Source: Lecture Notes of Prof. Guoqiang Tian, Texas A&M University
Tags: income consumption curve, ICC, normal good, inferior good, Giffen good, income effect, substitution effect, price elasticity of demand, elastic, inelastic, unit elastic, total revenue, consumer surplus, Edgeworth box, Pareto optimality, contract curve, competitive equilibrium, welfare economics
This section derives individual demand curves from the consumer's optimisation problem, then aggregates them into market demand. It introduces the income and substitution effects of a price change, the concept of a Giffen good, and the various elasticity measures. It also covers consumer surplus and then shifts to welfare economics: the Edgeworth box, Pareto efficiency, the contract curve, and the two fundamental welfare theorems linking competitive equilibrium to efficiency.
Income consumption curve (ICC)
Traces the consumer's optimal bundles as income changes, holding prices fixed.
Normal good
A good whose demand increases when income rises (with prices constant).
Inferior good
A good whose demand decreases when income rises (with prices constant). E.g. cheap staples like potatoes.
Giffen good
A good for which quantity demanded falls when its price falls. The income effect (which reduces demand because the good is inferior) outweighs the substitution effect. A Giffen good must be inferior, but an inferior good is not necessarily Giffen.
Substitution effect
The change in quantity demanded resulting solely from the change in relative prices, holding utility constant. Always moves in the opposite direction of the price change.
Income effect
The change in quantity demanded resulting from the change in real purchasing power caused by the price change. For normal goods, it reinforces the substitution effect. For inferior goods, it works against it.
Price elasticity of demand (Ed)
A unitless measure of the responsiveness of quantity demanded to changes in price. Ed = (percentage change in quantity demanded) / (percentage change in price). Typically negative, so we take the absolute value.
Elastic demand
|Ed| > 1. Quantity demanded is relatively responsive to price changes.
Inelastic demand
|Ed| < 1. Quantity demanded is relatively unresponsive to price changes.
Unit elastic demand
|Ed| = 1. Percentage change in quantity equals percentage change in price.
Perfectly inelastic demand
|Ed| = 0. Quantity demanded does not change at all when price changes (vertical demand curve).
Perfectly elastic demand
|Ed| = infinity. An infinitely small price change causes an infinitely large change in quantity demanded (horizontal demand curve).
Income elasticity of demand
Measures responsiveness of quantity demanded to changes in income.
Cross-price elasticity of demand
Measures responsiveness of demand for good x to changes in the price of good y. Positive for substitutes, negative for complements.
Consumer surplus
The difference between what a consumer is willing to pay for a good and what they actually pay. Graphically, it is the area between the demand curve and the market price, up to the quantity purchased.
Edgeworth box
A geometric diagram for a two-person, two-good pure exchange economy. Every point inside the box represents an allocation (division) of the two goods between the two consumers.
Pareto optimal (efficient) allocation
An allocation from which it is impossible to make one person better off without making someone else worse off. Characterised by MRS_A = MRS_B.
Contract curve
The locus of all Pareto-efficient allocations in the Edgeworth box. Connects all tangency points between the two consumers' indifference curves.
Competitive equilibrium
A set of prices and allocations where each consumer optimises given their budget, and markets clear (total demand equals total supply for each good).
To derive the demand curve for good x, hold py and I constant and vary px. At each px, solve the consumer's optimisation problem (tangency condition + budget constraint) to find the optimal x. Plotting px against x gives the demand curve.
Example: if the optimisation yields x = I/(3px), then with I = 50 and py = 2, the demand curve is x = 50/(3px), which is a downward-sloping hyperbola.
When px increases (py and I fixed):
The total effect on x can be decomposed into a substitution effect and an income effect.
To isolate the substitution effect, imagine compensating the consumer with enough income to reach the original utility level at the new price ratio. The movement along the original indifference curve to the compensated bundle is the substitution effect.
The remaining change (from the compensated bundle to the actual new bundle) is the income effect.
Total effect = substitution effect + income effect.
For a normal good, both effects reduce demand when price rises, so the demand curve slopes downward.
For an inferior good, the income effect partially offsets the substitution effect. If the income effect is larger in absolute value than the substitution effect, the good is a Giffen good and the demand curve slopes upward.
A $50 food stamp subsidy that can only be spent on food creates a kinked budget line. If the consumer would have spent more than $50 on food anyway, the food stamp is equivalent to a $50 cash grant. If the consumer would prefer to spend some of the $50 on other goods, the food stamp forces them onto a less-preferred bundle. The consumer is never better off with food stamps than with equivalent cash.
Market demand is the horizontal sum of all individual demand curves. At each price, add up the quantities demanded by every consumer.
The midpoint formula avoids the problem of different elasticities depending on which point is used as the base:
Ed = [change in q / average of q] / [change in p / average of p]
Elasticity along a straight-line demand curve is not constant. At the midpoint, |Ed| = 1. Above the midpoint (higher price, lower quantity), demand is elastic. Below the midpoint (lower price, higher quantity), demand is inelastic.
