Income and substitution effects; consumer and producer surplus – Consumer Behaviour (Senior 4 Economics) | Ganzaa

Consumer Behaviour

Lessons

Senior 4 · Economics

Consumer Behaviour

4 lessons

Lesson 4 of 4

Income and substitution effects; consumer and producer surplus

30 min

Cheaper potatoes, two reasons to buy more

When the price of a staple food falls after a good harvest, a household buys more of it for two separate reasons. Potatoes are now cheap compared with bananas and rice, so the family swaps some of those for potatoes. And the family is also better off: the money it used to spend on potatoes now stretches further, as if its income had risen. Economists split the response to a price change into these two parts, the substitution effect and the income effect, and the split explains even the strange case of a good whose demand rises when its price rises.

In unit 2 you saw that the demand curve usually slopes downwards. Here you will measure the two effects behind that slope on an indifference map, and then measure the gain that buyers and sellers get from a market: consumer and producer surplus.

Definition

Price effect: the total change in the quantity of a good bought when its price changes, other things equal.

Substitution effect: the part of the price effect caused by the change in relative prices alone, with the consumer kept on her original indifference curve (real income held constant).

Income effect: the part caused by the change in real income (purchasing power) that the price change brings, with relative prices held at their new level.

\text{Price effect} = \text{Substitution effect} + \text{Income effect}

Example: if a price fall raises purchases from 4 kg to 9 kg, and 2 kg of the rise would have happened even with real income unchanged, then the substitution effect is +2 kg and the income effect is +3 kg.

1. Separating the two effects on an indifference map

Uwera spends Frw 7,200 a week on Irish potatoes (X) and cooking bananas (Y). Bananas cost Frw 400 per kg. After a good harvest, potatoes fall from Frw 900 to Frw 400 per kg (illustrative prices). She ranks bundles by $U = X Y$ , so, as in lesson 3, she spends half her income on each good: $X = \frac{M}{2P_x}$ .

Point	Prices ( $P_{x}$ , $P_{y}$ )	Income	Bundle (X, Y)	Level of satisfaction
E₁, before	900, 400	7,200	$\left(\frac{7{,}200}{1{,}800},\ \frac{7{,}200}{800}\right) = (4,\ 9)$	$X Y = 36$ , on I₁
E₂, after	400, 400	7,200	$\left(\frac{7{,}200}{800},\ \frac{7{,}200}{800}\right) = (9,\ 9)$	$X Y = 81$ , on I₂
C, compensated	400, 400	4,800	$(6, 6)$	$X Y = 36$ , back on I₁

Finding C. Take away just enough income to put Uwera back on her old curve I₁, but at the new prices. At those prices the MRS must equal $\frac{400}{400} = 1$ , so $Y = X$ ; and $X Y = 36$ gives $X = Y = 6$ . That bundle costs $400 (6) + 400 (6) = 4,800$ francs, so the price fall is worth Frw 2,400 a week to her.

Reading the diagram. The move E₁ → C is along I₁, caused only by the new relative price: the substitution effect, +2 kg. The move C → E₂ is a parallel shift of the budget line, caused only by the rise in real income: the income effect, +3 kg. Together: $2 + 3 = 5$ kg, from 4 to 9. This method, which keeps the consumer on the original indifference curve, is due to Hicks.

Worked example 1: decomposing a price fall

A consumer with $U = X Y$ has Frw 4,800. $P_{y} = 200$ . The price of X falls from Frw 600 to Frw 150. Find the substitution and income effects on X.

Before: $X_1 = \frac{4{,}800}{2(600)} = 4$ , $Y_1 = \frac{4{,}800}{2(200)} = 12$ , so $X Y = 48$ .

After: $X_2 = \frac{4{,}800}{2(150)} = 16$ .

Compensated bundle C: at the new prices, $\frac{Y}{X} = \frac{150}{200} = 0.75$ , so $Y = 0.75 X$ . On the old curve: $X(0.75X) = 48 \Rightarrow X^2 = 64 \Rightarrow X = 8$ (and $Y = 6$ ).

Effects: substitution $8 - 4 = + 4$ ; income $16 - 8 = + 8$ ; total $16 - 4 = + 12$ units. Both effects are positive, so X is a normal good.

