Learning Outcomes

• Explain the premises of consumer behaviour
• Define and illustrate indifference curves
• Distinguish between perfect substitutes, perfect complements, and imperfect substitutes
• Define marginal rate of substitution (MRS) and interpret it as the slope of an indifference curve
• Relate marginal utilities to the MRS
• Describe and derive the consumer’s budget constraint
• Identify the optimal consumption bundle using indifference curves and the budget constraint

Consumer Choice and Premises

• Consumers have limited incomes and face trade-offs
• Consumer theory explains how consumers maximize their well-being given preferences and constraints
• Decisions cover consumption and savings based on preferences and constraints

Premises of Consumer Behaviour

• Preferences: tastes or rankings determine the pleasure from goods/services consumed
• Constraints: limits on choices (legal restrictions, income constraints, etc.)
• Objective: maximize well-being from consumption subject to constraints

Five Main Topics in Consumer Choice

• Preferences: predict which bundles are preferred
• Utility: numeric representation of preferences via utility functions
• Budget constraint: prices, income, and restrictions limit purchases
• Constrained consumer choice: maximization of pleasure given income
• Behavioral economics: deviations from rational, utility-maximizing behaviour observed in experiments

Preferences and Measurements

• Consumers rank bundles by taste; goods are ranked by the pleasure they provide
• Preference relations summarize rankings:
  • Strict preference: $a \succ b$
  • Weak preference: $a \succeq b$
  • Indifference: $a \sim b$

Assumptions about Consumer Preferences

1. Completeness: for any two bundles a and b, either $a \succ b$, $b \succ a$, or $a \sim b$.
2. Transitivity: if $a \succ b$ and $b \succ c$, then $a \succ c$ (rationality follows).
3. More is Better: all else equal, more of a good is preferred to less; goods are “goods” (not necessarily for bads like pollution).

Preference Maps

• Indifference Curve (IC): the set of all bundles viewed as equally desirable
• Indifference Map: the complete set of ICs, summarizing tastes

Indifference Curve Properties (Key Points)

• Higher ICs (farther from origin) are preferred to lower ICs
• ICs encompassing all possible bundles without gaps
• ICs cannot cross
• ICs slope downward (more of one good requires less of the other to remain equally preferred)
• ICs cannot be thick

Visualizing Preferences: Examples with Burritos (B) and Pizzas (Z)

• Lisa’s preferences: e, d, c, etc., points form ICs
• If bundle e is preferred to d and to f, and some bundles in area A are preferred to e, we infer indifference groups and potential ICs
• Impossible ICs arise when indifference implies both a ≻ b and b ≻ a, contradicting “more is better” or transitivity

WIllingness to Substitute: The MRS

• MRS between burritos (B) and pizzas (Z): the maximum amount of one good the consumer will sacrifice to obtain one more unit of the other
• MRS is the slope of the indifference curve
• Formal definition (for Z on x-axis, B on y-axis):
  MRS{Z,B} = -\frac{\Delta Z}{\Delta B} = -\frac{MUZ}{MU_B}
• In practice, from bundle a to b: e.g., MRS = -3 means the consumer would give up 3 burritos for 1 more pizza
• Examples from the transcript:
  • From bundle a to b: MRS = -3 (3 burritos for 1 pizza)
  • From b to c: MRS = -2
  • From a to b (other indexing): MRS = -3
• Key takeaway: MRS varies along the IC and typically diminishes as we move down and to the right along the curve (diminishing MRS)

Diminishing Marginal Rate of Substitution

• As you move down-right along an IC, MRS tends to shrink toward zero
• This reflects a diminishing willingness to substitute one good for another as you acquire more of one good
• Consumers generally prefer balanced baskets (diversified consumption)

Utility and Indifference Curves

• Utility: a numerical representation of preferences
• Utility function: a mapping from bundles to a utility level, $U(Z,B)$
• Examples:
  • $U(Z,B) = ZB$ (a Cobb-Douglas-like form)
  • 3D example: $U(X,Y) = X^{0.5}Y^{0.5}$
• Indifference curves are level curves of the utility function: $U(Z,B) = \hat{U}$
• Ordinal vs Cardinal Utility:
  • Ordinal: only the ranking matters (relative order)
  • Cardinal: absolute differences matter (e.g., money)

