Worked Solutions
Topic 4: Labour Markets — Worked Solutions (Preliminary Economics)
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Worked examples for Topic 4 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.
How to use these
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 — Calculating the unemployment rate
Question
In a given month an economy has a working-age population of 20 million. Of these, 12.8 million are employed and 1.2 million are unemployed.
(a) Calculate the size of the labour force. (1 mark)
(b) Calculate the unemployment rate and the labour force participation rate. (2 marks)
Solution
(a) The labour force is everyone employed plus everyone unemployed (actively seeking work): $12.8 + 1.2 = \mathbf{14\ \text{million}}$.
(b) The unemployment rate is unemployed as a share of the labour force: $\dfrac{1.2}{14} × 100 = 8.57\%$ (about 8.6%).
The participation rate is the labour force as a share of the working-age population: $\dfrac{14}{20} × 100 = \mathbf{70\%}$.
Watch the denominators — unemployment uses the labour force, participation uses the whole working-age population. Mixing them is the classic error.
(a) The labour force is made up of two groups: people with a job and people without one who are actively looking. So we add them: $12.8 + 1.2 = \mathbf{14\ \text{million}}$. Notice that people not working and not seeking work aren't counted here.
(b) The unemployment rate asks: of those in the labour force, what fraction can't find work? So we divide the unemployed by the labour force: $\dfrac{1.2}{14} × 100 ≈ \mathbf{8.6\%}$.
The participation rate asks a different question: of all working-age people, how many are in the labour force at all? So the denominator changes to the whole working-age population: $\dfrac{14}{20} × 100 = \mathbf{70\%}$. The key is to keep the two denominators straight — unemployment is measured against the labour force, participation against the working-age population.
(a) Labour force = employed + unemployed $= 12.8 + 1.2 = \mathbf{14\ \text{m}}$.
(b)
- Unemployment rate $= \dfrac{\text{unemployed}}{\text{labour force}} = \dfrac{1.2}{14} × 100 ≈ \mathbf{8.6\%}$.
- Participation rate $= \dfrac{\text{labour force}}{\text{working-age pop}} = \dfrac{14}{20} × 100 = \mathbf{70\%}$.
- Note: different denominators — labour force vs working-age population.
Where the marks go
- 1 mark: Calculates the labour force as 14 million (employed + unemployed)
- 1 mark: Calculates the unemployment rate ≈ 8.6%
- 1 mark: Calculates the participation rate = 70%
Key idea
The labour force is the employed plus the unemployed; the unemployment rate is measured against the labour force, the participation rate against the working-age population.
Example 2 — Wage determination and labour demand
Question
(a) Explain why the demand for labour is described as a derived demand. (2 marks)
(b) Using demand and supply of labour, explain how an increase in demand for a particular type of skilled worker would affect the equilibrium wage and level of employment in that market. (3 marks)
Solution
(a) Labour isn't wanted for its own sake — firms hire workers because of the goods and services those workers help produce. The demand for labour is therefore derived from the demand for the final product. If demand for the product rises, firms want more workers; if it collapses, so does the demand for that labour.
(b) Treat it as a standard market with wage on the vertical axis and quantity of labour on the horizontal.
- An increase in demand for skilled workers shifts the labour demand curve to the right.
- Supply is unchanged in the short run (skills take time to acquire).
- At the old wage there's now a shortage of these workers, so the equilibrium wage rises and the equilibrium quantity of labour employed rises too.
So both the wage and employment increase — the standard result of a rightward demand shift along an upward-sloping supply curve.
(a) When economists call labour a derived demand, they mean firms don't want workers for the sake of it — they want what workers produce. The demand for labour is derived from the demand for the goods and services it makes. Picture a café: it employs baristas only because customers want coffee. If demand for coffee jumps, the café wants more baristas; if it falls away, it needs fewer. The labour demand follows the product demand.
(b) Now think of the market for one type of skilled worker, with the wage on the vertical axis and the number of workers on the horizontal.
- A rise in demand for these workers shifts the demand curve to the right.
- The supply of skilled labour can't adjust instantly — it takes time and training to produce more of these workers — so supply stays put for now.
- With more firms chasing the same pool of workers, there's upward pressure on pay: the equilibrium wage rises. And because firms want to hire more at the new, higher demand, the quantity of labour employed also rises.
So the outcome is higher wages and higher employment for this group — exactly what we'd expect when demand grows against a relatively fixed supply.
(a)
- Labour demanded not for itself but for what it produces.
- Hence demand for labour is derived from demand for the final good/service.
- Example: more demand for the product → firms hire more workers.
(b) Market for skilled labour (wage vs quantity):
- Demand for skilled workers ↑ → demand curve shifts right.
- Supply fixed in short run (training takes time).
- Shortage at old wage → equilibrium wage ↑ and employment ↑.
- Result: both wage and quantity of labour rise.
Where the marks go
- 1 mark: States that labour is wanted for what it produces, not for itself
- 1 mark: Links the demand for labour to the demand for the final good/service (derived)
- 1 mark: Identifies a rightward shift of the labour demand curve
- 1 mark: Explains that the equilibrium wage rises
- 1 mark: Explains that the equilibrium level of employment rises
Key idea
Labour is a derived demand — it depends on demand for the goods it produces; a rightward shift in labour demand raises both the equilibrium wage and employment.