Source: Microeconomic Theory, Texas A&M University, Chapter 4
Tags: substitution effect, income effect, Giffen good, normal good, inferior good, market demand curve, horizontal summation, price elasticity of demand, elastic, inelastic, unit elasticity, consumer surplus, willingness to pay
A price change does two things at once: it changes the relative price of goods (substitution effect) and it changes real purchasing power (income effect). How these two effects combine determines whether the demand curve slopes downward or, in the rare Giffen case, upward. Market demand is built by horizontally summing individual demand curves. Consumer surplus measures the gap between what consumers would have been willing to pay and what they actually pay.
Substitution effect
The change in quantity demanded that results purely from a change in relative prices, holding real purchasing power (utility) constant. Always pushes consumption toward the good that became relatively cheaper. Always positive (in the direction of the price fall).
Income effect
The change in quantity demanded that results from the change in real purchasing power caused by a price change, holding relative prices constant at their new level.
Giffen good
A good with an upward-sloping demand curve: when its price falls, quantity demanded also falls. This happens when a negative income effect is large enough to dominate the positive substitution effect. A Giffen good must be a very strongly inferior good.
Auxiliary budget line
The hypothetical budget line drawn parallel to the new (post-price-change) budget line but tangent to the original indifference curve. It isolates the substitution effect by changing relative prices while holding utility constant.
Market demand curve
The curve relating the total quantity of a good that all consumers in a market will buy to its price. Obtained by horizontal summation of individual demand curves.
Price elasticity of demand (E_P)
Measures the responsiveness of quantity demanded to a change in price. Defined as E_P = (ΔQ/Q) / (ΔP/P) = Q′(P) · P / Q.
Inelastic demand
|E_P| < 1. Quantity responds less than proportionally to price. Total expenditure rises when price rises.
Elastic demand
|E_P| > 1. Quantity responds more than proportionally to price. Total expenditure falls when price rises.
Unit elasticity
E_P = −1. Total expenditure does not change when price changes.
Consumer surplus
The total benefit a consumer receives from consumption of a product, minus the total cost of purchasing it. Graphically, it is the area under the demand curve and above the market price, up to the quantity purchased.
Willingness to pay
For each point (Q, P) on the demand curve, the P coordinate represents the maximum the consumer would pay for the Q-th unit.
When the price of a good falls, two things happen simultaneously:
Substitution effect: the good is now cheaper relative to other goods, so the consumer substitutes toward it. This effect always increases quantity demanded of the cheaper good.
Income effect: the consumer's real purchasing power has increased (the same income buys more). Whether this increases or decreases quantity demanded depends on whether the good is normal or inferior.
The decomposition uses three budget lines:
Initial budget line (RS): the original prices and income. Optimal basket is A.
Auxiliary budget line (MN): drawn with the new relative prices (parallel to the final budget line) but shifted so it is tangent to the original indifference curve U₁. Optimal basket on this line is D. The move from A to D is the substitution effect.
Ultimate budget line (RT): the actual new budget line after the price change. Optimal basket is B. The move from D to B is the income effect.
Substitution effect: positive (more X purchased, moving from F₁ to E).
Income effect: positive (more X purchased, moving from E to F₂).
The two effects reinforce each other.
Total effect: positive. The demand curve slopes downward.
Substitution effect: positive (E − F₁ > 0).
Income effect: negative (F₂ − E < 0), because more purchasing power leads to less consumption of an inferior good.
The substitution effect dominates the income effect.
Total effect: still positive (F₂ − F₁ > 0). The demand curve still slopes downward.
Substitution effect: positive.
Income effect: negative and large enough to dominate the substitution effect.
Total effect: negative (F₁ − E < 0). When the price falls, quantity demanded falls. The demand curve slopes upward.
Good type | Substitution effect | Income effect | Total effect |
|---|---|---|---|
Normal | + | + | + |
Inferior (not Giffen) | + | − (smaller) | + |
Giffen | + | − (larger) | − |
A Giffen good is a very strongly inferior good. The negative income effect must be powerful enough to overpower the substitution effect, which is rare in practice.
If a demand curve is downward-sloping for some price range, the good could be Giffen at prices where it slopes upward.
If you can show that when price decreases from P_X to P′_X the quantity demanded increases, the good is not Giffen at that price.
Perfect complements have zero substitution effect (the auxiliary basket equals the initial basket) because consumption is locked in a fixed ratio. The entire change in quantity comes from the income effect.
The market demand curve is built by adding up the quantities demanded by every consumer at each price.
Example with three consumers:
Price ($) | Individual A | Individual B | Individual C | Market total |
|---|---|---|---|---|
1 | 6 | 10 | 16 | 32 |
2 | 4 | 8 | 13 | 25 |
3 | 2 | 6 | 10 | 18 |
4 | 0 | 4 | 7 | 11 |
5 | 0 | 2 | 4 | 6 |
At each price, read off each individual's quantity and sum them. This is called horizontal summation because you are adding quantities (the horizontal axis) at a given price (the vertical axis).
