Consumer Behavior and Utility Maximization HOW CONSUMERS MAKE CHOICES UNDER INCOME CONSTRAINTS...

Consumer Behavior and Utility Maximization

HOW CONSUMERS MAKE CHOICES UNDER INCOME CONSTRAINTS

UTILITY MAXIMIZATION

Introduction

The CONSUMER is essential to the arket.

Understanding how the consumer makes his/her purchasing decisions is key.

Utility The value a consumer places on a unit of a

good or service depends on the pleasure or satisfaction he or she expects to derive form having or consuming it at the point of making a consumption (consumer) choice.

In economics the satisfaction or pleasure consumers derive from the consumption of

consumer goods is called “utility”.

Within the limits of Consumer’s incomes, consumers make their consumption choices by evaluating and comparing consumer goods with regard to their

“utilities.”

1. Understanding Utility

Utility = Satisfaction/Happiness/Pleasure one gets from consuming a good.

Utility and usefulness are NOT synonymous in economics.

Utility is difficult to quantify, as it differs between people and situations ie. A blanket to a person living in Arizona vs. a

person living in Minnesota.

Measured in “utils” (a personal measure)

1. Understanding Utility

Total Utility (TU) Total amount of satisfaction or pleasure a person

derives from consuming a given quantity of that product

Marginal Utility (MU) The extra satisfaction a consumer derives from one

additional unit of that product. In other words, the change in Total Utility that results

from the consumption of one more unit

Total utility = Sum of marginal utilities

Total and Marginal Utility for Ice Cream

Q ($) TU ($) MU0 01 40 402 85 453 120 354 140 205 150 106 157 77 160 38 160 09 155 -510 145 -10

145

Total Utility

0

50

100

150

200

1 2 3 4 5 6 7 8 9 10 11

($) MU

-20

-10

0

10

20

30

40

50

1 2 3 4 5 6 7 8 9 1 11

Q ($) TU ($) MU0 01 40 402 85 453 120 354 140 205 150 106 157 77 160 38 160 09 155 -510 145 -10

145

Diminishing of Marginal Utility

Explains that the more of a good a person gets, the less utility he gets from each additional unit.

Consumer wants in general are insatiable, but wants for particular items can be satisfied for a time.Example: Durable goods such as an

automobile

law of diminishing marginal utility - marginal utility declines as more of a particular good is consumed in a given time period, ceteris paribus

even though marginal utility declines, total utility still increases as long as marginal utility is positive. Total utility will decline only if marginal utility is negative

Law of Diminishing Marginal Utility

Law of Diminishing Marginal Utility

0

10

20

30

1086420

-2

1 2 3 4 5 6 7

1 2 3 4 5 6 7

To

tal U

tilit

y (U

tils

)M

arg

inal

Uti

lity

(Uti

ls)

(1)Tacos

ConsumedPer Meal

(2)Total

Utility,Utils

(3)MarginalUtility,Utils

0

1

2

3

4

5

6

7

0

10

18

24

28

30

30

28

]]]]]]]

10

8

6

4

2

0

-2

TU

MU

Total Utility

Marginal Utility

Units Consumed Per Meal

Units Consumed Per Meal

Marginal utility

#of slices of pizza total utility marginal utility

00-

17070

211040

313020

414010

51455

6140-5

Utility Maximizing Rules

How much ice cream does Jill buy in a month?

Buying ice cream leaves Jill less money to buy other things: each dollar spent on ice cream could be spent on hamburger for ex.

In fact, consumers compare the (expected) utility derived from one additional dollar spent on one good to the utility derived from one additional dollar spent on another good.

Jill, like any other rational consumer, wishes to maximize her utility.

The opportunity cost of one dollar spent on ice cream is the forgone utility of one dollar that could be on hamburger.

.

Utility Maximizing Rules

A rational consumer would buy an additional unit of a good as long as the perceived dollar value of the utility of one additional unit of that good (say, its

marginal dollar utility) is greater than its market price.