Marginal Utility

• Marginal Utility (MU): extra utility from consuming one more unit of a good
• For good $Z$: MU_Z = \frac{\partial U}{\partial Z}
• For the 2D example with $U(Z,B)$, MU_Z is the slope of the utility function in the $Z$ direction holding $B$ constant
• Illustrative relation: as pizza consumption (Z) increases, MU_Z often declines (diminishing marginal utility) while keeping burritos (B) constant

Utility and Marginal Rates of Substitution (MRS) in detail

• The MRS is the negative ratio of the marginal utilities: MRS{Z,B} = -\frac{MUZ}{MU_B}
• Along an indifference curve (constant utility Ū): total differential gives the relation between changes in Z and B that keep utility constant
• At optimum (interior), MRS equals the budget’s MRT (tangent condition):
  MRS{Z,B} = MRT = -\frac{pZ}{p_B}
• Equivalent rearrangement expresses equal marginal utility per dollar spent: \frac{MUZ}{pZ} = \frac{MUB}{pB}

Budget Constraint

• The budget line shows all bundles affordable when the entire budget is spent on the two goods:
  pB B + pZ Z = Y
• Opportunity set includes all bundles inside and on the budget constraint
• Solving for Burritos (B) as a function of Pizza (Z):
  B = \frac{Y - pZ Z}{pB} = \frac{Y}{pB} - \frac{pZ}{p_B} Z
• Interpretation: the intercepts and slope reveal the trade-off between the two goods

Budget Constraint: Numerical Example and Slope

• Example: $pZ = 1$, $pB = 2$, $Y = 50$
  • Budget line: B = \frac{50 - 1 \cdot Z}{2} = 25 - \frac{1}{2}Z
• Intercepts: When $Z = 0$, $B = 25$; when $B = 0$, $Z = 50$
• Slope (MRT): MRT = -\frac{pZ}{pB} = -\frac{1}{2} = -0.5

Changes in the Budget Constraint

• Price of pizza doubles (from $pZ=1$ to $pZ=2$): slope becomes $-pZ/pB = -1$; the affordable region rotates steeper
• Income doubles (Y doubles): budget line shifts outward to the right without changing slope
• Graphical intuition: income and price changes shift or rotate the opportunity set

Constrained Consumer Choice and Optimal Bundle

• Given preferences and the budget, identify the optimal bundle as the affordable bundle that yields the highest utility
• Interior solution (tangency): where IC is tangent to the budget line, i.e., $MRS_{Z,B} = MRT$ or $MRS = MRT$
• Interior solution example (from slides): bundle e on the tangent point where the indifference curve touches the budget line
• Corner solution: occurs when the optimum lies at an axis (all spending on one good, none on the other); MRS at corner does not necessarily equal the price ratio
• Figure discussions show interior maximization with bundles on I2 and the tangent point e

Marginal Utility and Consumer Choice in detail

• When maximizing satisfaction, allocate budget so that marginal utility per dollar is equalized across goods:
  \frac{MUZ}{pZ} = \frac{MUB}{pB}
• This is equivalent to the MRS-MRT condition and explains why at the optimum the slope of the IC equals the slope of the budget line

Special Cases in Indifference Curves

• Corner solutions: occur when spending all on one good; MRS may not equal the price ratio in these cases
• Perfect Substitutes: U is linear in goods; indifference curves are straight lines with constant slope
  • Example: Coke and Pepsi as perfect substitutes: $U = aZ + bB$; slope (MRS) is constant, e.g., $-a/b$
  • Indifference curves are straight, parallel lines; $MRS = -a/b$ (constant)
• Perfect Complements: goods consumed in fixed proportions (L-shaped ICs)
  • Example: Maureen’s pie and ice cream in fixed ratio; utility $U = \min{aZ, bI}$; ICs are L-shaped
  • The consumer only gains utility by increasing both goods in fixed proportion
• Imperfect Substitutes: standard goods with convex ICs; consumers are willing to substitute but at diminishing rates

Automobile Application: Preferences in Car Design

• Designers weigh restyling vs. improved performance
• Higher styling and performance demand more cost; trade-offs between aesthetics and performance
• Visual intuition: different consumers place different emphasis on styling vs performance (as shown by the two scenarios A and B)

Curvature of Indifference Curves

• Convex to the origin is the typical shape for standard goods
• Special cases:
  • Perfect substitutes: straight lines (constant MRS)
  • Perfect complements: L-shaped (fixed proportions)
  • Standard goods: convex to origin (diminishing MRS)

Substitution: What Counts as Substitutes?

