cdae 254 - class 4 sept. 6 last class: 1.introduction 2.preferences and choice class exercise 1...

CDAE 254 - Class 4 Sept. 6

Last class:1. Introduction 2. Preferences and choiceClass exercise 1

Today: 2. Preferences and choice

Next class:2. Preferences and choice Quiz 1

Important date:Problem set 1: due today

Class exercise 1Class exercise 1(Tuesday, Sept. 4)(Tuesday, Sept. 4)

1. Derive the derivatives:(a) Y = 10 (b) Y = 100 + 2X + 0.1X2

2. If a company’s profit function is

profit = – 50 + 4 q – 0.01 q2

(a) What should be the profit-maximizing production level (q*)?

(b) What is the maximum profit?

3. Utility and choice2.1. Basic concepts

2.2. Assumptions about rational choice

2.3. Utility

2.4. Indifference curve and substitution

2.5. Marginal utility and MRS

2.6. Special utility functions

2.7. Budget constraints

2.8. Utility maximization

2.9. Applications

2.2. Assumptions about rational choice:A and B are two bundles of goods and services:

(1) Completeness:

A B or B A or A B

(2) Transitivity of preferences

If A B and B C, then A C

(3) Economic goods: More is better

Assumption 1: CompletenessAssumption 1: Completeness

A consumer can rank any two bundles of goods

only one of following is true: a consumer • prefers Bundle A to Bundle B• prefers Bundle B to Bundle A• is indifferent between A and B

Assumption 2: TransitivityAssumption 2: Transitivity

consumer's preference over bundles is consistent:

if consumer prefersBundle A to Bundle B and

Bundle B to Bundle C

then consumer prefers Bundle A to Bundle C

Assumption 3: More is betterAssumption 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 (e.g., pollution)

Bundles of Pizzas and Burritos Lisa Might Consume

B, Burritosper semester

(a) Ranking Regions

302515

Z, Pizzas per semester

25

20

15

10

0

da

b

e

c

f

A

B

2.3. Utility

(1) What is utility?

The pleasure or satisfaction that a consumer obtains from his or her activities.

(2) How to measure utility? -- No unit for utility (happiness)

-- Ordinal comparison of alternative choices

2.3. Utility (3) What is a utility function?

Given the three assumptions about rational choice, a consumer is able to rank alternative bundles in the order of her or his preferences.

The ordinal ranking expressed in a mathematical equation is called a utility function:

Utility = U (X1, X2, ……, Xn)

2.4. Indifference curve and substitution (1) What is an indifference curve?

A curve that represents all the combinations of goods or services that provide the same level

of utility.

(2) A graphical presentation (3) Marginal rate of substitution (MRS): The negative of the slope of an indifference

curve:MRS =

Interpretation:

Marginal Rate of Substitution

B, Burritosper semester

5

3

8

1–1

1

12

0

–2

– 3

3 4 5 6

Z, Pizzas per semester

a

b

c

d

I

2.4. Indifference curve and substitution (4) Indifference curve maps

(5) Indifference curves do not intersect

(6) An indifference curve should be “thin”

(7) Convex indifference curve -- Diminishing MRS: MRS decreases when X increases

-- Relatively balanced bundles are preferred to

relatively unbalanced bundles

B, Burritosper semester

Z, Pizzas per semester

I 1

I0a

be

Impossible Indifference Curves

B, Burritosper semester

a

b

Z, Pizzas per semester

I

Impossible Indifference Curves

B, Burritosper semester

Z, Pizzas per semester

I

a

b

2.5. Marginal utility and MRS (1) Marginal utility:

Change in utility associated with a one-unit change in the consumption of a good, holding other goods unchanged.

e.g., Utility = U(X1, X2, …, Xn)

Economic goods: MU > 0 Economic bads: MU < 0

11 X

UMU X

2.5. Marginal utility and MRS (2) Marginal utility and MRS

U= U(X, Y)

MRSMU

MU

dX

dY

Y

XU constant

2.6. Special utility functions

(1) Perfect substitutes

(2) Perfect complements

(3) A useless good

(4) An economic bad

Perfect substitutesPerfect substitutes

straight line indifference curves

Coke, Cansper week

Perfect Substitutes

1 2 3 4

Pepsi, Cans per week

1

0

2

3

4

I 1 I2 I3 I 4

Perfect complementsPerfect complements

right-angle indifference curvesMRS = 0 (Coffee-Cream)

Ice cream,Scoops per week

Perfect Complements

1 2 3

Pie, Slices per week

1

2

3

0

I 1

I 2

I 3

a

d

e c

b