Ch.3 Summary
Theory of Consumer Behaviour
Core Premise
Consumer theory analyzes how individuals decide to spend their income on goods and services to maximize satisfaction. It is built on the idea that we can infer what people like based on the choices they make under budget constraints.
Consumer Preferences
How consumers rank different bundles of goods.
Types of Preference Relations
| Type | Symbol | Meaning |
|---|---|---|
| Strict Preference | \(X > Y\) | Consumer definitely wants bundle X over Y. |
| Indifference | \(X \sim Y\) | Consumer is equally satisfied with X or Y. |
| Weak Preference | \(X \ge Y\) | X is at least as good as Y (preferred or indifferent). |
The Concept of Utility
Utility is the satisfaction or pleasure derived from consuming a good or service.
Key Characteristics:
- Not synonymous with Usefulness: A painting has utility to art lovers but may not be "useful" functionally.
- Subjective: Varies from person to person.
- Context Dependent: Varies by time and place.
Cardinal Utility Theory
Classic approach: Measuring satisfaction in "utils".
1. Major Assumptions
- Rationality: Consumer aims to maximize satisfaction given budget.
- Cardinal Measurement: Utility is measured in objective units (utils).
- Constant MU of Money: A unit of money retains fixed value/utility.
- Diminishing Marginal Utility (DMU): Utility from successive units declines.
- Total Utility Function: \( TU = f(X_1, X_2... X_n) \).
2. Relationship: Total (TU) vs. Marginal (MU)
Total Utility (TU)
Total satisfaction from specific quantity.
Marginal Utility (MU)
Extra satisfaction from one additional unit.
\( MU = \frac{\Delta TU}{\Delta Q} \)
- TU Increasing → MU is Positive (+)
- TU Maximized → MU is Zero (0)
- TU Decreasing → MU is Negative (-)
Limitations of Cardinal Approach
- Utility is subjective and cannot truly be quantified (measured).
- Assumption of constant MU of money is unrealistic (value of money changes with income).
Ordinal Utility Theory
Indifference Curve Analysis (Ranking Preferences).
1. Indifference Curves (IC)
A curve showing combinations of two goods that give the consumer the same level of satisfaction. (Indifference Map = Set of ICs).
Properties of ICs
- Negative Slope To keep utility constant, if you get more of X, you must give up Y.
- Convex to Origin Due to Diminishing Marginal Rate of Substitution (MRS). You trade less Y for X as you get more X.
- Higher is Better Curves further from origin represent higher utility levels.
- Never Intersect Crossing curves would imply contradictory preferences (violating transitivity).
Marginal Rate of Substitution (MRS)
The rate at which a consumer is willing to substitute Good Y for Good X while staying on the same IC.
\( MRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y} \)
Proof: Along an IC, total utility change is 0.
\( dU = MU_x dX + MU_y dY = 0 \)
\( \frac{dY}{dX} = - \frac{MU_x}{MU_y} \)
The Budget Line
The constraint on consumption (Income & Prices).
Mathematical Formulas
1. Standard Constraint Equation
\( M = P_x X + P_y Y \)
Income (M) equals spending on X plus spending on Y.
2. Slope-Intercept Form (for Graphing)
\( Y = \frac{M}{P_y} - \frac{P_x}{P_y}X \)
Income Shift
Parallel shift. Slope stays constant.
Income ↑ = Shift Right.
Price Rotation
Slope changes.
Price X ↓ = Line becomes flatter (X-intercept moves out).
Consumer Equilibrium
Optimization point.
Equilibrium Curve (Tangency)
Point E: Slope of Budget Line = Slope of IC
The Tangency Condition
The consumer maximizes utility where the budget line is tangent to the highest possible Indifference Curve.
Necessary Condition
\( MRS_{xy} = \frac{P_x}{P_y} \)
Or equivalently
\( \frac{MU_x}{MU_y} = \frac{P_x}{P_y} \)
Marginal utility per dollar spent is equal across goods.