Source: Microeconomic Theory, Texas A&M University, Final Exam M.1
Tags: consumer preferences, market basket, bundle, indifference curve, utility function, marginal rate of substitution, MRS, budget constraint, budget line, consumer choice, perfect substitutes, perfect complements, marginal utility, ECON 323
Consumer preference theory explains how rational consumers rank bundles of goods using three core assumptions (completeness, transitivity, more is better). Preferences are visualised with indifference curves, quantified with utility functions, and constrained by the budget line. The consumer's optimal choice sits where the indifference curve is tangent to the budget line, i.e. where MRS equals the price ratio.
Market basket (bundle)
A list specifying exact quantities of all goods a consumer could choose. Two baskets can be compared, and the consumer either prefers one or is indifferent between them.
Completeness (Assumption 1)
The requirement that a consumer can always compare any two baskets: prefer A to B, prefer B to A, or be indifferent. No basket pair is "unrankable."
Transitivity (Assumption 2)
If a consumer prefers basket A to B and basket B to C, they must also prefer A to C. Violated when an indifference curve is curved back on itself or thick.
More is better / non-satiation (Assumption 3)
Consumers always prefer more of any good to less. This means consumers are never fully satisfied. Violated when indifference curves intersect.
Indifference map
A graph containing a family of indifference curves, each representing a different satisfaction level.
Indifference curve
A curve showing every combination of goods that gives the consumer the same level of satisfaction.
Points on the same curve are equally preferred.
Curves further to the northeast represent higher satisfaction.
They slope downward, are thin, and never cross one another.
Utility
A numerical score representing the satisfaction a consumer gets from a given market basket. Ordinal, not cardinal: only the ranking matters.
Utility function
A formula assigning a utility level to each basket.
Linear form: U(x, y) = ax + by, where a, b > 0 (produces straight-line indifference curves).
Cobb-Douglas form: U(x, y) = cx^a · y^b, where a, b, c > 0 (produces curves that bend toward the origin).
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. It equals the magnitude of the slope of the indifference curve.
Diminishing MRS
As you move along an indifference curve consuming more of good F (x-axis), the MRS falls, meaning you sacrifice less of good C (y-axis) for each extra unit of F. This is the standard, well-behaved case.
Perfect substitutes
Goods with a constant MRS. The consumer cares only about the total quantity, not the mix. Indifference curves are straight lines. Violates diminishing MRS.
Perfect complements
Goods consumed in a fixed proportion. MRS is either zero or infinity (never interior). Indifference curves are L-shaped. Violates diminishing MRS.
Marginal utility (MU)
The additional satisfaction from consuming one more unit of a good.
Budget line
The set of all baskets whose total expenditure exactly equals income I: Px · x + Py · y = I.
Consumer surplus
The total benefit from consumption of a product, minus the total cost of purchasing it.
Completeness ensures every pair of baskets can be ranked.
Transitivity ensures rankings are logically consistent (no cycles).
More is better ensures indifference curves slope downward and don't intersect.
All three must hold for the standard indifference-curve model to work. When they fail, you get thick curves, intersecting curves, or upward-sloping curves, each of which is a signal that an assumption is violated.
Each curve is a contour of constant utility.
Moving northeast (more of both goods) reaches a higher curve.
Curves are thin, downward-sloping, and never cross. If two curves crossed, a single basket would sit on two different satisfaction levels, contradicting transitivity and non-satiation.
The utility function translates preferences into numbers. Two common forms:
Linear: U(x, y) = ax + by. Indifference curves are straight lines. Goods are perfect substitutes.
Cobb-Douglas: U(x, y) = cx^a · y^b. Indifference curves are convex toward the origin, which is the typical "well-behaved" shape.
MRS formula (slope form):
MRS = |ΔC / ΔF|
where F is on the horizontal axis and C is on the vertical axis.
MRS formula (marginal utility form):
MRS = MU_x / MU_y = Δy / Δx
As the consumer moves rightward along an indifference curve (more F), the MRS falls. This is diminishing MRS: each extra unit of F is worth less in terms of C.
Perfect substitutes: straight-line indifference curves, constant MRS. The consumer only cares about total quantity.
Perfect complements: L-shaped indifference curves. Consumed in a fixed ratio (not necessarily 1:1). MRS is zero on one segment and infinite on the other.
Both violate the assumption of diminishing MRS.
Marginal utility is the derivative of the utility function with respect to one good, holding the other constant. It links directly to MRS:
MRS = MU_x / MU_y
The budget line is the boundary of what the consumer can afford:
Px · x + Py · y = I
A change in income shifts the budget line in or out, parallel to the original.
A change in the price of one good rotates the line around the intercept of the other good.
The optimal bundle for smooth, convex preferences lies where the indifference curve is tangent to the budget line:
MRS = Px / Py, equivalently MU_x / MU_y = Px / Py
If MRS > Px / Py: the consumer values x more than the market does, so increase x and decrease y.
If MRS < Px / Py: the consumer values y more, so increase y and decrease x.
⚠️ Know all three preference assumptions and what happens visually when each is violated (thick curves, crossing curves, etc.).
⚠️ The tangency condition MRS = Px / Py is the single most tested optimality result in this module.
⚠️ Don't confuse the direction of adjustment: MRS > Px / Py means buy more x, not less.
⚠️ Perfect substitutes and perfect complements both violate diminishing MRS. Be ready to sketch both curve shapes.
⚠️ Budget line shifts (income change) vs. rotations (price change) are a common graphical question.
Q: What are the three assumptions of consumer preferences, and what does each guarantee?
A: Completeness (all baskets can be ranked), transitivity (rankings are consistent, no cycles), and more is better (consumers prefer more of any good). Together they produce well-behaved, downward-sloping, non-intersecting indifference curves.
Q: If two indifference curves cross, which assumption is violated?
A: More is better (non-satiation). A crossing point would place one basket on two different utility levels, which is a contradiction.
Q: State the consumer's optimality condition for an interior solution and explain what happens if MRS > Px / Py.
A: The optimality condition is MRS = Px / Py (equivalently, MU_x / MU_y = Px / Py). If MRS > Px / Py, the consumer gets more value per pound from x than the budget requires, so they should buy more x and less y until the equality holds.
Q: How does a change in income differ from a change in price on the budget line?
A: An income change shifts the budget line in parallel (same slope, different intercepts). A price change in one good rotates the line about the intercept of the other good (slope changes).
Q: What is the MRS for perfect substitutes, and what shape are the indifference curves?
A: The MRS is constant (does not diminish). Indifference curves are straight lines.
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