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
(a)MarginalUtility,Utils
(b)Marginal
UtilityPer Dollar(MU/Price)
(b)Marginal
UtilityPer Dollar(MU/Price)
(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
(a)MarginalUtility,Utils
(a)MarginalUtility,Utils
(b)Marginal
UtilityPer Dollar(MU/Price)
(b)Marginal
UtilityPer Dollar(MU/Price)
(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
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
(a)MarginalUtility,Utils
(a)MarginalUtility,Utils
(b)Marginal
UtilityPer Dollar(MU/Price)
(b)Marginal
UtilityPer Dollar(MU/Price)
(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
Again, Compare Per Dollar - MU/PriceChoose the HighestBuy One of Each – Budget Has $5 LeftProceed 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
(a)MarginalUtility,Utils
(a)MarginalUtility,Utils
(b)Marginal
UtilityPer Dollar(MU/Price)
(b)Marginal
UtilityPer Dollar(MU/Price)
(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
Again, Compare Per Dollar - MU/PriceBuy One More B – Budget Has $3 LeftProceed 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
(a)MarginalUtility,Utils
(a)MarginalUtility,Utils
(b)Marginal
UtilityPer Dollar(MU/Price)
(b)Marginal
UtilityPer Dollar(MU/Price)
(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
Again, Compare Per Dollar - MU/PriceBuy One of Each – Budget Exhausted
Theory of Consumer BehaviorNumerical Example:Utility-Maximizing Combination of Products A and B Obtainable with an Income of $10
(1)Unit of
Product
(a)MarginalUtility,Utils
(a)MarginalUtility,Utils
(b)Marginal
UtilityPer Dollar(MU/Price)
(b)Marginal
UtilityPer Dollar(MU/Price)
(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
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
(2)Product A:Price = $2
(3)Product B:Price = $5
UnitMUMu/pUnitMUMu/p
120101306
21052204
3633153
431.5451
510.55-51-
(2)Product A:Price = $2
(3)Product B:Price = $1
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
Review Questions – 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
Review Questions – 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
Review Questions – Utility
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.
Review Questions – Utility
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.
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