PPA 723: Managerial Economics The Maxwell School, Syracuse University Professor John Yinger PPA 723: Managerial Economics Lecture 5: Indifference Curves

Managerial Economics, Lecture 5: Indifference Curves Outline Properties of Consumer Preferences Indifference Curves

Managerial Economics, Lecture 5: Indifference Curves Tastes Individual tastes (preferences) determine the pleasure people derive from different goods and services Our objective is to determine how a consumer’s tastes influence its decisions (positive analysis), not to judge tastes (normative).

Managerial Economics, Lecture 5: Indifference Curves Standard Assumptions About Consumer Preferences 1. Completeness 2. Transitivity 3. More is better

Managerial Economics, Lecture 5: Indifference Curves Assumption 1: Completeness Consumer can rank any two bundles of goods Only one of the following is true: The consumer prefers Bundle x to Bundle y prefers Bundle y to Bundle x is indifferent between the two bundles

Managerial Economics, Lecture 5: Indifference Curves Assumption 2: Transitivity (Rationality) A consumer's preference over bundles is consistent: If a consumer prefers Bundle z to Bundle y and Bundle y to Bundle x Then that consumer prefers Bundle z to Bundle x

Managerial Economics, Lecture 5: Indifference Curves Assumption 3: More is Better More of a good is better than less of it. Good: commodity for which more is preferred to less at least at some levels of consumption Bad: something for which less is preferred to more, such as pollution Consumers are not satiated.

Managerial Economics, Lecture 5: Indifference Curves Figure 4.1a Bundles of Pizzas and Burritos Lisa Might Consume (a) Ranking Regions B , Burritos per semester c A 25 f 20 15 e a d 10 b B 15 25 30 Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Figure 4.1b Bundles of Pizzas and Burritos Lisa Might Consume (b) Indifference Curve B , Burritos per semester c 25 f 20 e 15 a d I 10 b 15 25 30 Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Figure 4.1c Bundles of Pizzas and Burritos Lisa Might Consume (c) Preference Map B , Burritos per semester c 25 f 20 I 2 e 15 d 10 I 1 I 15 25 30 Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Indifference Curve Properties Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin. There is an indifference curve through every possible bundle. Indifference curves cannot cross. Indifference curves are “thin”. Indifference curves slope down.

Managerial Economics, Lecture 5: Indifference Curves Figure 4.2a Impossible Indifference Curves (a) Crossing B , Burritos per semester e b I 1 a I Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Figure 4.2b Impossible Indifference Curves (b) Upward Sloping B , Burritos per semester b a I Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Willingness to Substitute Downward-sloping indifference curve  consumer is willing to substitute one good for the other. Marginal rate of substitution (MRS) of burritos (rise) for pizza (run), is slope of indifference curve:

Managerial Economics, Lecture 5: Indifference Curves Marginal Rate of Substitution B , Burritos per semester MRS = B/Z B Z I Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves MRS Varies Along an Indifference Curve Indifference curves bow away from the origin (called convex). Indicates diminishing marginal rate of substitution (MRS).

Managerial Economics, Lecture 5: Indifference Curves Figure 4.3a Marginal Rate of Substitution (a) Indifference Curve Convex to the Origin B , Burritos per semester a 8 – 3 b 5 1 – 2 c 3 1 d – 1 2 1 I 3 4 5 6 Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Unlikely Outcome: Concave Indifference Curve If indifference curve bows toward the origin (concave), Then (implausibly) the consumer has an increasing MRS.

Managerial Economics, Lecture 5: Indifference Curves Figure 4.3b Marginal Rate of Substitution B , Burritos (b) Implausible Indifference Curve that is Concave to the Origin per semester a 7 – 2 b 5 1 – 3 c 2 1 I 3 4 5 6 Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Figure 4.4a Perfect Substitutes Coke, Cans per week 4 3 2 1 I 1 I 2 I 3 I 4 1 2 3 4 Pepsi, Cans per week

Managerial Economics, Lecture 5: Indifference Curves Figure 4.4b Perfect Complements Ice cream, Scoops per week e c 3 I 3 b d 2 I 2 a 1 I 1 1 2 3 Pie, Slices per week

Managerial Economics, Lecture 5: Indifference Curves Figure 4.4c Imperfect Substitutes B , Burritos per semester I Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Utility Utility is a number that reflects the relative rankings of various bundles of goods If Lisa prefers bundle A to B, then utility from A must be greater than utility from B A utility function is a: relationship between a utility measure and every possible bundle of good succinct summary of information in an indifference curve map

Managerial Economics, Lecture 5: Indifference Curves Utility and Marginal Utility The marginal utility of Z is: MUZ is the change in utility from a small increase in Z holding B fixed

Managerial Economics, Lecture 5: Indifference Curves Utility U , Utils 350 Utility function, U (10, Z ) 250 D U = 20 230 D Z = 1 1 2 3 4 5 6 7 8 9 10 Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Marginal Utility MU , Marginal Z utility of pizza 130 20 MU Z 1 2 3 4 5 6 7 8 9 10 Z , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves Totals, Margins, and Averages Economic analysis often depends on the distinction between a total, a average, and a margin. In the case of utility U = total utility U/Z = average utility of Z MUZ = marginal utility of Z

Managerial Economics, Lecture 5: Indifference Curves Utility and the Marginal Rate of Substitution Let A = the good on the vertical axis and B = the good on the horizontal axis, Then (note the inversion):

Managerial Economics, Lecture 5: Indifference Curves Marginal Rate of Substitution Quantity of A MRS = A/B = - MUB/MUA Give up one unit of A A Gain MUA units of utility, which can “buy” MUA / MUB Units of B B I Quantity of B

Managerial Economics, Lecture 5: Indifference Curves Deriving the Marginal Rate of Substitution