Worked Solutions
Topic 1: Introduction to Economics — Worked Solutions (Preliminary Economics)
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Worked examples for Topic 1 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 — Opportunity cost on a production possibility frontier
Question
An economy can produce only two goods, wheat and machines. Its production possibility frontier passes through the following combinations:
| Point | Wheat (tonnes) | Machines (units) |
|---|---|---|
| A | 0 | 60 |
| B | 20 | 54 |
| C | 40 | 42 |
| D | 60 | 24 |
| E | 80 | 0 |
(a) Calculate the opportunity cost, in machines, of moving from point B to point C. (1 mark)
(b) State whether opportunity cost is increasing or constant as the economy produces more wheat, and explain your answer. (3 marks)
Solution
(a) Opportunity cost is what you give up. Moving B → C, wheat rises by 20 tonnes while machines fall from 54 to 42. That's a sacrifice of 12 machines.
(b) Compare each 20-tonne step of wheat: A→B costs 6 machines, B→C costs 12, C→D costs 18, D→E costs 24. The sacrifice grows each time, so opportunity cost is increasing.
The reason: resources aren't equally suited to both goods. As you push wheat production up, you must transfer resources that were better at making machines, so each extra batch of wheat costs more machines than the last. That's why the PPF bows outward.
(a) Let's start with what opportunity cost means — it's the value of the next best thing you give up. Here, to get more wheat we have to make fewer machines. Moving from B to C, wheat goes up by 20 tonnes (from 20 to 40), and machines fall from 54 to 42. The cost of that extra wheat is the 12 machines we no longer produce.
(b) Now look across the whole frontier. Each time wheat rises by 20 tonnes, count the machines lost: A→B loses 6, B→C loses 12, C→D loses 18, D→E loses 24. The amount sacrificed keeps growing, so opportunity cost is increasing.
Why does this happen? Resources aren't equally good at everything. The first land switched to wheat is the most fertile, so little is lost. But to keep expanding wheat, the economy has to reassign resources that were really productive at making machines — so each extra step costs more. This is exactly why a realistic PPF curves outward rather than being a straight line.
(a) B → C: wheat +20, machines 54 → 42.
- Opportunity cost = 12 machines.
(b) Machines given up per 20-tonne step of wheat:
- A→B: 6
- B→C: 12
- C→D: 18
- D→E: 24
Sacrifice rises each step → opportunity cost is increasing.
- Cause: resources not equally suited to both goods.
- Each extra unit of wheat draws on resources better at machines → rising cost.
- PPF therefore bows outward (concave to origin).
Where the marks go
- 1 mark: Correctly calculates the opportunity cost of B → C as 12 machines
- 1 mark: States that opportunity cost is increasing
- 1 mark: Supports the answer with evidence from the data (rising sacrifice per step)
- 1 mark: Explains why — resources are not equally suited to producing both goods
Key idea
Opportunity cost is what is given up to gain something else; on a bowed-out PPF it increases because resources are not equally productive across goods.
Example 2 — The economic problem
Question
Explain how the problem of relative scarcity gives rise to the three basic economic questions that every economy must answer. (4 marks)
Solution
Start with the core: wants are unlimited but resources are limited. That mismatch is relative scarcity — and it forces every economy to make choices.
Because resources can't satisfy every want, an economy must decide:
- What to produce — which goods and services, and in what quantities, given limited resources.
- How to produce — which combination of resources and methods to use to get the most out of what's available.
- For whom to produce — how output is distributed among the population.
Tie it back: each question only exists because of scarcity. With unlimited resources there'd be nothing to choose between. State the link explicitly — markers want to see scarcity driving the three questions, not just the questions listed.
The starting point is the economic problem itself: people's wants are effectively unlimited, but the resources available to satisfy them are limited. Economists call this relative scarcity — limited resources relative to unlimited wants.
Because we can't have everything, choices are unavoidable, and those choices boil down to three questions:
- What to produce? We can't make everything, so society must decide which goods and services, and how much of each.
- How to produce? Since resources are scarce, we want to use them efficiently — choosing the best mix of labour, capital and methods.
- For whom to produce? Output is limited, so we must decide how it's shared among people in the economy.
The thread connecting them is scarcity: if resources were unlimited, every want could be met and none of these questions would matter. It's precisely because choosing one thing means going without another that every economy — no matter how it's organised — has to answer all three.
Relative scarcity = unlimited wants, limited resources → choices unavoidable.
Three basic questions follow:
- What to produce — which goods/services and in what quantities.
- How to produce — which resources and methods (efficiency).
- For whom to produce — how output is distributed.
Link: scarcity forces a trade-off; unlimited resources would remove the need to choose. Each question is a consequence of scarcity.
Where the marks go
- 1 mark: Defines relative scarcity (unlimited wants, limited resources)
- 1 mark: Identifies and describes the 'what to produce' question
- 1 mark: Identifies and describes the 'how' and 'for whom' questions
- 1 mark: Explicitly links scarcity to the need to answer the three questions
Key idea
Relative scarcity — unlimited wants against limited resources — forces every economy to choose what, how and for whom to produce.