Source: Comprehensive Overview of Microeconomic Theory Concepts (Texas A&M University)
Tags: utility function, consumer preferences, completeness, transitivity, diminishing MRS, indifference curve, budget constraint, budget line, optimal choice, marginal rate of substitution, MRS, substitution effect, income effect, normal goods, inferior goods, consumer surplus, marginal utility
Consumer theory models how people choose between goods given their preferences and budget. Preferences are captured by utility functions and visualised as indifference curves; the budget line shows what a consumer can afford. The optimal bundle sits where the indifference curve is tangent to the budget line (MRS = price ratio). Price changes decompose into substitution and income effects, and consumer surplus measures the gain buyers enjoy from paying less than their maximum willingness to pay.
Utility function
A mathematical function that assigns a numerical value to each consumption bundle, representing the consumer's preferences. Higher values mean more-preferred bundles.
Consumption bundle
A specific combination of goods (e.g. x units of good X and y units of good Y) that a consumer might choose.
Completeness (of preferences)
The assumption that a consumer can rank any two bundles: either one is preferred, or the consumer is indifferent between them.
Transitivity (of preferences)
If bundle A is preferred to B, and B is preferred to C, then A must be preferred to C. Ensures consistent ranking.
Indifference curve
A curve on a graph showing all bundles that give a consumer the same level of utility. Bundles on a higher indifference curve are preferred.
Marginal Rate of Substitution (MRS)
The rate at which a consumer is willing to give up one good in exchange for more of another, while staying at the same utility level. Equal to the slope of the indifference curve at a given point.
Diminishing MRS
The tendency for the MRS to fall as a consumer moves along an indifference curve, substituting more of one good for the other. Reflects convex indifference curves and diminishing marginal utility.
Linear preferences
Preferences where the MRS is constant (indifference curves are straight lines). The consumer views the two goods as perfect or near-perfect substitutes at a fixed rate.
Budget line (budget constraint)
The set of all bundles a consumer can just afford given their income and the prices of the two goods. Shown as a straight line with slope equal to –(P_x / P_y).
Optimal choice
The bundle that maximises utility subject to the budget constraint. Found where the indifference curve is tangent to the budget line, i.e. MRS = P_x / P_y.
Marginal utility (MU)
The additional utility gained from consuming one more unit of a good, holding consumption of other goods constant.
Substitution effect
The portion of a change in quantity demanded that results from the good becoming relatively cheaper or more expensive, holding real purchasing power constant.
Income effect
The portion of a change in quantity demanded that results from the change in the consumer's real purchasing power when a price changes.
Normal good
A good for which demand increases when income rises. Both income and substitution effects work in the same direction when price falls.
Inferior good
A good for which demand decreases when income rises. The income effect works against the substitution effect when price falls.
Consumer surplus
The difference between what consumers are willing to pay (shown by the demand curve) and what they actually pay (the market price). Represents the net benefit buyers receive from participating in the market.
A utility function u(x, y) maps every bundle (x, y) to a number. Higher numbers mean greater satisfaction.
Three key properties underpin well-behaved preferences:
Completeness: every pair of bundles can be ranked.
Transitivity: rankings are internally consistent (no cycles).
Diminishing MRS: the more of good X you already have, the less of good Y you are willing to sacrifice for another unit of X.
Linear utility functions, such as u(x, y) = 200x + 199y, produce straight-line indifference curves with a constant MRS. The consumer treats the goods as near-perfect substitutes.
The budget line equation: P_x · x + P_y · y = I, where I is income.
Slope of the budget line: –P_x / P_y. This tells you the market trade-off rate between the two goods.
An increase in income shifts the budget line outward in parallel (same slope, more purchasing power).
A change in one good's price rotates the budget line around the intercept of the other good.
The consumer's goal is to maximise utility subject to the budget constraint.
At the optimum, the indifference curve is tangent to the budget line.
Tangency condition: MRS_xy = P_x / P_y.
Intuitively, the consumer's personal trade-off rate between the goods (MRS) equals the market's trade-off rate (price ratio). There is no further gain from reallocating spending.
MRS_xy = MU_x / MU_y.
It tells you how many units of Y a consumer would willingly give up to get one more unit of X, staying on the same indifference curve.
Diminishing MRS (the typical case) means indifference curves are convex to the origin: consumers prefer variety.
When the price of a good falls, two things happen simultaneously:
Substitution effect: the good is now relatively cheaper, so the consumer buys more of it (and less of the other good).
Income effect: the consumer's real purchasing power has increased, which changes demand for both goods.
For normal goods, both effects push demand in the same direction (price falls, demand rises).
For inferior goods, the income effect opposes the substitution effect. If income rises (because of a price fall), the consumer wants less of the inferior good, partially offsetting the substitution effect.
Consumer surplus is the area between the demand curve and the horizontal line at the market price, up to the quantity purchased.
It captures the total "bonus" consumers enjoy by paying a single market price rather than each buyer's individual maximum willingness to pay.
A lower market price means more consumer surplus; a higher price means less.
Budget line:
P_x · x + P_y · y = I
Slope = –P_x / P_y
MRS formula:
MRS_xy = MU_x / MU_y
Optimality (tangency) condition:
MRS_xy = P_x / P_y
Consumer surplus (graphical):
Area below the demand curve and above the market price line, from 0 to Q purchased.
⚠️ The tangency condition MRS = P_x / P_y is the single most important result in consumer theory. Know how to derive it and what it means intuitively.
⚠️ Be clear on the difference between the substitution effect (holding utility constant) and the income effect (change in real purchasing power). Exam questions often ask you to decompose a price change into the two.
⚠️ Normal vs inferior goods: for normal goods the income effect reinforces the substitution effect; for inferior goods the income effect works against it. A Giffen good is the extreme case where the income effect dominates, causing an upward-sloping demand curve.
⚠️ Linear preferences (constant MRS) produce corner solutions: the consumer spends their entire budget on whichever good delivers more utility per pound. Watch for this when utility functions are of the form u = ax + by.
⚠️ Consumer surplus questions often ask you to calculate the area of a triangle between the demand curve and the price line. Brush up on the geometry.
Q: What does it mean for preferences to satisfy transitivity?
A: If a consumer prefers bundle A to B, and B to C, then they must also prefer A to C. Rankings cannot cycle.
Q: A consumer has income of £100, P_x = £5, and P_y = £10. What is the slope of their budget line?
A: Slope = –P_x / P_y = –5/10 = –0.5.
Q: At the consumer's optimum, what is the relationship between MRS and the price ratio?
A: MRS_xy = P_x / P_y. The consumer's willingness to trade between goods matches the rate at which the market allows them to trade.
Q: If the price of good X falls and X is a normal good, how do the substitution and income effects each affect the quantity of X demanded?
A: Both increase it. The substitution effect increases demand because X is now relatively cheaper. The income effect increases demand because the consumer's real purchasing power has risen and, for a normal good, higher real income means more X.
Q: What does consumer surplus measure, and how is it shown on a graph?
A: It measures the difference between consumers' willingness to pay (the demand curve) and the price they pay (the market price). Graphically, it is the area below the demand curve and above the market price line, from zero to the quantity purchased.
Q: Jane has utility function u(x, y) = 200x + 199y. What shape are her indifference curves, and what type of solution will she choose?
A: Her indifference curves are straight lines (linear preferences) with a constant MRS of 200/199. She will choose a corner solution, spending her entire budget on good X (since it delivers marginally more utility per unit, assuming equal prices; the exact corner depends on the price ratio).
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