Source: Microeconomic Theory, Texas A&M University, Final Exam M.1
Tags: individual demand, price consumption curve, demand curve, income consumption curve, Engel curve, normal good, inferior good, Giffen good, substitution effect, income effect, market demand, elasticity of demand, consumer surplus, ECON 323
Chapter 4 builds on consumer choice to derive demand curves. A price change traces out the price-consumption curve; an income change traces out the income-consumption curve and the Engel curve. Every price change decomposes into a substitution effect (always buy more of the cheaper good) and an income effect (purchasing power shifts). Whether those effects reinforce or oppose each other determines whether a good is normal, inferior, or the rare Giffen good. Market demand sums individual demands, and elasticity measures responsiveness.
Price-consumption curve (PCC)
The curve that traces the utility-maximising baskets as the price of one good changes, holding income and the other price constant.
Individual demand curve
The curve relating the quantity of a good a single consumer will buy to its price. Derived from the PCC.
Income-consumption curve (ICC)
The curve that traces utility-maximising baskets as income changes, holding prices constant.
Engel curve
A graph relating the quantity of a good consumed to income level.
Upward-sloping: normal good.
Downward-sloping: inferior good.
Normal good
A good for which an increase in income leads to an increase in quantity consumed. The Engel curve slopes upward and the ICC bends in a "well-behaved" direction.
Inferior good
A good for which an increase in income leads to a decrease in quantity consumed. The Engel curve slopes downward.
Giffen good
An extreme inferior good whose demand curve slopes upward. The negative income effect is so large it dominates the positive substitution effect.
Substitution effect
The change in quantity demanded due purely to the change in relative prices, holding utility constant. Always positive: a price fall always makes you buy more of that good (along the same indifference curve).
Income effect
The change in quantity demanded due to the change in real purchasing power caused by the price change. Can be positive (normal good) or negative (inferior good).
Substitutes
Two goods where an increase in the price of one leads to an increase in the quantity demanded of the other.
Complements
Two goods where an increase in the price of one leads to a decrease in the quantity demanded of the other.
Independent goods
An increase in the price of one good does not affect the quantity demanded of the other.
Market demand curve
The horizontal sum of all individual demand curves at each price level.
Price elasticity of demand (E)
The percentage change in quantity demanded divided by the percentage change in price. Measures responsiveness.
Consumer surplus
The difference between what consumers are willing to pay and what they actually pay. Graphically, the area under the demand curve and above the price line, up to the quantity purchased.
At every point on the individual demand curve, the consumer is maximising utility by satisfying MRS = Px / Py. As the price of x falls, the budget line rotates outward, the tangency shifts, and the quantity of x demanded rises (for a normal good). Connecting those tangencies gives the price-consumption curve; plotting price against quantity gives the demand curve.
Key properties of the demand curve:
The level of utility attained changes as you move along it (different prices, different optimal bundles).
It shows the consumer's willingness to pay for each successive unit.
It also shows the willingness to give up units as price rises.
As income rises (prices held constant), the budget line shifts outward in parallel. Tracing the new tangencies gives the ICC.
Two methods to classify a good as normal or inferior:
ICC method: look at the slope and direction the curve bends. If consuming more of the good as income rises, it is normal in that range.
Engel curve method: plot quantity of the good against income. Upward slope means normal; downward slope means inferior.
A good can be normal over one income range and inferior over another.
When the price of good x falls, two things happen simultaneously:
Substitution effect: the good is now relatively cheaper, so the consumer buys more of it. Isolated by drawing an auxiliary (imaginary) budget line parallel to the new budget line but tangent to the original indifference curve. The movement along the original curve from the old bundle to the auxiliary tangency is the substitution effect.
Income effect: the consumer's real purchasing power has risen, so they can reach a higher indifference curve. The movement from the auxiliary tangency to the final bundle is the income effect.
Case 1: Normal good
Substitution effect is positive (buy more x).
Income effect is positive (higher real income, buy more x).
Both reinforce each other. Demand curve slopes downward.
Case 2: Inferior good (not Giffen)
Substitution effect is positive.
Income effect is negative (higher real income, buy less x because it is inferior).
Substitution effect dominates. Demand curve still slopes downward, but the response is smaller than for a normal good.
Case 3: Giffen good
Substitution effect is positive.
Income effect is negative and large enough to dominate the substitution effect.
Net effect: quantity demanded falls when price falls. Demand curve slopes upward. This is extremely rare in practice.
The market demand curve is the horizontal summation of every individual consumer's demand curve. At each price, add up the quantities each consumer wants.
Price elasticity of demand:
E = (% change in quantity demanded) / (% change in price)
Elasticity interpretation:
|E| < 1: inelastic. A price increase raises total expenditure (revenue).
|E| > 1: elastic. A price increase lowers total expenditure (revenue).
|E| = 1: unit elastic. Total expenditure does not change when price changes.
Consumer surplus (graphical):
CS = area under the demand curve, above the price line, from 0 to quantity purchased.
Expenditure = price × quantity purchased.
Consumer surplus captures the "bonus" a buyer gets from paying a uniform market price rather than their maximum willingness to pay for each unit.
The surplus on a particular unit is the gap between the consumer's willingness to pay for that unit and the actual price.
Total consumer surplus is the sum of these gaps across all units purchased, which equals the area under the demand curve and above the horizontal price line.
⚠️ Be able to draw the auxiliary budget line for the substitution/income effect decomposition. It is parallel to the new budget line but tangent to the original indifference curve.
⚠️ The substitution effect is always positive (more of the cheaper good). The income effect's sign is what separates normal, inferior, and Giffen goods.
⚠️ Giffen good: income effect is negative and dominates the substitution effect. This is the only case where the demand curve slopes upward.
⚠️ Know both methods of identifying normal vs. inferior: ICC direction and Engel curve slope.
⚠️ Elasticity and total expenditure: inelastic means a price rise increases revenue; elastic means a price rise decreases revenue. This is a very common exam question.
⚠️ Consumer surplus is the area under the demand curve and above price, not below price.
Q: A fall in the price of good x has two effects. Name them and state the sign of each for a normal good.
A: The substitution effect (positive, buy more x because it is relatively cheaper) and the income effect (positive for a normal good, because higher real purchasing power leads to more consumption of x). Both reinforce each other.
Q: What distinguishes an inferior good from a Giffen good?
A: Both have a negative income effect when price falls. For a standard inferior good, the positive substitution effect dominates, so the demand curve still slopes downward. For a Giffen good, the negative income effect dominates the substitution effect, producing an upward-sloping demand curve.
Q: How do you construct the auxiliary budget line used to isolate the substitution effect?
A: Draw a budget line that is parallel to the new (post-price-change) budget line but tangent to the original indifference curve. The shift along the original curve to this tangency point is the substitution effect; the remaining shift to the final optimum is the income effect.
Q: If the price elasticity of demand is -0.6, what happens to total consumer expenditure when price rises?
A: |E| = 0.6, which is less than 1, so demand is inelastic. Total expenditure increases when price rises (quantity falls proportionally less than price rises).
Q: What is the difference between the Engel curve and the income-consumption curve?
A: The income-consumption curve plots optimal bundles (both goods) as income changes. The Engel curve plots the quantity of a single good against income. The Engel curve is essentially one axis of the ICC projected against income.
Q: Two goods are complements. What happens to the quantity demanded of good y when the price of good x increases?
A: The quantity demanded of good y decreases. By definition, complements move in the same direction in response to a price change in either good.
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