EM

Consumer Choice — Key Concepts

Premises of Consumer Behaviour

  • Consumers have tastes/preferences that determine satisfaction from goods and services.

  • Consumers face constraints (income, prices, legal restrictions).

  • Consumers maximize well-being from consumption given constraints.

Five main topics

  • Preferences: predict bundles a consumer prefers

  • Utility: summarises preferences via utility functions

  • Budget constraint: prices, income limit purchases

  • Constrained consumer choice: maximize pleasure given income and prices

  • Behavioral economics: experiments show deviations from full rationality

Preferences and preference relations

  • Preferences are used to rank bundles; denote strict preference (e.g., a ≻ b), weak preference (a ≽ b), and indifference (a ~ b).

  • A consumer has a complete and transitive ranking of all bundles.

Assumptions about consumer preferences

  • Completeness: any two bundles can be ranked (a ≽ b, b ≽ a, or a ~ b).

  • Transitivity: if a ≽ b and b ≽ c, then a ≽ c.

  • More is Better: given the same other factors, more of a good is preferred to less (with exceptions for bads).

Indifference curves and maps

  • Indifference curve: set of bundles that yield the same level of utility.

  • Indifference map: complete set of indifference curves summarising a consumer’s tastes.

Properties of indifference maps

  • Bundles farther from the origin are preferred to those closer.

  • An indifference curve goes through every possible bundle.

  • Indifference curves cannot cross.

  • Indifference curves slope downward.

  • Indifference curves cannot be thick (no two bundles on a single curve should imply a strict preference for one over the other).

Impossibility of thick indifference curves

  • If a curve contained two bundles more of both goods than another, it would violate "more is better".

Willingness to substitute between goods (MRS)

  • MRS is the maximum amount of one good a consumer will sacrifice to obtain one more unit of the other good.

  • MRS is the slope of the indifference curve.

  • Formal: ext{MRS} = -\frac{\partial Z}{\partial B} = -\frac{MUZ}{MUB} where Z = pizzas and B = burritos.

  • Along an indifference curve, MRS can vary; often diminishing (convex to the origin).

  • Example: from bundle a to b, from b to c, etc., MRS can change (e.g., -3, -2, …).

  • Diminishing MRS: as you move down-right along an indifference curve, the MRS approaches zero; balanced baskets are preferred.

Utility and indifference curves

  • Utility: a numeric measure of satisfaction; indifference curves represent levels of utility.

  • Utility function: U(Z,B); e.g., U(Z,B) = Z^{0.5} B^{0.5}.

  • Marginal utility: the extra utility from consuming one more unit of a good; MUZ = \frac{\partial U}{\partial Z}, \quad MUB = \frac{\partial U}{\partial B}.

  • Marginal utility curves illustrate diminishing MU as consumption of the good rises.

Marginal rate of substitution and utility

  • At any point on an indifference curve, the MRS equals the slope of the curve: ext{MRS} = -\frac{MUZ}{MUB}.

  • Relationship to utility: the MRS is derived from the marginal utilities and shows how substitutions affect utility.

Budget constraint

  • Budget line: all bundles affordable with given income and prices; pB B + pZ Z = Y.

  • Opportunity set: all bundles on or inside the budget constraint.

  • Solving for burritos: B = \frac{Y - pZ Z}{pB} = \frac{Y}{pB} - \frac{pZ}{p_B} Z.

  • Example: if pZ=1, pB=2, Y=50, then B = 25 - \tfrac{1}{2}Z.

  • Slope of the budget constraint (MRT): \text{slope} = \frac{\Delta B}{\Delta Z} = -\frac{pZ}{pB}.

Shifts in the budget constraint

  • If price of pizza doubles (p_Z from 1 to 2), slope changes from -1/2 to -1 (steeper in B-Z space).

  • If income increases, the budget line shifts right (more affordable combinations).

Constrained consumer choice and optimum

  • The optimal bundle is the affordable bundle that yields the highest utility.

  • Interior solution: tangency condition where indifference curve is tangent to the budget line, i.e., ext{MRS} = \text{MRT} = \frac{pZ}{pB} or equivalently \frac{MUZ}{MUB} = \frac{pZ}{pB}.

  • Corner solution: occurs when tangency cannot be achieved within the budget; MRS may not equal MRT.

The cost-per-dollar rule for optimality

  • At optimum, utility per dollar spent should be equalized across goods:

  • \frac{MUZ}{pZ} = \frac{MUB}{pB} (assuming interior solution).

Special cases in preferences and indifference curves

  • Perfect substitutes: indifference curves are straight lines; consumers are indifferent between equal-rate substitutions; MRS is constant (e.g., slope -1 for 1-for-1 trade).

  • Perfect complements: indifference curves are L-shaped; goods are consumed in fixed proportions; no substitution.

  • Imperfect substitutes (standard goods): indifference curves are convex to the origin.

Practical examples and figures (conceptual summaries)

  • Joe’s two candy bars and one cake as perfect substitutes: MRS = -2 when moving between combos (slope -2 in the plotted space).

  • Indifference curves cannot be thick; attempting to form thick curves leads to violations of preference properties.

  • Utility function examples: 3D utility, e.g., U(X,Y) = X^{0.5} Y^{0.5}; MUX and MUY are the slopes of the utility surface.

Ordinal vs cardinal preferences

  • Ordinal: only ranking matters (relative order); does not quantify how much better.

  • Cardinal: absolute differences matter (e.g., money), but in consumer choice, ordinal utility is usually the focus.

Key takeaways (concise)

  • Preferences are complete, transitive, and “more is better” in standard cases.

  • Indifference curves are downward-sloping, convex (except in special cases), cannot cross or be thick.

  • MRS is the slope of the indifference curve and equals the negative ratio of marginal utilities: \text{MRS} = -\frac{MUZ}{MUB}.

  • Budget constraint shows all affordable bundles; slope equals the MRT: \text{MRT} = \frac{pZ}{pB}.

  • Interior optimum occurs where \text{MRS} = \text{MRT} or equivalently \frac{MUZ}{MUB} = \frac{pZ}{pB}; at optimum, \frac{MUZ}{pZ} = \frac{MUB}{pB}.

  • Special cases: perfect substitutes (straight-line ICs), perfect complements (L-shaped ICs), standard goods (convex ICs).

Practice questions (summary)

  • Q1: If preferences are complete and transitive, what does this imply? -> Consistent rankings of bundles.

  • Q2: The MRS between X and Y is: -\frac{MUY}{MUX} and equals the slope of the indifference curve; at optimum, equals the MRT (i.e., ratio of prices).

  • Q3: Not a property of indifference curves? They cannot cross; they slope downward; they cannot be thick; they farther from origin imply higher utility.

  • Q4: At consumer optimum (interior): \text{MRS} = \text{MRT} and all income is allocated to goods that give the most utility per dollar when possible.