Consumer theory is the microeconomic model of how individuals decide what to buy, given limited income and a set of prices. It's the formal foundation underneath the demand curve you already know from Unit 2 — instead of just assuming demand slopes downward, consumer theory actually derives it from how a rational person maximizes satisfaction subject to a budget.

Total & Marginal Utility

Utility is the satisfaction a consumer gets from consuming a good — not measured in real units, but treated as a number for the purpose of comparison. Total utility (TU) is the overall satisfaction from a given quantity consumed. Marginal utility (MU) is the additional utility from consuming one more unit.

Indifference Curves

An indifference curve shows every combination of two goods that gives a consumer the exact same total utility — the consumer is "indifferent" between any point on the curve.

• Downward sloping — to keep utility constant, gaining more of one good means giving up some of the other.
• Convex to the origin — the curve gets flatter as you move right, reflecting a diminishing willingness to trade one good for the other.
• Never cross — two indifference curves crossing would imply a logical contradiction about the consumer's preferences.
• Higher curves mean higher utility — a curve further from the origin represents more of both goods, and therefore more total satisfaction.

The Marginal Rate of Substitution

The marginal rate of substitution (MRS) is the slope of an indifference curve at any point — how much of one good a consumer is willing to give up for one more unit of the other, while keeping utility constant.

MRS diminishes as you move along a typical indifference curve — the more of Good X you already have relative to Good Y, the less additional Y you're willing to give up for one more unit of X. This is exactly what makes the curve convex.

The Budget Constraint

The budget constraint (or budget line) shows every combination of two goods a consumer can afford, given income and prices.

The slope of the budget line is −P_x/P_y — the rate at which the market lets a consumer trade Good X for Good Y. A rise in income shifts the whole line outward (parallel); a change in either price rotates the line around one axis intercept.

Consumer Equilibrium: Utility Maximization

A consumer maximizes utility at the point where the budget line is tangent to the highest indifference curve it can reach — the single affordable bundle where MRS exactly equals the price ratio.

This says the consumer gets equal "bang for the buck" from the last dollar spent on each good — if one side were larger, the consumer could increase total utility by shifting spending toward that good.

Full Worked Example

Suppose a consumer has utility function U = XY, income M = $100, the price of Good X is $2, and the price of Good Y is $4. What bundle maximizes utility?

Income & Substitution Effects

When the price of a good falls, two separate things happen to quantity demanded at once — consumer theory is what lets economists formally separate them.

• Substitution effect — the good is now relatively cheaper compared to other goods, so the consumer substitutes toward it, regardless of income. This effect always pushes quantity demanded in the opposite direction of the price change.
• Income effect — a lower price effectively increases the consumer's real purchasing power, as if income had risen. How this affects quantity demanded depends on what kind of good it is.

Giffen goods are a genuine theoretical curiosity rather than something you'll encounter often — they require a good that's both strongly inferior and takes up a very large share of a very poor consumer's budget, historically illustrated with staple foods during famine conditions.

From Consumer Theory to the Demand Curve

If you repeat the utility-maximization process at different prices for Good X — lowering P_x and re-solving for the new optimal X* each time — and then plot each resulting price-quantity pair, you get exactly the downward-sloping demand curve from Unit 2. Consumer theory is the "why" underneath the demand curve you'd otherwise just take as given.

Common Mistakes

1. Confusing marginal utility with total utility. Total utility can still be rising even while marginal utility is falling — they only move in the same direction some of the time, and TU peaks exactly where MU hits zero.
2. Drawing indifference curves that cross. This is a very common diagram mistake and always signals a logical error — no two indifference curves can ever intersect.
3. Setting MRS equal to MUx/Px instead of the full tangency condition. The correct equilibrium condition compares "utility per dollar" on both goods: MUx/Px = MUy/Py, not just the MRS alone.
4. Assuming all price falls increase quantity demanded the same way. The income effect's direction depends entirely on whether the good is normal, inferior, or (rarely) Giffen.