Indifference Curve

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

25

A f

20 15

e d

10

a b

B 0

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 25

c f

20 e

15

a 10

0

d

b

I

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 25

c f

20 e

15 10

I2

d

I1

I0 0

15 25 30 Z, Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves

Indifference Curve Properties 1. Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin. 2. There is an indifference curve through every possible bundle. 3. Indifference curves cannot cross. 4. Indifference curves are “thin”. 5. Indifference curves slope down.

Two Indifferent Managerial Economics, Lecture 5: Indifference Curves

Figure 4.2a Impossible Indifference Curves (a) Crossing

B, Burritos per semester

e

b a

I1 I0

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:

∆B MRS = ∆Z

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 5 3 2

0

b 1 –2 1 –1

3 4 5

c d 1

I 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 per semester

(b) Implausible Indifference Curve that is Concave to the Origin

a

7 –2

b

5

1 –3 c

2

1 I

0

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 I1 0

I2

I3

I4

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

3

d

2

a

1

0

1

c b

I3 I2 I1

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: ∆U MU Z = ∆Z

 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 )

250 230

0

∆ Z =1

1

2

3

4

∆ U = 20

5

6 Z

7 8 9 10 , Pizzas per semester

Managerial Economics, Lecture 5: Indifference Curves

Marginal Utility

MU Z, Marginal utility of pizza 130

20 0

MUZ 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):

MU B ∆A MRS = =− ∆B MU A

Marginal Rate of Substitution Quantity of A

Give up one unit of A Gain MUA units of utility, which can “buy” MUA / MUB Units of B

∆ A

MRS = ∆ A/∆ B = - MUB/MUA

∆ B

I Quantity of B

Managerial Economics, Lecture 5: Indifference Curves

Deriving the Marginal Rate of Substitution

∆U = 0 = ∆A( MU A ) + ∆B ( MU B ) = MU A + ∆B( MU B ) MU A ∆B = − MU B

MU B ∆A −1 MRS = = =− ∆B MU A / MU B MU A