Pearson Edexcel International Advanced Level Economics: Revenue and short-run costs (YEC11)

This guide covers section 3.3.2 (Revenue, costs and profits), items 1 and 2, of the Pearson Edexcel International Advanced Subsidiary/Advanced Level Economics (YEC11) specification, Issue 2, June 2018. Units 1 and 2 make up the International AS. Unit 3, Business behaviour, is extra International A2 content: the specification labels it an IAL compulsory unit, so it is not part of the IAS alone. Items 3 and 4 of 3.3.2 (scale, profits and shutdown points) are taught elsewhere.

Use the Edexcel A Level Economics hub and the printable checklist to track progress. Unsure where you stand? Try the free 10-minute diagnostics. After this guide, use the revision notes and the practice questions. Elasticity is first met in rational choice, demand and elasticities.

Every number below is invented for teaching. The firm, the country and the currency units (cu) are fictional.

What this guide covers

Item	What you must be able to do
1a	Use and relate the formulae for total, average and marginal revenue
1b	Link price elasticity of demand (PED) to revenue, including calculations
2a	Derive short-run cost curves from diminishing marginal productivity
2b	Explain the law of diminishing returns
2c	Use and relate the formulae for TC, TFC, TVC, ATC, AFC, AVC and MC
2d	Relate MP to MC, average product to average cost, TP to TC, and short-run to long-run costs

1a Revenue: TR, AR and MR

Total revenue (TR) is the money a firm receives from sales: TR = price x quantity = P x Q. Average revenue (AR) is revenue per unit sold: AR = TR / Q. Because TR = P x Q, AR is always equal to price, so a firm’s AR curve is its demand curve. Marginal revenue (MR) is the extra revenue from selling one more unit: MR = change in TR / change in Q.

A firm that must cut its price to sell more has a downward-sloping AR curve. The price cut applies to every unit sold, not just the extra one. So the extra unit adds its own price, but earlier units now sell for less, and MR falls below AR. A firm that is a price taker sells every unit at the same market price, so AR = MR = P (a horizontal line).

Worked example. Country A has a small bicycle workshop with the linear demand P = 84 - 3Q, where Q is repairs per week.

Q	P = AR (cu)	TR (cu)	MR = 84 - 6Q (cu)
4	72	288	60
8	60	480	36
12	48	576	12
14	42	588	0
16	36	576	-12
20	24	480	-36

Read the pattern. While MR is positive, TR rises. At Q = 14, MR = 0 and TR is at its maximum of 588. Beyond that MR is negative and TR falls. For a straight-line demand curve, the MR curve starts at the same price intercept as AR and has twice the slope. Check from the table: moving from Q = 8 to Q = 12, TR rises by 96 over 4 extra units, so MR = 24, which lies between 36 and 12.

In words for a diagram: put price and revenue in cu on the vertical axis and quantity on the horizontal axis. AR slopes down from 84. MR starts at 84 and cuts the horizontal axis at Q = 14, halfway to where AR meets it at Q = 28. TR is an arch that peaks at Q = 14.

1b PED and revenue

PED = % change in quantity demanded / % change in price. It is normally negative, because demand slopes down, but you may quote its size. Demand is elastic when PED is greater than 1 in size, inelastic when it is less than 1 in size, and unitary when it is exactly 1 in size.

Demand	Price rises	Price falls
Elastic (size above 1)	TR falls	TR rises
Unitary (size equal to 1)	TR unchanged	TR unchanged
Inelastic (size below 1)	TR rises	TR falls

The reason is that TR = P x Q. When demand is elastic, the percentage change in Q outweighs the percentage change in P. When demand is inelastic, the price effect wins.

Worked example, using the workshop. The price falls from 60 cu to 48 cu, so repairs rise from 8 to 12.

%change in P = (48 - 60)/60 x 100 = -20%
%change in Q = (12 - 8)/8 x 100 = +50%
PED = 50 / -20 = -2.5   (elastic)
TR before = 60 x 8 = 480;  TR after = 48 x 12 = 576;  change = +96

The result matches the rule: elastic demand, price cut, revenue up. The same demand curve has different elasticity at different points. At Q = 14 and P = 42, PED = -1.0 (unitary) and TR is at its peak. Above that price demand is elastic; below it, demand is inelastic. A straight-line demand curve is therefore not “constant elasticity”. MR also links to PED: MR = P x (1 + 1/PED). At P = 60 and PED = -2.5, MR = 60 x 0.6 = 36, as in the table. MR is positive only where demand is elastic.

2a and 2b Diminishing marginal productivity and returns

In the short run at least one factor is fixed (here, the workshop’s space and tools) and the others are variable (labour). Total product (TP) is output. Marginal product (MP) is the extra output from one more worker. Average product (AP) is TP / workers.