• Perfect substitutes: straight-line ICs; MRS is constant
• Perfect complements: L-shaped ICs; MRS undefined at the kink; utility depends strictly on fixed proportions
• Imperfect substitutes: convex ICs; MRS changes along the curve

Practice: Constructing Indifference Curves (Higher-Order Concepts)

• Example question: If Joe views two candy bars and one piece of cake as perfect substitutes, what is the MRS between candy bars and cake? (Candy on Y-axis, Cake on X-axis)
  • Options: (a) 1 (b) -1 (c) 2 (d) -2
• Joe’s indifference curve for perfect substitutes with 2 candy bars = 1 cake has a slope of -2 in the coordinate setup given in the slides
• Answer key is not provided here; use the substitution ratio to identify the slope

Utility Functions and Graphical Intuition

• Utility measures used to compare bundles; not directly observed, but inferred from preferences
• Indifference curves are graphical representations of constant utility levels
• Utility functions translate preferences into mathematical form for analysis

Summary: Key Takeaways (From Slides)

• Preferences are ranked, rational (complete, transitive), and more is better
• Indifference curves are downward-sloping, convex (except in special cases), cannot cross
• MRS is the rate at which a consumer is willing to trade one good for another; equals the slope of the indifference curve; equals the ratio of marginal utilities MRS = -\frac{MUZ}{MUB}
• Special cases: perfect substitutes (straight lines), perfect complements (L-shaped), standard goods (convex curves)
• Budget constraint shows all affordable bundles given income & prices; slope equals the marginal rate of transformation (MRT), i.e., MRT = -\frac{pZ}{pB}
• Consumer optimum occurs at tangency where MRS = MRT; equivalently, \frac{MUZ}{pZ} = \frac{MUB}{pB} or \frac{MUZ}{MUB} = \frac{pZ}{pB}
• Special-case outcomes include corner solutions where all income is spent on one good

Practice MCQs (from transcript)

• Q1: If preferences are complete and transitive, what does this imply?
  (a) Consumers can always make consistent rankings of bundles.
  (b) Consumers always prefer balanced bundles.
  (c) Consumers never choose corner solutions.
  (d) Indifference curves cannot slope downward.
• Q2: The marginal rate of substitution (MRS) between goods X and Y is:
  (a) The slope of the budget line.
  (b) The maximum amount of Y a consumer is willing to give up for one more unit of X.
  (c) The change in utility from consuming more of Y.
  (d) The income effect of a price change.
• Q3: Which of the following is not a property of indifference curves?
  (a) Indifference curves farther from the origin represent higher utility.
  (b) Indifference curves can intersect.
  (c) Indifference curves slope downward.
  (d) Indifference curves cannot be thick.
• Q4: At the consumer’s optimum (interior solution), which condition must hold?
  (a) MRS = MRT
  (b) MUx = MUy
  (c) All income is spent on one good.
  (d) Budget constraint is irrelevant.

Notes on Notation Used in the Transcript

• Goods: Burritos (B) and Pizzas (Z)
• Utility function: U(Z,B)
• MUZ = ∂U/∂Z; MUB = ∂U/∂B
• Budget: pB B + pZ Z = Y
• Indifference curve: U(Z,B) = Ū
• MRS: MRS{Z,B} = -\frac{MUZ}{MU_B}; relates to the slope of the IC
• MRT (budget): MRT = -\frac{pZ}{pB}; slope of the budget line
• Tangency condition: MRS_{Z,B} = MRT

Quick Connections to Foundational Principles

• The model connects preferences (psychological/comparative tastes) with constraint-based optimization (income and prices)
• The “more is better” principle anchors the downward-sloping ICs and prevents thick ICs
• The Tangency condition links consumer choice to market prices, giving rise to demand curves in more advanced treatments
• Special cases (substitutes/complements) illustrate how the shape of ICs changes substitution possibilities and welfare analysis

Practical Implications and Real-World Relevance

• Budgeting decisions rely on trade-offs between two goods, which is common in consumer budgeting (food, housing, leisure vs. work, etc.)
• Understanding MRS helps in predicting how changes in prices or income shift consumption patterns
• Behavioral economics suggests that actual behavior sometimes deviates from the purely rational model, informing policy design and market interventions