Total revenue (TR) = p * q.
If demand is elastic (|Ed| > 1): price increase causes TR to fall.
If demand is inelastic (|Ed| < 1): price increase causes TR to rise.
If demand is unit elastic (|Ed| = 1): TR is constant when price changes.
When demand is elastic, price and total revenue move in opposite directions. When inelastic, they move in the same direction.
Consumer surplus = total benefit - total cost = area under the demand curve above the market price.
Example: a consumer buys 6 cups of espresso at price $3. The marginal valuations are $8, $7, $6, $5, $4, $3. Total benefit = 33, total cost = 18, consumer surplus = 15.
A fall in price increases consumer surplus, and the gain is measured by the area between the old and new price lines, bounded by the demand curve.
The Edgeworth box: consumer A's origin is at the bottom-left, consumer B's at the top-right. The box dimensions equal total endowments. Any point in the box is a feasible allocation.
Pareto efficiency: where indifference curves are tangent, MRS_A = MRS_B. At such points there is no mutually beneficial trade remaining. All tangency points form the contract curve.
Important: MRS_A = MRS_B is necessary but not sufficient for efficiency. The allocation must also satisfy the balance condition (total consumption of each good equals total endowment).
Proposition 1 (First Welfare Theorem): A competitive equilibrium allocation is Pareto efficient. Since both consumers face the same prices, they each set MRS = px/py, so MRS_A = MRS_B. The market-clearing condition ensures the balance condition holds.
Proposition 2 (Second Welfare Theorem): Any Pareto-efficient allocation can be achieved as a competitive equilibrium, given an appropriate redistribution of initial endowments. This means efficiency and equity are separable concerns.
Total effect = substitution effect + income effect
Price elasticity: Ed = (% change in qd) / (% change in p)
Midpoint formula: Ed = [delta q / ((q1 + q2)/2)] / [delta p / ((p1 + p2)/2)]
Total revenue: TR = p * q
Consumer surplus = area under demand curve above price
Pareto efficiency condition: MRS_A = MRS_B
Competitive equilibrium condition: MRS = px/py for each consumer, plus market clearing
⚠️ Be able to decompose a price change into substitution and income effects graphically. The compensating variation method (shifting the new-price budget line back to the original indifference curve) is a standard exam question.
⚠️ A Giffen good must be inferior, but not all inferior goods are Giffen. The income effect must dominate the substitution effect.
⚠️ Elasticity varies along a straight-line demand curve. It is not the same as slope.
⚠️ Know the elasticity-total revenue relationship cold. If |Ed| > 1 and price rises, TR falls.
⚠️ The First Welfare Theorem is a centrepiece of microeconomic theory: competitive markets produce efficient outcomes. The Second Welfare Theorem says any efficient outcome is reachable through competitive markets with the right initial endowments.
⚠️ In the Edgeworth box, MRS_A = MRS_B alone is necessary but not sufficient for efficiency. The balance (feasibility) condition must also hold.
Q: What is the relationship between a Giffen good and an inferior good?
A: Every Giffen good is an inferior good, but not every inferior good is a Giffen good. A Giffen good arises only when the good is inferior and the income effect is larger in absolute value than the substitution effect, causing the demand curve to slope upward.
Q: If demand is elastic and the firm raises its price, what happens to total revenue?
A: Total revenue falls. When demand is elastic, the percentage decrease in quantity demanded exceeds the percentage increase in price.
Q: Along a linear demand curve, where is demand unit elastic?
A: At the midpoint of the demand curve. Above the midpoint, demand is elastic; below it, demand is inelastic.
Q: What does the contract curve represent in the Edgeworth box?
A: The contract curve connects all Pareto-efficient allocations, i.e. all points where the indifference curves of the two consumers are tangent (MRS_A = MRS_B) and the feasibility condition holds. No mutually beneficial trade is possible at any point on the contract curve.
Q: Why does a competitive equilibrium achieve Pareto efficiency?
A: Each consumer sets MRS equal to the common price ratio px/py. Since prices are the same for both, MRS_A = MRS_B. The market-clearing condition ensures that total demand equals total supply, satisfying the balance condition. Together, these conditions characterise a Pareto-efficient allocation.
Q: A consumer buys 4 units of a good at $5 each. Their marginal valuations for units 1 through 4 are $10, $8, $6, $5. What is the consumer surplus?
A: Total benefit = 10 + 8 + 6 + 5 = 29. Total cost = 4 * 5 = 20. Consumer surplus = 29 - 20 = 9.
individual demand, market demand, demand derivation, income consumption curve, Engel curve, normal good, inferior good, Giffen good, substitution effect, income effect, Slutsky decomposition, price elasticity, income elasticity, cross-price elasticity, elastic, inelastic, unit elastic, midpoint formula, total revenue test, consumer surplus, willingness to pay, Edgeworth box, pure exchange economy, Pareto optimality, Pareto efficiency, contract curve, competitive equilibrium, First Welfare Theorem, Second Welfare Theorem, general equilibrium, welfare economics, ECON 323