OxfordAQA AS and A-level Economics: Cost, revenue, profit and elasticity (9640)

This guide follows the OxfordAQA International AS and A-level Economics specification (9640), version 1.2, and covers quantitative skills QS6 (cost, revenue and profit, including averages and totals) and QS8 (calculating elasticity and interpreting the result) from section 3.5. These skills can be assessed in any unit. The economics they rely on sits in sections 3.1.2.2, 3.1.2.4 and 3.1.3.3 to 3.1.3.5, which are International AS content, and in sections 3.3.2.4 and 3.3.2.5, which are extra International A2 content. The specification says that for A2 assessments you must also calculate marginal values. All the firms, countries and figures below are made up as illustrations.

Where to go next: revision notes, practice questions, the operation of markets guide, the costs, scale and revenue guide, the course hub, the printable checklist and the free 10-minute diagnostics.

What you must be able to do

Skill	What the specification asks	Stage
QS6	Calculate cost, revenue and profit, including average and total values	AS and A2
QS6	Calculate marginal values	A2 assessments
QS8	Calculate price, income and cross elasticity of demand, and price elasticity of supply, and interpret the result	AS and A2
3.1.2.2	Link price elasticity of demand to total revenue (total expenditure)	AS and A2
3.3.2.4	Link marginal revenue, total revenue and price elasticity of demand	A2

QS6: cost, revenue and profit

Total, average and marginal values. Learn each formula, and what it measures.

Measure	Formula
Total cost (TC)	fixed cost (FC) + variable cost (VC)
Average fixed cost (AFC)	FC ÷ output
Average variable cost (AVC)	VC ÷ output
Average cost (AC)	TC ÷ output, which equals AFC + AVC
Marginal cost (MC), A2 assessments	change in TC ÷ change in output
Total revenue (TR)	price × quantity sold
Average revenue (AR)	TR ÷ quantity, which equals price if every unit sells at one price
Marginal revenue (MR), A2 assessments	change in TR ÷ change in output
Profit	TR − TC

Worked example 1: a mobile car-wash business

Fixed cost is 120 a day. Output is cars washed. Working for 30 cars: VC = 520 − 120 = 400; AFC = 120 ÷ 30 = 4.00; AVC = 400 ÷ 30 = 13.33; AC = 520 ÷ 30 = 17.33, and AFC + AVC = 4.00 + 13.33 = 17.33, which checks it. MC over the step from 20 to 30 cars = (520 − 380) ÷ (30 − 20) = 14.

Cars	TC	VC	AFC	AVC	AC	MC (per car over the step)
10	260	140	12.00	14.00	26.00	14
20	380	260	6.00	13.00	19.00	12
30	520	400	4.00	13.33	17.33	14
40	720	600	3.00	15.00	18.00	20
50	1,000	880	2.40	17.60	20.00	28

Read the table. AC falls to 30 cars, then rises. MC is below AC while AC falls (14 against 19 at the 20 to 30 step) and above AC once it rises (20 against 17.33 for the step to 40 cars). If a new unit costs less than the average, it pulls the average down; if it costs more, it pulls the average up.

A rise in fixed cost to 200 at 30 cars: TC = 200 + 400 = 600, so AC = 600 ÷ 30 = 20.00, up from 17.33 (+15.4%). AVC and MC do not change, because they do not include fixed cost.

Worked example 2: a pottery studio’s revenue, cost and profit

Demand is price = 44 − 4 × quantity (mugs a day), and fixed cost is 30.

Mugs	Price (AR)	TR	MR	TC	MC	Profit
1	40	40	40	50	20	−10
2	36	72	32	68	18	4
3	32	96	24	84	16	12
4	28	112	16	102	18	10
5	24	120	8	124	22	−4
6	20	120	0	150	26	−30

Working for 4 mugs: TR = 28 × 4 = 112; MR = 112 − 96 = 16; profit = 112 − 102 = 10. Profit is highest at 3 mugs (12). MR is above MC at the third mug (24 against 16), so that mug adds to profit. At the fourth mug MR (16) is below MC (18), so it lowers profit. Marginal values explain why the profit peak is where it is. The A2 content in 3.3.2.4 asks you to calculate and interpret these revenue values.

A profit per unit check: AR − AC at 3 mugs is 32 − 28 = 4, and 4 × 3 = 12, the same as TR − TC.

QS8: elasticity

Every elasticity has the same shape: a percentage change in one thing divided by the percentage change in another.

Elasticity	Formula	What the sign tells you
Price elasticity of demand (PED)	% change in quantity demanded ÷ % change in price	Negative for a normal demand curve
Income elasticity of demand (YED)	% change in quantity demanded ÷ % change in income	Positive: normal good. Negative: inferior good
Cross elasticity of demand (XED)	% change in quantity demanded of A ÷ % change in price of B	Positive: substitutes. Negative: complements
Price elasticity of supply (PES)	% change in quantity supplied ÷ % change in price	Positive for a normal supply curve

Method. Find each percentage change as (new − old) ÷ old × 100, using the same starting point throughout. Divide, keep the sign, and then say what it means. If a question tells you to use a particular method, follow it.

Size. Ignoring the sign, a value above 1 is elastic (quantity responds proportionally more than the cause), below 1 is inelastic, and exactly 1 is unit elastic. A value of 0 is perfectly inelastic. Many writers quote PED without the minus sign, so state which you are doing.

