Source: Chapter 3, Consumer Behavior
Tags: consumer preferences, market basket, bundle, indifference curve, indifference map, utility function, completeness, transitivity, more is better, nonsatiation, MRS, marginal rate of substitution, ECON 323
Consumer preferences describe how people rank different combinations of goods (market baskets) based on what they like, without considering prices or budgets. Three core assumptions – completeness, transitivity, and more is better – give indifference curves their characteristic shape: downward-sloping, thin lines that never cross. A utility function is simply a formula that assigns a number to each basket, letting you work with preferences algebraically.
Market basket (bundle)
A list with specific quantities of one or more goods. For example, 90 meals, 20 gallons of gas, and 1 piece of clothing per month.
Completeness (Assumption 1)
The requirement that a consumer can compare and rank every possible pair of baskets. If you simply cannot decide between two options (and you are not indifferent), completeness is violated.
Transitivity (Assumption 2)
If a consumer prefers basket A to basket B, and basket B to basket C, then the consumer must also prefer A to C. Circular preferences violate this assumption.
More is better / nonsatiation (Assumption 3)
Goods are assumed to be desirable: consumers always prefer more of any good to less, and they are never fully satisfied.
Indifference curve
A curve showing all combinations of market baskets that give a consumer the same level of satisfaction.
Indifference map
A graph containing a set of indifference curves. It is a complete picture of a consumer's preferences. There are infinitely many curves on the map, though we typically draw only a few.
Utility
A numerical score representing the satisfaction a consumer gets from a given market basket.
Utility function
A formula that assigns a level of utility to individual market baskets. For example, U(x, y) = x + 2y.
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. Formally: MRS_FC = |ΔC / ΔF| = −ΔC / ΔF.
Diminishing marginal rate of substitution (Assumption 4)
As a consumer acquires more of Good X, they are willing to give up less and less of Good Y to get another unit of X. This makes indifference curves convex (bowed in towards the origin).
Perfect substitutes
Two goods for which the MRS is constant. The utility function is linear: U(x, y) = ax + by. Indifference curves are straight lines.
Perfect complements
Two goods consumed in fixed proportions; leftover units of either good add no value. The utility function takes the form U(x, y) = min{ax, by}. Indifference curves are L-shaped.
Marginal utility (MU)
The additional satisfaction obtained from consuming one additional unit of a good.
When discussing preferences, prices and budgets are set aside entirely. You are only thinking about what you like.
Completeness: you can always say which of two baskets you prefer, or that you are indifferent between them. An inability to rank at all (not indifference, but genuine inability to compare) violates this.
Transitivity: preferences must be logically consistent. Preferring Honda Accord over Toyota Camry, Camry over Ford Fusion, yet Fusion over Accord is a circular contradiction.
More is better (nonsatiation): in a two-good world, a basket with more of at least one good and no less of the other is always preferred.
Given the three assumptions above, indifference curves must be:
Downward sloping. An upward-sloping section would mean one basket has more of both goods than another on the same curve, violating more is better.
Thin lines, not thick bands. A thick curve contains two points where one has more of both goods, again violating more is better.
Non-intersecting. If two curves crossed at a point, transitivity and more is better would produce a contradiction (a basket on the higher curve would have to be indifferent to one on the lower curve, yet also strictly preferred).
Curves further to the northeast represent higher satisfaction.
A utility function translates preferences into algebra. To plot indifference curves from a utility function:
Set U(x, y) equal to a constant c.
Solve for y in terms of x.
Plot the resulting equation for several values of c.
Example with a linear function: U(x, y) = x + 2y. Set x + 2y = 1, solve for y: y = −0.5x + 0.5. This is a straight line, and every indifference curve for this function is a parallel straight line.
Example with a Cobb-Douglas-style function: U(F, C) = FC. Set FC = 25, solve for C: C = 25/F. This produces a downward-sloping curve that bows in towards the origin.
Finding the indifference curve through a specific point:
Step 1: compute the utility at that point. For U(F, C) = FC passing through (1, 9): U = 1 × 9 = 9.
Step 2: set the utility function equal to that value. FC = 9.
Step 3: solve for C. C = 9/F.
If U(x, y) = ax + by (with a, b > 0), indifference curves are downward-sloping straight lines (perfect substitutes).
