What is the profit-maximising rule for a monopoly?

Set marginal revenue equal to marginal cost, then read the price from the demand curve.

Why is marginal revenue below price under monopoly?

Selling more requires a lower price on every unit, so the lost revenue on existing units is deducted.

What does a higher Lerner index mean?

Price is further above marginal cost, so market power is greater.

How do competitive and monopoly output compare?

With the same demand and cost, the monopolist produces less and charges more.

S5 Economics paper 4: error drills on revenue and monopoly pricing

2026-11-10

Tutor Prep Guide · S5 Economics Market Structures

Ten items target the usual slips: treating price as revenue, forgetting the slope of marginal revenue, and assuming a higher price always means more profit.

Direct answers　Items 01 to 03 redrill total revenue, profit and average cost, 04 to 06 marginal revenue and MR = MC, 07 to 09 monopoly pricing, the competitive comparison and the Lerner index, and 10 corrects the highest-price fallacy.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S5 Economics Market Structures and Monopoly
Level	S5

02　Questions (10 items)

FoundationA firm sells 150 units at $80 each. Find total revenue.
FoundationA firm has total revenue of $9,600 and total cost of $7,200. Find its profit.
FoundationTotal cost is $4,500 at an output of 300 units. Find average cost.
IntermediateDemand is P = 100 – 2Q. Write the marginal revenue function and find marginal revenue at Q = 10.
IntermediateA firm has MC = 4Q and MR = 60 – 2Q. Find the profit-maximising output.
IntermediatePrice is $100 and the price elasticity of demand is 5. Find marginal revenue.
ChallengeDemand is P = 140 – 2Q and total cost is TC = 0.5Q^2 + 20Q + 50. Find the profit-maximising output, price and profit.
ChallengeIn the same market under perfect competition the price equals marginal cost of $20. Use P = 140 – 2Q to find output and compare with monopoly.
ChallengeFor the monopolist in item 07 at its profit-maximising output, find the Lerner index.
Error redoA student claims that a monopolist should charge the highest price on the demand curve because a higher price always means more profit. Correct the mistake.

03　Answers and one-line notes

#	Answer	One-line note
1	Total revenue is $12,000 (80 x 150).	Total revenue equals price times quantity.
2	Profit is $2,400 (9,600 – 7,200).	Profit equals total revenue minus total cost.
3	Average cost is $15 (4,500 / 300).	Average cost equals total cost divided by output.
4	MR = 100 – 4Q; at Q = 10, MR = $60.	With linear demand the marginal revenue curve is twice as steep.
5	Q = 10, where 4Q = 60 – 2Q.	Profit is maximised where marginal revenue equals marginal cost.
6	MR is $80 (100 x (1 – 1/5)).	MR = P(1 – 1/elasticity), so a more elastic demand brings MR closer to price.
7	Q = 24, P = $92, profit = $1,390.	Set MR = 140 – 4Q equal to MC = Q + 20 to get Q = 24, then read the price off demand.
8	Q = 60, which is 36 units more than the monopolist output of 24.	A competitive market sets output where price equals marginal cost.
9	0.522, that is (92 – 44) / 92.	The Lerner index measures how far price exceeds marginal cost.
10	At the highest price sales are zero, so profit cannot be maximised; set MR = MC for output, then read the price off demand.	Profit depends on the gap between revenue and cost, not on price alone.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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