Worked example 3: PED and total revenue

A tram fare rises from 2.00 to 2.40, and daily passengers fall from 5,000 to 4,400.

%ΔP = (2.40 − 2.00) ÷ 2.00 × 100 = +20.0%; %ΔQ = (4,400 − 5,000) ÷ 5,000 × 100 = −12.0%; PED = −12.0 ÷ 20.0 = −0.6.

Demand is inelastic. TR before = 2.00 × 5,000 = 10,000; after = 2.40 × 4,400 = 10,560, a rise of 5.6%.

A bowling alley cuts a session price from 10 to 8 and weekly sessions rise from 640 to 960. %ΔP = −20.0%, %ΔQ = +50.0%, PED = 50.0 ÷ −20.0 = −2.5. Demand is elastic. TR rises from 6,400 to 7,680 (+20.0%).

PED (ignoring sign)	Price rise	Price fall
Below 1 (inelastic)	TR rises	TR falls
Equal to 1	TR unchanged	TR unchanged
Above 1 (elastic)	TR falls	TR rises

Why: TR = price × quantity. With elastic demand the percentage change in quantity outweighs the percentage change in price, and with inelastic demand it is the other way round. This is the link between PED and total revenue (total expenditure) in section 3.1.2.2.

Worked example 4: elasticity changes along a straight line

Demand is Q = 200 − 10P. At a price of 8, Q = 120. At 9, Q = 110: %ΔQ = −8.33%, %ΔP = +12.5%, PED = −0.67. At a price of 12, Q = 80; at 13, Q = 70: %ΔQ = −12.5%, %ΔP = +8.33%, PED = −1.5. TR at 8 is 960 and at 9 is 990, so a rise raises TR where demand is inelastic. At 12 the TR is 960 and at 13 it is 910, so the rise lowers TR where demand is elastic. A straight-line demand curve has the same slope everywhere but a different elasticity at each price, because the same unit change is a bigger percentage at low quantities. Also note the direction: the move from 13 back to 12 gives %ΔQ = +14.3% and %ΔP = −7.7%, so PED is −1.86. Calculations depend on the starting point, so always use the one the question gives you.

Worked example 5: YED and XED

Household income rises from 3,000 to 3,150 (+5.0%). Takeaway meals rise from 8 to 9 a month (+12.5%), so YED = +2.5: a normal good, income elastic. Bags of budget rice fall from 40 to 38 (−5.0%), so YED = −1.0: an inferior good.

The price of tea rises from 4.00 to 4.40 (+10.0%) and demand for coffee rises from 500 to 540 (+8.0%): XED = +0.8, so they are substitutes. If the price of printers rises 20% and demand for ink cartridges falls 30%, XED = −1.5, so they are complements. The larger the number, the closer the link.

Worked example 6: PES

A farm cooperative sees the price of its crop rise from 50 to 55 (+10.0%) and quantity supplied rise from 2,000 to 2,100 tonnes (+5.0%): PES = 5.0 ÷ 10.0 = 0.5. Supply is inelastic. This fits a product that takes a season to grow, where output cannot rise quickly. If a price fall of 20% cuts quantity supplied by 30%, PES = +1.5, elastic.

A2: marginal revenue and PED

When a firm cuts price to sell more, it gains from the extra units and loses on the units it could have sold at the higher price. The balance depends on PED. For a firm with a downward-sloping demand curve, MR = P × (1 + 1/PED), with PED as a negative number. This is a shortcut result, so check your method matches the question. At a price of 12 on the demand curve in example 4, PED is −1.5, so MR = 12 × (1 − 0.667) = 4. Using a straight-line demand curve P = 20 − 0.1Q, MR = 20 − 0.2Q = 4 at Q = 80, which agrees.

PED	MR	TR if output rises
Elastic (below −1)	Positive	Rises
Unit elastic (−1)	Zero	At a maximum
Inelastic (between 0 and −1)	Negative	Falls

A firm maximising profit will therefore not choose a point where demand is inelastic, because MR is negative and MC cannot be.

Interpreting and evaluating

A number is not an answer. Add a chain: the value, what it means for buyers or sellers, and what a firm or government should do. For example, a PED of −0.6 means a 10% fare rise loses only about 6% of passengers, so TR rises, and a transport firm may raise fares. Then evaluate: elasticity values come from past data and may not hold now; they assume other things stay equal; short-run and long-run values differ (substitutes appear over time); and a bigger revenue is not automatically a bigger profit, because costs fall when output falls.

Common errors

• Using the new value as the base for a percentage change.
• Dividing the wrong way round (price over quantity).
• Dropping the sign, then calling a negative YED “elastic” instead of “inferior”.
• Calling PED of 0.6 “elastic” because it feels like a large number.
• Writing MC as TC ÷ output (that is AC).
• Using AC instead of MC to explain the profit-maximising output.
• Forgetting fixed cost when moving from profit per unit to total profit.
• Claiming a revenue rise means a profit rise.

Official syllabus

OxfordAQA International AS and A-level Economics (9640), version 1.2, published by OxfordAQA: section 3.5 (QS6 and QS8), and sections 3.1.2.2, 3.1.2.4, 3.1.3.3 to 3.1.3.5, 3.3.2.4 and 3.3.2.5.