Difficulty: Intermediate | Prerequisites: Basic algebra, familiarity with graphing functions
Consumer theory explains how rational individuals choose what to buy, given their preferences and budget. You model preferences with indifference curves, constrain them with a budget line, and find the optimal bundle where MRS equals the price ratio. Price changes split into substitution and income effects, which matter for predicting demand and understanding why some goods (Giffen goods) seem to break the usual rules.
Preferences
A ranking system over bundles of goods. If A > B, the consumer prefers bundle A. If A ~ B, the consumer is indifferent. If A ≥ B, A is at least as good as B. Think of it as a complete ordering of everything you could possibly buy.
Completeness
For any two bundles, exactly one of three things must be true: you prefer A, you prefer B, or you are indifferent. In simple terms, you can always compare any two options.
Transitivity
If A is preferred to B, and B is preferred to C, then A must be preferred to C. In simple terms, your rankings are logically consistent and do not cycle.
More is better (monotonicity)
More of a good is always preferred to less, all else equal. This rules out situations where extra units make you worse off.
Marginal Rate of Substitution (MRS)
The rate at which a consumer is willing to trade one good for another while staying on the same indifference curve. Equals the negative ratio of marginal utilities: MRS = -(MUx / MUy). Think of it as "how much Y would I give up for one more unit of X and feel the same?"
Marginal Rate of Transformation (MRT)
The rate at which a consumer can trade one good for another in the market, given prices. Equals the negative price ratio: MRT = -(Px / Py). Think of it as the slope of the budget constraint, the trade-off the market imposes on you.
Indifference curve
A curve showing all bundles that give the consumer the same level of utility. Points on the same curve are equally preferred. Points above the curve are better; points below are worse.
Budget constraint
The set of all bundles a consumer can afford at given prices and income. The boundary line has slope -(Px / Py) and intercepts at M/Px and M/Py.
Income consumption curve (ICC)
The path of optimal bundles as income changes, with prices held constant. Traces out how your chosen mix of goods shifts when you get richer or poorer.
Price consumption curve (PCC)
The path of optimal bundles as the price of one good changes, with income and the other price held constant.
Engel curve
Shows the relationship between income and the quantity of a single good purchased. A normal good has an upward-sloping Engel curve; an inferior good has a downward-sloping one.
Demand curve
Shows the quantity demanded at each possible price, holding other factors constant. Derived from the PCC by plotting price against quantity.
Giffen good
A good for which a decrease in price causes quantity demanded to decrease. This happens when the income effect on an inferior good is so strong it outweighs the substitution effect. Very few real-world examples exist.
Income effect
The change in quantity demanded that results from a change in purchasing power (real income) after a price change. Equals x** - xc.
Substitution effect
The change in quantity demanded that results purely from the change in relative prices, holding utility constant. Equals xc - x*. Always moves opposite to the price change.
Compensated demand curve (Hicksian)
A demand curve that holds utility constant rather than income constant. Isolates the substitution effect by asking: at the new prices, what income would keep the consumer on the original indifference curve?
Consumer preferences are built on three axioms: completeness, transitivity, and "more is better." These assumptions guarantee that indifference curves are well-behaved (downward-sloping, convex, and non-intersecting).
Preference notation:
A > B means A is strictly preferred to B
A ~ B means the consumer is indifferent between A and B
A ≥ B means A is at least as good as B
The consumer's optimum occurs where the highest attainable indifference curve just touches the budget constraint. At that point:
MRS = MRT
-(MUx / MUy) = -(Px / Py)
In words: the rate at which you are willing to trade equals the rate at which the market lets you trade. If MRS > MRT, you value good X more than the market does, so you should buy more X. The logic runs the other way if MRS < MRT.
All bundles on the same indifference curve yield the same utility. Bundles above and to the right of the curve are preferred (more is better). Bundles below and to the left are worse.
Key properties:
Downward-sloping (giving up some of one good requires more of the other to stay indifferent)
Convex to the origin (diminishing MRS, meaning consumers prefer balanced bundles)
Cannot cross (if they did, transitivity would be violated)
The budget line shows every bundle that exactly exhausts the consumer's income: Px * X + Py * Y = M.
Slope = -(Px / Py)
X-intercept = M / Px (spend everything on X)
Y-intercept = M / Py (spend everything on Y)
Bundles above the line are unaffordable. Bundles below the line leave money unspent.
Income consumption curve (ICC): vary income while holding prices fixed. The ICC traces the optimal bundles. For normal goods it slopes upward in both dimensions; for an inferior good it bends back.
Price consumption curve (PCC): vary the price of one good while holding income and the other price fixed. The PCC traces the new optima.
Engel curve: derived from the ICC. Plot income on the vertical axis and quantity of one good on the horizontal. Normal goods have a positive slope; inferior goods have a negative slope.
Demand curve: derived from the PCC. Plot price on the vertical axis and quantity on the horizontal. For most goods, demand slopes downward.
A Giffen good is an inferior good whose income effect is large enough to dominate the substitution effect. When its price falls, the consumer feels richer and buys less of the inferior good, even though the substitution effect says to buy more.
The classic textbook example involves a very poor consumer whose budget is dominated by a staple food (potatoes, rice). A price drop frees up income to buy something better, so consumption of the staple actually falls. Real-world examples are extremely rare.