2. Normal, inferior and Giffen goods

The substitution effect always works against the price change: when a good becomes relatively cheaper, a consumer kept on the same indifference curve buys more of it, because indifference curves are convex. The income effect can go either way, depending on the type of good.

Type of good (price falls)	Substitution effect	Income effect	Total effect on quantity	Demand curve
Normal good	+ (buy more)	+ (more income, buy more)	Rises, by more than the substitution effect	Downward sloping
Inferior good	+	− (more income, buy less), but smaller	Rises, by less than the substitution effect	Downward sloping
Giffen good	+	− and larger than the substitution effect	Falls	Upward sloping

So every Giffen good is an inferior good, but very few inferior goods are Giffen goods. For the income effect to win, the good must be inferior and take a large share of a very poor household's budget. Robert Jensen and Nolan Miller (2008) found such behaviour among very poor households in China: when the price of rice, their staple, was subsidised, some of them bought less rice and more meat.

Warning

The substitution effect is never "perverse". For a Giffen good it is the income effect that runs the wrong way and outweighs the substitution effect. Saying "for a Giffen good the substitution effect is positive when price rises" is wrong.

Definition

Consumer surplus (CS): the difference between the most consumers are willing to pay for a quantity of a good and what they actually pay. On a diagram it is the area below the demand curve and above the price.

Producer surplus (PS): the difference between the price producers receive and the lowest price at which they would have been willing to supply. It is the area above the supply curve and below the price.

Total (economic) surplus: $C S + P S$ , the net gain to society from trade in the market.

Example: if you would pay up to Frw 1,000 for a brochette and it costs Frw 800, your consumer surplus on it is Frw 200.

3. Consumer and producer surplus

Consumer surplus rests on diminishing marginal utility. Each unit is worth less to buyers than the one before, yet every unit is sold at the same market price, so the earlier units bring a surplus. In a market for tomatoes at one town market (illustrative), demand is $P = 1,200 - 3 Q$ and supply is $P = 200 + 2 Q$ , with Q in kg per day and P in Frw per kg.

Equilibrium: $1{,}200 - 3Q = 200 + 2Q \Rightarrow 5Q = 1{,}000 \Rightarrow Q^* = 200$ , and $P^* = 1{,}200 - 3(200) = 600$ .

CS = \tfrac{1}{2} \times 200 \times (1{,}200 - 600) = 60{,}000 \qquad PS = \tfrac{1}{2} \times 200 \times (600 - 200) = 40{,}000

Reading the diagram. The blue triangle is the gain buyers get by paying Frw 600 for kilograms they value at up to Frw 1,200. The orange triangle is the gain sellers get by receiving Frw 600 for kilograms some would have supplied for as little as Frw 200. Total surplus is Frw 100,000 a day, and it is largest at the free-market equilibrium.

Uses of the concepts. They measure who gains and loses from a tax, a subsidy or a price control; they show how a firm that charges different prices for different blocks of a good can turn consumer surplus into revenue (price discrimination); and governments use them in cost–benefit analysis, for example to value the time and money a new road saves its users.

Electricity transmission towers beside a dirt road in rural Rwanda. How electricity is priced decides how much consumer surplus households keep. Photo: roadroid via Mapillary, CC BY-SA 4.0, via Wikimedia Commons.

Worked example 2: Rwanda's household electricity tariff

From 1 October 2025, households pay Frw 89 per kWh for their first 20 kWh in a month, Frw 310 per kWh from above 20 to 50 kWh, and Frw 369 per kWh above 50 kWh (VAT and regulatory fee excluded; REG, under RURA).

(a) Bill for 60 kWh. $20 (89) + 30 (310) + 10 (369) = 1,780 + 9,300 + 3,690 = 14,770$ francs.

(b) Compared with a flat Frw 369 on every kWh: $60 (369) = 22,140$ francs, so the block tariff leaves this household $22,140 - 14,770 = 7,370$ francs more consumer surplus, if it uses the same 60 kWh.

(c) Evaluation. The cheap first block protects the surplus of small users (a household using 20 kWh pays Frw 1,780 instead of Frw 7,380), while the higher blocks charge more where use, and willingness to pay, is greater. The tariff is a form of price discrimination by blocks: it collects part of the surplus of large users to keep basic lighting and phone charging affordable.

