Difficulty: Intermediate | Prerequisites: Basic supply and demand, introductory algebra
Consumer theory explains how people allocate limited income across goods to get the most satisfaction (utility) possible. The core idea: a rational consumer keeps spending until the last pound spent on every good delivers the same marginal utility. Budget constraints, indifference curves and the marginal rate of substitution are the tools that make this precise.
Indifference curve
A curve representing all combinations of market baskets that provide a consumer with the same level of satisfaction (utility). Indifference curves do not cross, slope downward, and are typically convex to the origin.
In simple terms: every point on the same curve makes you equally happy, so you have no reason to prefer one bundle over another along it.
Marginal Rate of Substitution (MRS)
The maximum amount of one good a consumer is willing to give up to obtain one additional unit of another good. Equals the slope of the indifference curve.
MRS = -(Change in Good 2 / Change in Good 1) = Pa / Pb at the optimum.
Think of it as the personal "exchange rate" between two goods in your head, before prices enter the picture.
Diminishing MRS
As you consume more of one good, you are willing to give up less and less of the other to get still more of it. This is why indifference curves are convex to the origin.
Budget line (budget constraint)
All combinations of goods for which the total amount of money spent equals income. The slope equals the negative of the price ratio, -(Px / Py).
In simple terms: the boundary of what you can afford. Everything on the line spends your income exactly; everything inside it leaves money unspent.
Perfect complements
Two goods for which the MRS is zero or infinite, consumed in fixed proportions. Indifference curves are L-shaped. Example: hot dogs and hot dog buns, left shoes and right shoes.
Perfect substitutes
Two goods for which the MRS is constant. Indifference curves are straight lines. If U = x + y, the consumer treats one unit of x as interchangeable with one unit of y.
Marginal utility
The additional satisfaction from consuming one more unit of a good. Formally, MU = dU/dQ for that good.
Diminishing marginal utility
As more of one good is consumed, the consumption of additional amounts yields smaller additions to utility.
Equal Marginal Principle
Utility is maximised when the consumer has equalised the marginal utility per dollar of expenditure across all goods: (MUa / Pa) = (MUb / Pb).
In simple terms: keep shifting spending from the good giving you less bang-per-pound to the one giving you more, until they match.
Ordinal utility function
Generates a ranking of market baskets from most to least preferred. Only the order matters, not the size of the numbers.
Cardinal utility function
Describes how much one market basket is preferred to another. The numerical difference between utility levels carries meaning.
Composite good
When analysing bundles with more than two goods, all goods other than the one under study are combined into a single "composite good."
Revealed preference
If a consumer chooses one market basket over another, and the chosen basket is more expensive than the alternative, then the consumer must prefer the chosen basket.
Bad
A good for which less is preferred rather than more (e.g., pollution, noise).
Completeness. For any two baskets A and B, the consumer can say A is preferred, B is preferred, or they are equally good.
Transitivity. If A is preferred to B and B is preferred to C, then A is preferred to C.
More is better than less. Consumers always prefer more of a good to less (non-satiation).
Each curve connects all bundles yielding the same utility level.
Curves slope downward (giving up one good requires more of another to stay equally satisfied).
Curves cannot cross (that would violate transitivity).
Convexity to the origin reflects diminishing MRS: as you accumulate more of one good, each extra unit is worth less to you in terms of the other.
Special shapes:
Perfect substitutes: straight-line indifference curves (constant MRS). Example: U = x + y.
Perfect complements: L-shaped indifference curves. The consumer gains nothing from extra units of one good without matching units of the other. Example: hot dogs and buns consumed 1:1.
A strict vegetarian's indifference curves for meat (horizontal axis) and vegetables (vertical axis) are horizontal lines, because meat is a neutral good (or a "bad") and only vegetables contribute to utility.
The budget line equation: Px * X + Py * Y = Income.
Slope of the budget line = -(Px / Py).
If the price of one good rises while the other price and income stay the same, the budget line rotates inward from the intercept on the axis of the good that did not change.
If income rises while both prices stay the same, the budget line shifts outward with no change in slope.
If both prices and income all double, the budget line does not change.
The optimal basket must:
Lie on the budget line (all income is spent).
Give the consumer the most preferred combination of goods.
At the optimum, satisfaction is maximised when marginal benefit equals marginal cost, which translates to the equal marginal principle: MUa / Pa = MUb / Pb.
Alternatively, at the tangency of the indifference curve and the budget line, MRS = Px / Py.
Elaine views hot dogs and hot dog buns as perfect complements, and the corners of her indifference curves follow the 45-degree line (1:1 ratio). The price of hot dogs is $5 per package, the price of buns is $3 per package, and her budget is $48 per month.
Because she consumes equal packages: let H = B. Budget: 5H + 3H = 48, so 8H = 48, giving H = 6. Her optimal choice is 6 packages of hot dogs and 6 packages of buns.
Bellatrix consumes only goods A and B. MUa = 1/Qa, MUb = 1/Qb. Pa = $0.50, Pb = $4.00, income = $120.
Set MUa / Pa = MUb / Pb: (1/Qa) / 0.50 = (1/Qb) / 4.00, which gives Qb = Qa / 8.
