Consumer Behavior: Preferences, Constraints, and Choice

Chapter 3: Consumer Behavior

Introduction

This chapter explores how consumers allocate their limited incomes among different goods and services to maximize their well-being. The analysis of consumer behavior is foundational in microeconomics and is structured around three main steps: understanding consumer preferences, recognizing budget constraints, and analyzing consumer choices.

3.1 Consumer Preferences

Market Baskets

• Market basket (or bundle): A list with specific quantities of one or more goods.

Market Basket	Units of Food	Units of Clothing
A	20	30
B	10	50
D	40	20
E	30	40
G	10	20
H	10	40

Definitions and Notation about Preferences

• > : Strictly preferred (e.g., A > B)

• ~ : Indifferent between two bundles (e.g., A ~ B)

• ≥ : Weakly preferred (e.g., A ≥ B)

Basic Assumptions about Preferences

1. Completeness: Consumers can compare and rank all possible baskets. For any two baskets A and B, the consumer will prefer A to B, B to A, or be indifferent.

2. Transitivity: If a consumer prefers A to B and B to C, then they also prefer A to C. This ensures consistency.

3. More is better than less: Goods are desirable; consumers always prefer more of any good to less, and are never fully satisfied (never satiated).

Indifference Curves

• Indifference curve: A curve representing all combinations of market baskets that provide a consumer with the same level of satisfaction.

• Indifference curves cannot intersect.

Indifference maps show a set of indifference curves, each representing different levels of utility. Higher curves represent higher utility.

The Shape of Indifference Curves

• The marginal rate of substitution (MRS) is the slope of the indifference curve and measures the rate at which a consumer is willing to substitute one good for another while maintaining the same level of satisfaction.

• Typically, the MRS diminishes as we move down the curve, reflecting a diminishing marginal rate of substitution and convexity of preferences.

Perfect Substitutes and Perfect Complements

• Perfect substitutes: Two goods for which the MRS of one for the other is constant (straight-line indifference curves).

• Perfect complements: Two goods for which the MRS is zero or infinite; indifference curves are right angles.

• Bad: A good for which less is preferred rather than more.

3.2 Budget Constraints

The Budget Line

• Budget constraint: The limits imposed on consumer choices by income and prices.

• Budget line: All combinations of goods for which the total amount of money spent equals income.

The budget line equation is:

$P_F F + P_C C = I$

where $P_F$ and $P_C$ are the prices of food and clothing, $F$ and $C$ are the quantities, and $I$ is income.

The slope of the budget line is $-P_F/P_C$.

The Effects of Changes in Income and Prices

• Income changes: Shift the budget line parallel to itself (outward for increases, inward for decreases).

• Price changes: Rotate the budget line about one intercept.

3.3 Consumer Choice

The optimal market basket must:

1. Be located on the budget line.

2. Give the consumer the most preferred combination of goods and services.

At the optimal point, the indifference curve is tangent to the budget line, and:

$MRS = \frac{P_F}{P_C}$

Satisfaction is maximized when the marginal benefit (measured by the MRS) equals the marginal cost (the price ratio).

Corner Solutions

• Corner solution: Occurs when the consumer maximizes satisfaction by consuming only one of the two goods, typically when the MRS does not equal the price ratio at any interior point.

3.4 Revealed Preference

If a consumer chooses one market basket over another, and the chosen basket is more expensive, the consumer must prefer the chosen basket. This principle allows economists to infer preferences from observed choices.

3.5 Marginal Utility and Consumer Choice

• Marginal utility (MU): The additional satisfaction from consuming one more unit of a good.

• Diminishing marginal utility: As more of a good is consumed, the additional utility from each extra unit decreases.

Key equations:

$0 = MU_F (\Delta F) + MU_C (\Delta C)$

$-(\Delta C/\Delta F) = MU_F / MU_C$

$MRS = MU_F / MU_C$

$MRS = P_F / P_C$

$MU_F / P_F = MU_C / P_C$

This is known as the equal marginal principle: utility is maximized when the consumer has equalized the marginal utility per dollar spent across all goods.

Lagrange Multiplier Method

• Used to solve constrained optimization problems in consumer choice.

For maximizing $U(X, Y)$ subject to $P_X X + P_Y Y = I$:

1. Form the Lagrangian: $U(X, Y) - \lambda (P_X X + P_Y Y - I)$

2. Differentiate with respect to $X$, $Y$, and $\lambda$, set derivatives to zero.

3. Solve the equations simultaneously for the optimal bundle.

3.6 Cost-of-Living Indexes

• Cost-of-living index: The ratio of the present cost of a typical bundle of consumer goods and services compared with the cost during a base period.

• Ideal cost-of-living index: The cost of attaining a given level of utility at current prices relative to the cost at base-year prices.

• Laspeyres price index: Measures the cost of purchasing a base-year bundle at current prices divided by the cost at base-year prices. Tends to overstate the cost of living.

• Paasche price index: Measures the cost of purchasing the current bundle at current prices divided by the cost at base-year prices. Tends to understate the cost of living.

• Chain-weighted price index: Accounts for changes in quantities of goods and services over time.

Summary Table: Comparing Cost-of-Living Indexes

Index	Bundle Used	Bias
Laspeyres	Base-year bundle	Overstates cost of living
Paasche	Current-year bundle	Understates cost of living
Ideal	Utility-based	Accurate (theoretical)

Key Terms and Concepts

• Indifference curve

• Marginal rate of substitution (MRS)

• Budget constraint

• Utility and utility function

• Marginal utility

• Equal marginal principle

• Cost-of-living index

Examples and Applications

• Designing new automobiles: Indifference curves can describe preferences for car attributes such as acceleration and interior space.

• Consumer choice of health care: Indifference curves show trade-offs between health care and other goods, and how budget constraints affect choices.

• College trust fund: Constraints on spending (e.g., must spend on education) can lead to corner solutions.

• Marginal utility and happiness: Research shows happiness increases with income, but at a diminishing rate, illustrating diminishing marginal utility.