If U(x, y) = cx^a × y^b (with a, b, c > 0), indifference curves are downward-sloping curves bowed in towards the origin.
MRS_FC is the magnitude of the slope of the indifference curve, measuring how much clothing a consumer will sacrifice for one more unit of food.
Formula: MRS_XY = MU_X / MU_Y.
Derivation: along an indifference curve, utility is constant, so MU_X × ΔX + MU_Y × ΔY = 0. Rearranging gives ΔY/ΔX = −MU_X / MU_Y.
Example: for U(x, y) = xy, MU_X = y and MU_Y = x, so MRS_XY = y/x.
Think of food (F) on the horizontal axis and clothing (C) on the vertical axis:
When F is low and C is high ("warm but hungry"), you would trade a lot of clothing for one more unit of food. MRS is high.
When F is high and C is low ("full but cold"), you would not trade much clothing for more food. MRS is low.
This declining willingness to substitute is what makes the curve convex.
MRS is constant everywhere.
Indifference curves are straight lines.
The MRS does not have to equal 1.
Example: a consumer who cares only about total glasses of juice, regardless of whether it is orange or apple.
Violates the assumption of diminishing MRS.
MRS is either zero or infinity (flat segments and vertical segments).
Indifference curves are L-shaped, with kinks along a line from the origin (not necessarily the 45-degree line).
Example: left shoes and right shoes, consumed in a 1:1 ratio.
Violates the assumption of diminishing MRS.
Budget-free preference ranking: compare baskets using "more is better" when one basket dominates; otherwise, you need an indifference curve.
Indifference curve from U(x, y): set U = c, solve for y.
MRS_XY = MU_X / MU_Y (ratio of marginal utilities).
Linear utility U = ax + by → straight-line indifference curves with slope −a/b.
Cobb-Douglas utility U = cx^a y^b → convex curves bowed towards the origin.
Perfect complements U = min{ax, by} → L-shaped curves with kinks along y = (a/b)x.
⚠️ The three assumptions (completeness, transitivity, more is better) are the foundation for every indifference-curve property. Know why each curve property follows from which assumption.
⚠️ A common exam question: "Can indifference curves slope upward / be thick / cross?" The answer is always no, and you need to explain which assumption is violated.
⚠️ Be able to derive indifference curves from a utility function and identify the curve passing through a given point. This is a reliable exam problem.
⚠️ The "more is better" violation example in the notes has a subtle twist: Kathy prefers (3F, 3C) to (2F, 1C), which is consistent with more is better, not a violation. Watch for trick questions like this.
⚠️ MRS_XY = MU_X / MU_Y holds everywhere on the indifference map, not just at the optimum.
⚠️ Know the difference: perfect substitutes have linear utility and constant MRS; perfect complements have min-function utility and L-shaped curves.
Q: What are the three basic assumptions about consumer preferences?
A: Completeness (consumers can rank all baskets), transitivity (if A is preferred to B and B to C, then A is preferred to C), and more is better (consumers always prefer more of any good to less).
Q: Why can indifference curves never cross?
A: If two curves crossed at a point, transitivity and more is better would create a contradiction. A basket on the higher curve would be indifferent to the crossing point (same curve), and that crossing point would be indifferent to a basket on the lower curve, implying the higher-curve basket equals the lower-curve basket in satisfaction. But more is better says the higher-curve basket is strictly preferred.
Q: Given U(F, C) = 4FC², what is the equation of the indifference curve through (1, 9)?
A: U(1, 9) = 4 × 1 × 81 = 324. Set 4FC² = 324, so C² = 81/F, giving C = 9/F^0.5.
Q: For U(x, y) = xy, what is MRS_XY?
A: MU_X = y, MU_Y = x. MRS_XY = MU_X / MU_Y = y/x.
Q: If a consumer's indifference curves are straight lines, what type of goods are X and Y?
A: Perfect substitutes. The MRS is constant, and the utility function is linear (U = ax + by).
Q: A Ford Explorer owner values space highly. Would their indifference map (space vs. acceleration) show steep or flat curves?
A: Flat curves. They are not willing to give up much space for extra acceleration, so MRS (of acceleration for space) is low, meaning the curves are relatively flat.
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