failure
Question
The weekly demand and supply for a good are given by:
| Price (\$) | Quantity demanded | Quantity supplied |
|---|---|---|
| 4 | 900 | 300 |
| 6 | 700 | 500 |
| 8 | 500 | 500 |
| 10 | 300 | 700 |
(a) Identify the equilibrium price and quantity, and explain how the market reaches it. (3 marks)
(b) Explain how a negative externality in production is an example of market failure. (2 marks)
Solution
(a) Equilibrium is where quantity demanded equals quantity supplied. From the table that's at a price of \$8, where both equal 500 units.
The market gets there through price signals. At \$6, demand (700) exceeds supply (500) — a shortage — so buyers bid the price up. At \$10, supply (700) exceeds demand (300) — a surplus — so sellers cut the price. These pressures push the price toward \$8, where the plans of buyers and sellers match and there's no tendency to change.
(b) A negative externality in production is a cost imposed on third parties not involved in the transaction — for example, pollution from a factory. The market fails because the firm only counts its private costs and ignores the external cost, so the price is too low and the good is over-produced relative to what's best for society. Resources are misallocated.
(a) Market equilibrium is the price at which the quantity buyers want to buy equals the quantity sellers want to sell. Scanning the table, the two columns are equal at a price of \$8, where both quantity demanded and quantity supplied are 500 units — so that's our equilibrium.
How does the market settle there? Through the price mechanism. At a lower price like \$6, buyers want 700 but sellers only offer 500, leaving a shortage of 200; competition among buyers pushes the price up. At a higher price like \$10, sellers offer 700 but buyers want only 300, creating a surplus; sellers lower the price to clear stock. These forces keep nudging the price until it lands at \$8, where there's neither a shortage nor a surplus and the market clears.
(b) A negative externality in production happens when producing a good imposes a cost on people outside the transaction — classically, pollution from a factory affecting nearby residents. This is market failure because the firm bases its decisions only on its own private costs and ignores the cost borne by society. As a result the good is priced too cheaply and produced in greater quantity than is socially desirable, so resources are not allocated efficiently.
(a) Equilibrium: $Q_d = Q_s$.
- Occurs at **\$8**, where $Q_d = Q_s = 500$.
- Below \$8 → shortage ($Q_d > Q_s$) → price bid up.
- Above \$8 → surplus ($Q_s > Q_d$) → price cut down.
- Price mechanism converges to \$8 (market clears).
(b) Negative externality in production = cost on third parties (e.g. pollution).
- Firm counts private cost only, ignores external cost.
- Good is under-priced and over-produced vs social optimum.
- → resource misallocation = market failure.
Where the marks go
- 1 mark: Identifies equilibrium price (\$8) and quantity (500 units)
- 1 mark: Explains shortage below and surplus above equilibrium
- 1 mark: Explains the price mechanism driving the market to equilibrium
- 1 mark: Defines a negative externality in production with an example
- 1 mark: Explains why it causes market failure (over-production / misallocation)
Key idea
Equilibrium is where quantity demanded equals quantity supplied; shortages and surpluses move price toward it, while externalities cause market failure by distorting price and output.