Note that Individual A drops out of the market at P = $4. The market demand curve can have kinks at prices where individual consumers enter or exit.
E_P = (ΔQ/Q) / (ΔP/P) = Q′(P) · (P / Q)
Worked example: Q(P) = 100/P.
Q′(P) = −100/P².
E_P = (−100/P²) · P / (100/P) = −1.
This demand function has unit elasticity everywhere.
Elasticity and total expenditure:
|E_P| < 1 (inelastic): price increase raises total expenditure (P · Q). The quantity drop is proportionally smaller than the price rise.
|E_P| > 1 (elastic): price increase lowers total expenditure. The quantity drop is proportionally larger than the price rise.
|E_P| = 1 (unit elastic): total expenditure stays the same.
Each point on the demand curve tells you the maximum a consumer would pay for that particular unit. In the rock-concert-ticket example:
1st ticket: willing to pay $20
2nd ticket: $19
3rd ticket: $18
...down to the 7th ticket at $14.
The surplus on any single unit is the difference between willingness to pay and the actual price.
If the market price is $14 per ticket:
1st ticket surplus: $20 − $14 = $6
2nd ticket surplus: $19 − $14 = $5
3rd ticket surplus: $4
4th ticket surplus: $3
5th ticket surplus: $2
6th ticket surplus: $1
7th ticket surplus: $0
Consumer surplus is the sum of the surpluses on all units purchased.
At $14 per ticket: $6 + $5 + $4 + $3 + $2 + $1 + $0 = $21.
Consumer surplus is the area under the demand curve and above the horizontal price line, up to the quantity purchased. It forms a triangle (or step-shaped area with discrete units).
Total expenditure is the rectangle: price multiplied by quantity.
The area under the demand curve down to the horizontal axis (up to Q purchased) represents the total value the consumer places on those units. Consumer surplus is total value minus expenditure.
Substitution effect: Move from initial basket A to auxiliary basket D (on original indifference curve, at new price ratio).
Income effect: Move from auxiliary basket D to ultimate basket B (from auxiliary budget line to actual new budget line, same slope).
Total effect = Substitution effect + Income effect
Price elasticity of demand: E_P = Q′(P) · P / Q
Consumer surplus (continuous): CS = ∫₀^Q* [P(Q) − P*] dQ, where P* is the market price and Q* is the quantity purchased.
Consumer surplus (discrete, step demand): CS = Σ (willingness to pay for each unit − market price)
⚠️ The substitution effect is always positive (in the direction of the cheaper good). The income effect can go either way. Know which direction it goes for normal, inferior, and Giffen goods.
⚠️ A Giffen good must be inferior, but most inferior goods are not Giffen. The income effect has to be strong enough to dominate the substitution effect.
⚠️ For perfect complements, the substitution effect is zero. The auxiliary basket and the initial basket are the same point (you cannot substitute along an L-shaped indifference curve). The entire change is income effect.
⚠️ Market demand is horizontal summation: add quantities at each price, not prices at each quantity.
⚠️ Know the link between elasticity and total expenditure. If demand is inelastic and price rises, the firm collects more revenue. If elastic, it collects less.
⚠️ Consumer surplus is the triangle above price and below the demand curve. Do not confuse it with total expenditure (the rectangle).
Q: A price fall for good X leads to a positive substitution effect and a negative income effect, but the total effect is still positive. What type of good is X?
A: X is an inferior good that is not a Giffen good. The substitution effect dominates the income effect.
Q: What distinguishes a Giffen good from an ordinary inferior good?
A: For both, the income effect is negative. For an ordinary inferior good, the positive substitution effect dominates, so the demand curve still slopes downward. For a Giffen good, the negative income effect dominates, making the demand curve slope upward.
Q: How do you construct the market demand curve from individual demand curves?
A: By horizontal summation. At each price, add up the quantities demanded by all consumers. Plot the resulting (price, total quantity) pairs.
Q: If Q(P) = 100/P, what is the price elasticity of demand?
A: E_P = −1 everywhere. This demand function has unit elasticity.
Q: If demand is inelastic and the price of a good increases, what happens to total consumer expenditure on that good?
A: Total expenditure increases. The percentage fall in quantity is smaller than the percentage rise in price.
Q: The market price of concert tickets is $14 and a consumer's willingness to pay for the 3rd ticket is $18. What is the surplus on that unit?
A: $18 − $14 = $4.
Q: For perfect complements, what is the substitution effect of a price change?
A: Zero. The consumer cannot substitute between goods along an L-shaped indifference curve, so the auxiliary basket is the same as the initial basket. The entire quantity change is due to the income effect.
substitution effect, income effect, Slutsky decomposition, Giffen good, inferior good, normal good, auxiliary budget line, compensated demand, price-consumption curve, market demand, horizontal summation, price elasticity of demand, elastic, inelastic, unit elasticity, total expenditure, total revenue, consumer surplus, willingness to pay, demand curve area, ECON 323, microeconomic theory, Texas A&M, chapter 4