Tip

"Triangle above the price is the buyers'; triangle below is the sellers'." For straight-line curves, each surplus is $\frac{1}{2} \times \text{base} \times \text{height}$ : the base is the equilibrium quantity and the height is the gap between the price and where the curve meets the price axis.

Important

Discuss. If the price of a staple food rises sharply, which households lose most consumer surplus: those who spend a large share of their budget on it, or those who spend a small share? Use the income effect and the EICV7 food share from lesson 2 in your answer.

tutor2u, "Indifference Curves - Income and Substitution Effects for Normal Goods I A Level and IB Economics". Watch how the presenter draws the compensated budget line parallel to the new one and tangent to the old indifference curve, exactly as in the potato diagram above.

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Practice

Distinguish between the substitution effect and the income effect of a price change.
With the help of an indifference-curve diagram, show the substitution and income effects of a fall in the price of a normal good.
A consumer with $U = X Y$ has Frw 3,600, and $P_{y} = 200$ . The price of X falls from Frw 900 to Frw 100. Find the substitution, income and total effects on X.
Explain why every Giffen good is an inferior good, but not every inferior good is a Giffen good.
Demand is $Q_{d} = 500 - P$ and supply is $Q_{s} = 2 P - 400$ . Find the equilibrium, consumer surplus and producer surplus.
Five buyers would pay at most Frw 5,000, 4,000, 3,500, 3,000 and 2,000 for a phone case. The price is Frw 3,000. How many cases are sold (assume a buyer who is indifferent buys), and what is the total consumer surplus?
Using the tariff in force from 1 October 2025, calculate a household's bill for 45 kWh in a month (VAT and fee excluded).
Using a demand diagram, explain how a fall in the price of a good changes consumer surplus, and who gains.

Show answersHide answers

The substitution effect is the change in quantity due only to the change in relative prices, with real income (the indifference curve) held constant. The income effect is the change due only to the change in real income, at the new relative prices.
Draw E₁ on I₁; pivot the budget line out for the price fall to reach E₂ on I₂; draw a line parallel to the new one tangent to I₁ at C. E₁ → C is the substitution effect, C → E₂ the income effect; both raise X.
Before: $X = \frac{3{,}600}{1{,}800} = 2$ , $Y = \frac{3{,}600}{400} = 9$ , $X Y = 18$ . After: $X = \frac{3{,}600}{200} = 18$ . Compensated: $\frac{Y}{X} = \frac{100}{200} = 0.5$ , $0.5X^2 = 18 \Rightarrow X = 6$ (and $Y = 3$ ). Substitution +4, income +12, total +16.
For quantity to fall when price falls, the income effect must run against the substitution effect (an inferior good) and be larger than it. Most inferior goods have a small income effect, because they take a small share of the budget, so the substitution effect wins and demand still slopes down.
$500 - P = 2P - 400 \Rightarrow P = 300,\ Q = 200$ . Demand meets the price axis at 500 and supply at 200. CS $= \frac{1}{2}(200)(500 - 300) = 20{,}000$ ; PS $= \frac{1}{2}(200)(300 - 200) = 10{,}000$ .
Four are sold. CS $= (5,000 - 3,000) + (4,000 - 3,000) + (3,500 - 3,000) + 0 = 3,500$ francs.
$20 (89) + 25 (310) = 1,780 + 7,750 = 9,530$ francs.
Consumer surplus grows in two parts: existing buyers pay less on the units they already bought (a rectangle), and new units are bought that are worth more than the new price (a small triangle). Buyers gain; some of the gain is producer surplus lost by sellers.

Quick check

The price of a normal good falls. How do the substitution effect and the income effect act on the quantity bought?

Key points

Price effect = substitution effect + income effect. Hicks's method finds them with a compensated budget line tangent to the original indifference curve.
The substitution effect always moves quantity against the price; the income effect depends on whether the good is normal or inferior.
A Giffen good is an inferior good whose income effect outweighs the substitution effect, so its demand curve slopes upwards.
Consumer surplus is the area below demand and above price; producer surplus is the area above supply and below price.

1Cheaper potatoes, two reasons to buy more

21. Separating the two effects on an indifference map

32. Normal, inferior and Giffen goods

43. Consumer and producer surplus

Cheaper potatoes, two reasons to buy more

1. Separating the two effects on an indifference map

2. Normal, inferior and Giffen goods

3. Consumer and producer surplus