Substitute into the budget: 0.50Qa + 4.00(Qa/8) = 120, so 0.50Qa + 0.50Qa = 120, giving Qa = 120. She purchases 120 units of A.
Jules uses his entire budget to buy 5 cans of Sprite ($1 each) and 3 hamburgers ($2 each). MU from Sprite is 4, MU from hamburgers is 6.
MU per dollar: Sprite = 4/1 = 4, Hamburgers = 6/2 = 3. Sprite delivers more utility per dollar, so Jules should increase Sprite consumption and reduce hamburger consumption.
Utility function: u(F, C) = F + 4C. If clothing consumption falls by 2 units, the utility lost = 4 * 2 = 8. Food must increase by 8 units to maintain the same utility level.
Consumption decisions are influenced by current income and expectations about future income and needs. The intertemporal budget is determined by yearly income, spending, investment and borrowing.
Budget constraint: Px * X + Py * Y = I (income)
Slope of budget line: -(Px / Py)
Marginal Rate of Substitution: MRS = -(Change in Good 2 / Change in Good 1) = MUx / MUy
Equal Marginal Principle: MUa / Pa = MUb / Pb
Equivalent condition at the optimum: 0 = MUa(Change in A) + MUb(Change in B)
Marginal utility: MU = dU / dQ (the derivative of the utility function with respect to that good)
Perfect complements (1:1 ratio on the 45-degree line): consume equal quantities, so set X = Y and substitute into the budget constraint to solve.
The equal marginal principle is the logic behind any household splitting a weekly grocery budget: you stop buying extra coffee once the satisfaction from one more bag falls below what that money would add in, say, fresh fruit. Budget constraints and indifference curves are also the backbone of policy analysis, such as modelling how a food-stamp programme changes the set of bundles a low-income household can reach.
Students often think indifference curves can cross. They cannot: if they did, transitivity would be violated because one bundle would simultaneously be equal to two bundles that are not equal to each other.
Students sometimes confuse the slope of the indifference curve (MRS) with the slope of the budget line (price ratio). At the optimum the two are equal, but they measure different things: MRS is about willingness to trade, the price ratio is about the market's terms of trade.
A common mistake is thinking that "more utility" from a higher indifference curve number means a specific amount more. With ordinal utility, only the ranking matters, not the gap between numbers.
Students often assume that when prices and income all change by the same proportion, the budget line moves. It does not.
⚠️ The equal marginal principle (MUa/Pa = MUb/Pb) is tested frequently. Know how to apply it numerically, including deciding which good to buy more of when the ratio is unequal.
⚠️ Perfect complements problems almost always require setting quantities equal and solving the budget constraint. Expect a numerical answer.
⚠️ Be ready to state what happens to the budget line when one price changes, when income changes, or when both prices and income change proportionally.
⚠️ Ordinal vs cardinal utility: indifference curve labels are meaningful only in an ordinal way. Exams often test this with a true/false statement.
⚠️ Know the difference between a movement along the budget line (reallocation) and a shift of the budget line (income or price change).
True or false: If U = x + y, the goods are perfect complements. (False, they are perfect substitutes.)
Fill in the blank: The slope of the budget line equals ______. (-(Px / Py))
True or false: If both prices and income double, the budget line shifts outward. (False, it stays the same.)
Fill in the blank: At the utility-maximising bundle, the MRS equals ______. (the price ratio, Px / Py)
True or false: Indifference curves for perfect complements are L-shaped. (True.)
Q: A consumer has $100 per day to spend on product A (unit price $7) and product B (unit price $15). Good A is on the horizontal axis, good B on the vertical axis. What is the slope of the budget line?
A: Slope = -(Pa / Pb) = -(7/15) = -7/15.
Q: Elaine views hot dogs and buns as perfect complements (1:1). Hot dogs cost $5 per package, buns cost $3 per package, and her budget is $48. What is her optimal choice?
A: Set H = B. Budget: 5H + 3H = 48, so H = 6. She buys 6 packages of each.
Q: Jules buys 5 Sprites ($1 each, MU = 4) and 3 hamburgers ($2 each, MU = 6). How should he change his spending?
A: MU per dollar: Sprite = 4/1 = 4, hamburgers = 6/2 = 3. Sprite gives more per dollar, so he should increase Sprite consumption and reduce hamburger consumption.
Q: If u(F, C) = F + 4C and clothing falls by 2 units, how much more food is needed to keep utility constant?
A: Lost utility = 4 * 2 = 8. Food must increase by 8 units.
Q: Bellatrix has MUa = 1/Qa, MUb = 1/Qb, Pa = $0.50, Pb = $4.00, income = $120. How much of good A does she buy?
A: 120 units. Set (1/Qa)/0.50 = (1/Qb)/4.00, giving Qb = Qa/8. Substitute: 0.50Qa + 0.50Qa = 120, so Qa = 120.
Q: If prices and income in a two-good economy all double, what happens to the budget line?
A: Nothing. The budget line is unchanged because the ratios are the same.
Consumer theory feeds directly into demand theory: the individual demand curve is derived by varying the price of one good and tracing the optimal quantities along successive budget lines. The substitution and income effects (covered in the Demand Theory notes) decompose a price change into its two parts. The same optimisation logic reappears on the production side, where isoquants replace indifference curves and isocost lines replace budget lines.
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