The Two-Good Rule

MUI MUH

--------- = ---------- $PI $PH

Optimal Purchase Mix: Ice Cream and Hamburger

Q MUI PI MUI/PI MUH PH MUH/PH1 40 10 4 45 6 7.52 45 10 4.5 30 6 53 35 10 3.5 20 6 3.34 20 10 2 15 6 2.55 10 10 1 10 6 1.76 7 10 0.7 6 6 17 3 10 0.3 3 6 0.58 0 10 0 0 6 0

Utility Maximization under An Income constraint

Consumers’ spending on consumer goods is constrained by their incomes:

Income = Px Qx + Py Qy + Pw Ow + ….+Pz Qz While the consumer tries to equalize MUx/Px ,

MUy/ Py, MUw/Pw,………. and MUz/Pz , to maximize her utility her total spending cannot exceed her income.

For example, with an and income of $86 Jill is trying to decide how much ice cream and how much hamburger she should buy.

Jill’s income = 5x10 + 6 x 6 = 86

The Budget Line Income = QI.PI + QH.PH = (5 x 10)+(6 x 6) = 86

Ice Cream

Hamburger

o

8.6

14.33

5

6

86/10

86/6

Slope = PH/PI = 6/10 = 8.6/14.33 = 0.6

Consumer equilibrium

1.

2. All income is spent.

The first condition listed above is sometimes referred to as the

"equimarginal principle."

Theory of Consumer BehaviorNumerical Example:Find the Utility-Maximizing Combination of A and B, if you have an Income of $10

(1)Unit of

Product

(a)MarginalUtility,Utils


(b)Marginal

UtilityPer Dollar(MU/Price)

(b)Marginal


(2)Product A:Price = $1

(3)Product B:Price = $2

First

Second

Third

Fourth

Fifth

Sixth

Seventh

10

8

7

6

5

4

3

24

20

18

16

12

6

4

10

8

7

6

5

4

3

12

10

9

8

6

3

2

Theory of Consumer Behavior

Numerical Example:Utility-Maximizing Combination of Products A and B Obtainable with an Income of $10

(1)Unit of

Product



(b)Marginal


(b)Marginal




First

Second

Third

Fourth

Fifth

Sixth

Seventh

10

8

7

6

5

4

3

24

20

18

16

12

6

4

10

8

7

6

5

4

3

12

10

9

8

6

3

2

Compare Marginal UtilitiesThen Compare Per Dollar - MU/PriceChoose the HighestCheck Budget - Proceed to Next Item

Theory of Consumer BehaviorNumerical Example:Utility-Maximizing Combination of Products A and B Obtainable with an Income of $10

(1)Unit of

Product



(b)Marginal


(b)Marginal




First

Second

Third

Fourth

Fifth

Sixth

Seventh

10

8

7

6

5

4

3

24

20

18

16

12

6

4

10

8

7

6

5

4

3

12

10

9

8

6

3

2

Again, Compare Per Dollar - MU/PriceChoose the HighestBuy One of Each – Budget Has $5 LeftProceed to Next Item


(1)Unit of

Product



(b)Marginal


(b)Marginal




First

Second

Third

Fourth

Fifth

Sixth

Seventh

10

8

7

6

5

4

3

24

20

18

16

12

6

4

10

8

7

6

5

4

3

12

10

9

8

6

3

2

Again, Compare Per Dollar - MU/PriceBuy One More B – Budget Has $3 LeftProceed to Next Item


(1)Unit of

Product



(b)Marginal


(b)Marginal




First

Second

Third

Fourth

Fifth

Sixth

Seventh

10

8

7

6

5

4

3

24

20

18

16

12

6

4

10

8

7

6

5

4

3

12

10

9

8

6

3

2

Again, Compare Per Dollar - MU/PriceBuy One of Each – Budget Exhausted


(1)Unit of

Product



(b)Marginal


(b)Marginal




First

Second

Third

Fourth

Fifth

Sixth

Seventh

10

8

7

6

5

4

3

24

20

18

16

12

6

4

10

8

7

6

5

4

3

12

10

9

8

6

3

2

Final Result – At These Prices, Purchase 2 of Item A and 4 of B

Theory of Consumer BehaviorAlgebraic Restatement:

MU of Product A

Price of A

MU of Product B

Price of B=

8 Utils

$1

16 Utils

$2=

Optimum Achieved - Money Income is Allocated so that the Last Dollar

Spent on Each Good Yields the Same Extra or Marginal Utility

From ‘Utils’ to ‘Benefit’

Because Utils cannot be compared between people, and cannot be compared to dollars… economists must measure satisfaction in

Benefit.