The law of diminishing returns says that when extra units of a variable factor are added to a fixed factor, there comes a point where each additional unit adds less to output than the one before. MP then falls. It does not say output falls, only that it rises more slowly. At first MP may rise, because workers share tools and specialise.

Worked example. The workshop pays each worker 400 cu a week. Fixed costs (rent, tools) are 600 cu a week. Q equals TP.

Workers	TP	MP	AP
1	8	8	8.0
2	22	14	11.0
3	42	20	14.0
4	58	16	14.5
5	70	12	14.0
6	78	8	13.0
7	82	4	11.7

MP peaks at the third worker. Diminishing returns begin with the fourth. TP keeps rising, so this is falling MP, not falling TP. AP peaks at the fourth worker (14.5). MP is above AP up to that worker and below it from the fifth, because a marginal value above the average pulls the average up and one below pulls it down.

2c Cost formulae

Measure	Formula
TC	TFC + TVC
AFC	TFC / Q
AVC	TVC / Q
ATC (AC)	TC / Q = AFC + AVC
MC	change in TC / change in Q (= change in TVC / change in Q)

Fixed costs do not change with output in the short run. Variable costs rise with output. Marginal cost ignores fixed cost completely.

Costs for the workshop: TVC = 400 x workers, TC = 600 + TVC.

Workers	Q	TC	AFC	AVC	ATC	MC
1	8	1,000	75.00	50.00	125.00	50.00
2	22	1,400	27.27	36.36	63.64	28.57
3	42	1,800	14.29	28.57	42.86	20.00
4	58	2,200	10.34	27.59	37.93	25.00
5	70	2,600	8.57	28.57	37.14	33.33
6	78	3,000	7.69	30.77	38.46	50.00
7	82	3,400	7.32	34.15	41.46	100.00

Method for one row, workers = 4. Q = 58. TVC = 4 x 400 = 1,600. TC = 600 + 1,600 = 2,200. AFC = 600 / 58 = 10.34. AVC = 1,600 / 58 = 27.59. ATC = 2,200 / 58 = 37.93, which equals 10.34 + 27.59. MC = 400 / 16 = 25.00, or (2,200 - 1,800) / (58 - 42) = 25.00. Each MC here is the cost per extra unit over the step from the previous row.

2d Relationships between curves

MP and MC. If the wage is constant, MC = wage / MP. When MP rises, MC falls; when MP falls, MC rises. Compare the tables: MP peaks at 20 with the third worker, and MC bottoms at 20 cu. So the U shape of MC is diminishing marginal productivity seen from the cost side. In words: MC falls from 50 to 20, then rises to 100 at the seventh worker.

AP and average cost. AVC = wage x workers / Q = wage / AP. AP peaks at the fourth worker, so AVC is lowest there (27.59). ATC is also fed by AFC, which keeps falling as fixed cost is spread. So ATC keeps falling after AVC has started to rise, and bottoms later, at 5 workers (37.14). MC cuts AVC and ATC at their lowest points, for the same average-and-marginal reason. Check ATC: at the fifth worker MC (33.33) is below ATC, so ATC is still falling to 37.14. At the sixth worker MC (50.00) is above ATC, so ATC rises to 38.46.

TP and TC. The TC curve is the TP curve turned around. While TP rises at an increasing rate (MP rising), TC rises at a decreasing rate. After diminishing returns begin, TP flattens and TC steepens. TC starts on the vertical axis at TFC (600), not at the origin.

Short run and long run. In the short run some factors are fixed, so diminishing returns apply and the curves above are U-shaped. In the long run all factors are variable, so there are no fixed costs and every cost is variable. A firm that expands its plant moves to a new short-run cost curve. The long-run average cost curve links the lowest cost of each output level. Why it slopes as it does is the topic of economies and diseconomies of scale, which is a separate unit.

Evaluation points

• Firms rarely know their demand curve exactly. A PED estimate is a guess, so a revenue forecast from it is uncertain.
• PED applies to a price change over a set time. Over a longer period demand is usually more elastic, so a price rise that raises revenue today may not later.
• Higher revenue does not mean the firm gains more. Extra output has extra cost, and that cost rises once diminishing returns begin.
• The tidy U-shaped curves assume one variable factor, fixed wage rates and the same quality of labour. Real firms have several fixed and variable inputs.

Common errors

• Calling AR and price different things. They are the same.
• Drawing MR above AR for a firm with a downward-sloping demand curve.
• Saying “total output falls” when MP falls.
• Including fixed costs in MC.
• Saying elastic demand means a price rise raises revenue. It lowers it.
• Forgetting that AFC falls all the way but never reaches zero.
• Using only the quantity change in a PED calculation. Use both percentage changes.

Official syllabus

Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics (YEC11), specification Issue 2, June 2018, section 3.3.2 items 1 and 2, published by Pearson Education Limited.