Source: Demand Theory in Economics, Texas A&M University
Tags: demand theory, consumer theory, budget constraint, indifference curve, indifference map, optimal bundle, tangency condition, income-consumption curve, ICC, Engel curve, normal goods, inferior goods, luxury goods, substitution effect, income effect, Slutsky decomposition, price change decomposition, demand curve derivation, demand schedule
Consumer demand is built from two ideas: what you can afford (budget constraint) and what you prefer (indifference curves). Where those two meet determines the optimal bundle. Shifting prices or income traces out the demand curve, the income-consumption curve, and the Engel curve, each showing a different angle on how consumption responds to changing conditions.
Budget constraint
The set of all combinations of goods a consumer can purchase given their income and the prices of those goods. Graphically, it is a straight line whose slope equals the negative ratio of the two prices (–P₁/P₂).
Indifference curve
A curve showing every combination of two goods that yields the same level of utility (satisfaction) to the consumer. Higher curves represent higher utility.
Indifference map
The full collection of a consumer's indifference curves, covering all utility levels.
Optimal bundle (consumer's optimal choice)
The affordable combination of goods that maximises utility. Found at the point where the highest attainable indifference curve is tangent to the budget constraint.
Tangency condition
At the optimal bundle, the marginal rate of substitution (MRS) between the two goods equals the price ratio. This is the geometric condition that the indifference curve just touches the budget line.
Demand curve
A graph of the relationship between the price of a good and the quantity demanded, derived by tracing optimal bundles as the price changes, holding income and other prices constant.
Demand schedule
A table listing prices alongside the corresponding quantities demanded, the numerical counterpart of the demand curve.
Income-consumption curve (ICC)
The locus of optimal bundles as income changes while prices stay fixed. It slopes upward when the good is normal and downward when the good is inferior.
Engel curve
A plot of the quantity consumed of a good against the consumer's income. Upward-sloping for normal goods, downward-sloping for inferior goods.
Normal good
A good for which demand rises as income rises (positive income elasticity).
Inferior good
A good for which demand falls as income rises (negative income elasticity).
Luxury good
A subset of normal goods where demand grows proportionally faster than income, producing a convex-upward Engel curve.
Substitution effect
The change in consumption that results purely from the change in relative prices, holding utility constant. Consumers shift toward the good that has become relatively cheaper.
Income effect
The change in consumption that results from the change in real purchasing power caused by a price change.
A budget constraint represents every bundle a consumer can afford at current prices and income.
Depicted as a straight line in a two-good diagram.
Its slope reflects relative prices (–P₁/P₂).
A price change rotates the line around one intercept; an income change shifts it in or out in parallel.
An indifference map layers multiple indifference curves across the same diagram.
Each curve is a set of bundles yielding equal satisfaction.
Curves further from the origin represent higher utility.
Curves cannot cross (that would violate transitivity of preferences).
The consumer's optimal choice sits where the highest reachable indifference curve is tangent to the budget constraint.
At that point, the rate at which the consumer is willing to trade one good for another (MRS) equals the rate at which the market allows the trade (price ratio).
Changing the price of one good and re-solving for the tangency each time traces out the individual demand curve.
The ICC connects optimal bundles as income varies, prices held constant.
If the ICC slopes upward in both goods, both goods are normal at those income levels.
If the ICC bends back for one good, that good is inferior at higher incomes.
The Engel curve translates the same information into a quantity-vs-income graph for a single good.
Normal good: upward slope.
Inferior good: downward slope.
Luxury good: the Engel curve is convex upward, meaning consumption accelerates as income grows.
These tools are useful for understanding how demand shifts when an economy grows or when income is redistributed across groups.
When a price changes, the total effect on quantity demanded is split into two components.
Substitution effect
Isolates the impact of changed relative prices, holding the consumer's utility level constant.
Graphically, this involves a hypothetical (compensated) budget line at the new price ratio that is tangent to the original indifference curve.
The substitution effect always moves consumption toward the good that has become relatively cheaper.
Income effect
Captures the remaining change, from the compensated bundle to the new actual equilibrium.
Reflects the gain or loss in real purchasing power caused by the price change.
For a normal good whose price falls, the income effect reinforces the substitution effect (both increase quantity demanded).
For an inferior good whose price falls, the income effect works against the substitution effect (real-income gain reduces demand for that good).
Total effect = substitution effect + income effect. This decomposition is sometimes called the Slutsky decomposition (using a compensated budget that holds purchasing power constant) or Hicks decomposition (using one that holds utility constant).
Budget constraint (two goods)
M = P₁Q₁ + P₂Q₂
Where M is income, P₁ and P₂ are prices, Q₁ and Q₂ are quantities.
Tangency (optimality) condition
MRS = P₁ / P₂
The marginal rate of substitution equals the price ratio at the optimum.
Total effect decomposition
ΔQ(total) = ΔQ(substitution) + ΔQ(income)
⚠️ The tangency condition (MRS = price ratio) is the single most tested idea in consumer theory. Know it cold.
⚠️ Be clear on the direction of each effect. The substitution effect always goes toward the cheaper good. The income effect depends on whether the good is normal or inferior.
⚠️ Engel curves and ICC are easy marks if you remember the slope rules: upward for normal, downward for inferior, convex-upward for luxury.
⚠️ A common exam mistake is confusing a shift of the budget line (income change) with a rotation of the budget line (price change). Income shifts the whole line; a single-good price change pivots it.
Q: What condition must hold at the consumer's optimal bundle?
A: The marginal rate of substitution (MRS) between the two goods must equal the ratio of their prices (P₁/P₂), and the bundle must lie on the budget constraint.
Q: If a consumer's income rises and they buy less of Good X, what type of good is Good X?
A: Good X is an inferior good, because demand moves inversely with income.
Q: How does the Engel curve for a luxury good differ from the Engel curve for an ordinary normal good?
A: Both slope upward, but the luxury good's Engel curve is convex upward, meaning consumption increases at an accelerating rate as income grows. An ordinary normal good's Engel curve rises more steadily (concave upward or roughly linear).
Q: A price fall for Good A increases the quantity demanded. How would you determine whether this increase is driven more by the substitution effect or the income effect?
A: Construct a compensated budget line at the new prices tangent to the original indifference curve. The movement from the original bundle to the compensated bundle is the substitution effect; the movement from the compensated bundle to the new equilibrium is the income effect. Whichever is larger in magnitude is the dominant driver.
Q: The substitution effect for a price decrease always increases quantity demanded of the cheaper good. True or false?
A: True. By definition, holding utility constant, a lower relative price leads the consumer to substitute toward that good.
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