Benefit is the same concept as utility, but it is measured in dollars (according to the consumer’s WILLINGNESS TO PAY.

Total Benefit ($), Marginal Benefit ($)

Golden Rule of Consumption

ASSIGMENT Two-Good Practice ProblemGiven MU, and an income/budget constraint of $20… find the Utility-Maximizing Combination of A and B



UnitMUMu/pUnitMUMu/p

120101306

21052204

3633153

431.5451

510.55-51-



UnitTUMUMU/PUnitTUMUMU/P

122-110-

23210521663

3408432042

4466342221

54884520-2-1

Given TU, and an income/budget constraint of $9… find the Utility-Maximizing Combination of A and B

Two-Good Practice Problem

The Problem with Utils

Answer the following problem:If Henry derives 5 utils from the 1st candy

bar, 3 utils from the 2nd candy bar, 0 utils from the 3rd candy bar, and -5 utils from the 4th candy bar… How many candy bars should Henry consume if

each candy bar … Is absolutely free (MC = 0) Costs $2 Costs $4

Review Questions – Utility

What is the marginal utility of the third cup of peanuts Brian consumes?

A. 3 units of utilityB. 9 units of utilityC. 12 units of utilityD. 2 units of utilityE. 14 units of utility


If the price of peanuts is $1 per cup and the price of jelly beans is $2 per cup, and Brian wants to maximize his utility, what should he purchase first?

A. 1 cup of peanuts because peanuts produce a lower total utility

B. 1 cup of peanuts because the price of peanuts is lower

C. 1 cup of peanuts, because the marginal utility per dollar for peanuts is lower than the marginal utility per dollar of jelly beans

D. 1 cup of jelly beans, because the marginal utility per dollar for jelly beans is higher than the marginal utility per dollar of peanuts

E. 1 cup of jelly beans, because jelly beans produce a higher total utility


If TU = total utility, MU = marginal utility, and P = price, in order to maximize utility, a consumer should purchase the mix of hamburgers and hot dogs where

A. the MU of hamburgers equals the MU of hot dogs

B. the MU equals the TU of hamburgers, and the MU equals the TU of hot dogs

C. the TU of hamburgers equals the TU of hot dogsD. the MU / P of hamburgers equals the MU / P of

hot dogsE. the TU / P of hamburgers equals the TU / P of

hot dogs


Every day Molly spends her lunch money consuming apples, at $1 each, and oranges, at $2 each. At her current level of consumption, molly’s marginal utility of apples is 12 and her marginal utility of oranges is 18. If she has already spent all of her lunch money, how should Molly change her consumption decision to maximize utility?

A. She should make no changes; she is consuming the utility maximizing combination of apples and oranges.

B. She should increase her apple consumption and decrease her orange consumption until the marginal utility per dollar is equal for both.

C. She should decrease her apple consumption and increase her orange consumption until the marginal utility per dollar is equal for both.

D. She should increase her apple consumption and decrease her orange consumption until the marginal utility is equal for both.

E. She should decrease her apple consumption and increase her orange consumption until the marginal utility is equal for both.


If generic peanut butter is an inferior good, a decline in consumer income causes

A. the price of generic peanut butter to go down.B. the demand for name-brand peanut butter to

go up.C. the supply of generic peanut butter to go up.D. the demand for generic peanut butter to go

up.E. the price of bread to go down.

Consumer Behavior and Utility Maximization HOW CONSUMERS MAKE CHOICES UNDER INCOME CONSTRAINTS...

Documents

Transcript of Consumer Behavior and Utility Maximization HOW CONSUMERS MAKE CHOICES UNDER INCOME CONSTRAINTS...