When the price of X falls, the total effect on quantity demanded of X can be split into two parts:
Substitution effect (xc - x):* hold utility constant, let prices change. The consumer slides along the original indifference curve to a point where MRS equals the new price ratio. This effect always moves in the opposite direction to the price change.
Income effect (x - xc):** the price change makes the consumer's budget stretch further (or less far). This is equivalent to an income change at the new prices.
Total effect = substitution effect + income effect.
For a normal good, both effects push in the same direction (price falls, buy more). For an inferior good, they push in opposite directions. For a Giffen good, the income effect is so strong that it reverses the total effect.
The compensated income M' is the income level that, at the new prices, places the consumer on the original indifference curve. The compensated demand curve (Hicksian) traces quantity demanded against price at that constant utility level.
Budget constraint: Px * X + Py * Y = M
MRS: -(MUx / MUy)
MRT: -(Px / Py)
Optimality condition: MRS = MRT, which gives MUx / MUy = Px / Py
Substitution effect: xc - x* (movement along original indifference curve to new price ratio)
Income effect: x** - xc (shift from compensated bundle to new optimal bundle)
Total effect: x** - x* = substitution effect + income effect
Compensated income M': the income that, at new prices, returns the consumer to the original utility level. Solve U(x, y) = U* subject to Px' * X + Py * Y = M'.
Students often confuse MRS with MRT. MRS is the slope of the indifference curve (willingness to trade). MRT is the slope of the budget constraint (ability to trade). At the optimum they are equal, but they measure different things.
Students sometimes think a Giffen good is just any inferior good. It is not. A Giffen good is an inferior good where the income effect is strong enough to reverse the law of demand. Most inferior goods still have downward-sloping demand curves.
A common error is graphing the substitution effect by drawing a parallel budget line. The compensated budget line must be tangent to the original indifference curve at the new price ratio, not merely parallel to the new budget line.
Students often forget that the substitution effect always goes in the "expected" direction (price falls, buy more). The income effect is the only part that can go the other way.
⚠️ The income/substitution effect problem is one of the seven large problems on the final. Expect to find the optimal bundle, re-solve after a price change, calculate compensated income M', and decompose the total effect into substitution and income components, then graph everything.
⚠️ You will likely need to draw the compensated demand curve alongside the ordinary (Marshallian) demand curve. Know which one holds utility constant and which holds income constant.
⚠️ Be ready to classify a good as normal, inferior, or Giffen based on the signs of the income and substitution effects.
⚠️ The tangency condition MRS = MRT appears everywhere in this course, from consumer theory through general equilibrium. Nail it here and it will carry forward.
True or false: Indifference curves can cross if the consumer has unusual preferences. (False, crossing violates transitivity.)
Fill in the blank: At the consumer's optimum, MRS = ______. (MRT, or equivalently Px/Py)
True or false: The substitution effect can go in the same direction as the price change. (False, it always goes opposite.)
Fill in the blank: A Giffen good must be a(n) ______ good. (Inferior)
True or false: The Engel curve for a normal good slopes downward. (False, it slopes upward.)
Q: A consumer has utility function U = X * Y, income M = 100, Px = 5, Py = 10. What is the optimal bundle?
A: Set MRS = MRT. MUx = Y, MUy = X, so MRS = Y/X. MRT = 5/10 = 1/2. Setting Y/X = 1/2 gives X = 2Y. Substituting into the budget constraint: 5(2Y) + 10Y = 100, so 20Y = 100, Y = 5, X = 10. Optimal bundle: (10, 5).
Q: If Px falls from 5 to 2.50 in the example above, describe how you would decompose the change in X into income and substitution effects.
A: First, find the new optimal bundle at the new prices (this is the total effect). Then find compensated income M' that places the consumer back on the original indifference curve U = 10 * 5 = 50, but at the new price ratio. Solve the tangency condition at new prices with U = 50 to get the compensated bundle. Substitution effect = compensated X minus original X. Income effect = new X minus compensated X.
Q: Can a good be inferior but not a Giffen good? Explain.
A: Yes. For an inferior good, the income effect works against the substitution effect, but as long as the substitution effect is larger, demand still rises when price falls. A Giffen good is the special case where the income effect is so large it overwhelms the substitution effect entirely.
Q: What does the compensated demand curve isolate, and how does it differ from the ordinary demand curve?
A: The compensated (Hicksian) demand curve isolates the substitution effect by holding utility constant. The ordinary (Marshallian) demand curve holds income constant and captures both income and substitution effects. For a normal good, the ordinary curve is flatter (more responsive to price) because both effects reinforce each other.
The tangency condition MRS = MRT reappears in general equilibrium, where Pareto efficiency requires MRS_A = MRS_B = MRT. The Edgeworth box is built directly on the preference machinery introduced here.
Income and substitution effects underpin the derivation of market demand curves, which feed into the supply/demand/elasticity/taxes topic.
The concept of the budget constraint carries over to the firm's isocost line in producer theory, with wages and rental rates replacing consumer prices.
Related Terms / Search Tags
consumer choice, utility maximisation, budget line, indifference map, optimal consumption bundle, Slutsky decomposition, Hicksian demand, Marshallian demand, compensating variation, normal good, inferior good, Giffen paradox, income effect, substitution effect, MRS, MRT, tangency condition, Cobb-Douglas utility, perfect substitutes, perfect complements, Engel curve, ICC, PCC, price consumption curve, income consumption curve