Maximize Utility with Marginal Analysis

MANAGERIAL ECONOMICS
BUS 525 [4 &5]: FALL 2022
NSU, SBE

CHAPTER: 3+4 CONSUMER CHOICE
 Topics to discuss
- Consumer Preferences
- Budget Constraints
- Consumer Choice
- Revealed Preference
- Marginal Utility and Consumer Choice
2

CONSUMER BEHAVIOR
 Theory of consumer behavior: Description of how
consumers allocate incomes among different goods
and services to maximize their well-being or utility or
satisfaction.
 Consumer behavior is best understood in three
distinct steps:
1. Consumer preferences (willingness factor)
2. Budget constraints (ability factor)
3. Consumer choices (demanding for the goods)
3

Chapter
3:
Consumer
Behavior
4 of 37
Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 8e.
CONSUMER PREFERENCES
Market Baskets
● Market basket (or bundle) List with specific quantities
of one or more goods.
TABLE 3.1 Alternative Market Baskets
A 20 30
B 10 50
D 40 20
E 30 40
G 10 20
H 10 40
Market Basket Units of Food Units of Clothing
To explain the theory of consumer behavior, we will ask
whether consumers prefer one market basket to another.

5-5
Consumer Theory
 Assumes buyers are completely informed
about:
 Range of products available
 Prices of all products
 Capacity of products to satisfy
 Their income
 Requires that consumers can rank all
consumption bundles based on the level of
satisfaction they would receive from
consuming the various bundles

 Few assumptions
 Completeness: Preferences are assumed to be complete.
In other words, consumers can compare and rank all possible
baskets. Thus, for any two market baskets A and B, a
consumer will prefer A to B, will prefer B to A, or will be
indifferent between the two. [ A and B give same utility;
indifferent giving same satisfaction ]
 Transitivity: Preferences are transitive. Transitivity means
that if a consumer prefers basket A to basket B and basket B
to basket C, then the consumer also prefers A to C.
 More is better than less: Goods are assumed to be
socially desirable. Consumer would prefer a basket of 4X and
3Y basket over a basket of 2X and 2Y.
[Goods: Higher is better than lower. Fuel efficient cars]
[Bads: less is better than more; Less pollution is preferred over
more pollution]. 6

© 2010 Pearson Addison-Wesley
Preferences
The choice that Lisa makes depends on her
preferences—her likes and dislikes.
Her benefit or satisfaction from consuming a good or
service is called utility.
Total Utility
Total utility ( TB :Total Benefit) is the total benefit a
person gets from the consumption of goods. Generally,
more consumption gives more total utility.
Consumption Choice

Marginal Utility
Marginal utility from a good is the change in total utility
that results from a unit-increase in the quantity of the good
consumed.
As the quantity consumed of a good increases, the
marginal utility from it decreases.
We call this decrease in marginal utility as the quantity of
the good consumed increases the principle of diminishing
marginal utility.
Maximizing Utility

Utility-Maximizing Choice
Assume Budget = $ 40;
In row C,
[ Pm*m+Ps*S = M= budget line]
MUm/Pm. = MUS/PS
( Equal Marginal Principle]
Lisa is maximizing utility.

M/Pm = $40/$8 = 5 [ Pm = Price of Movie]
M/Ps = $40/$4 = 10 [ Ps = Price of Soda, M =
Income/Budget]
M/Ps / M/Pm = Pm/Ps = price ratio of two products
Px/Py
M = $ 40 , Nominal Income = $40, with $ 40, you can
buy 5 movie tickets [ Real Income, It is expressed in
terms of goods and services that we can from our
income]

Two products: X, Y
Px = Taka 5 , Py = Taka10 [ Px*X+Py*Y = M = Taka 200= Budget line]
U( X, Y) = 0.4x^2*y^2 [ Indifferent curve (same satisfaction at each point); utility
curve]
Slope of Budget line = Px/Py= Price ratio of two products = Taka5/Taka10 = 1/2
Slope of Indifference Curve = MUx/MUy = Utility ratio of two goods/services
MUx/MUy = 0.8Xy^2/0.8x^2y = y/x = utility ratio
dU/dX = MUx = 0.8XY^2 ; dU/dY = MUy= 0.8X^2Y
Px/Py = MUx/MUy [ budget line slope = indifference curve slope]
In general rule: Px/Py = MUx/Muy [ Budget line slope = Indifference curve slope
Rearrange: MUx/Px = MUy/Py = Equal marginal principle[ per Taka spent on X
or Y give same satisfaction]
Utility Maximization

Apply two step approach:
Step 1: Px/Py = MUx/Muy [ This is utility maximization principle]
½ = y/x; X = 2Y [1]
Step 2: Write the budget equation
Px*X+Py*Y = M
5X + 10Y = 200
5*2y + 10Y = 200
20Y = 200; Y = 10
X = 2Y = 2*10 = 20
Bundle is: 20X, 10Y [ Px*X+Py*Y = 200; [5*20+ 10*10 = 200]
U( x, y) = 0.4x^2*y^2 = 0.4*20^2*10^2 = 16000 = UTIL (Util is a unit of
measurement of satisfaction]
Solve it

MARGINAL UTILITY AND CONSUMER CHOICE
● Marginal utility (MU) Additional satisfaction obtained from consuming
one additional unit of a good.
● diminishing marginal utility Principle that as more of a good is
consumed, the consumption of additional amounts will yield smaller
additions to utility*.
( / ) ( )
C F MU MU C
F C
     
0 ( ) ( )
MU F MU C
F C
   
/ (3.5)
MRS MU MU
F C

/ (3.6)
MRS P P
F C

/ /
MU MU P P
F F
C C

/ / (3.7)
MU P MU P
F F C C

● Equal marginal principle: Principle that utility is maximized
when the consumer has equalized the marginal utility per dollar of
expenditure across all goods.
* Please read right hand side of equation two as: MUf/MUc

5-16
Utility Maximization
 Consumer allocates income so that the
marginal utility per dollar spent on each good
is the same for all commodities purchased
MUx/MUy = Px/Py
MUx/Px = MUy/Py
X Y
X Y
MU MU
P P


Example
The price of television ads is $400 per ad, the price of Radio Ad. is $ 300
MUt/Pt = MUrad/Prad [ 0.75 ; 2T, 4Rad ; PtT + Prad*Rad =
$400*2+$300*4 = 2000 [ 0.5; 6T, 5R; PtT + Prad*Rad = $400*6+$300*5 =
3900; Optimum Combination for Budget $2000 is 2T, 4Radio]

Example
A] If the decision maker chooses to use one unit of X, one unit of Y, and one unit of Z,
the total benefit [TB] that results is $ . [TB = 10*$1 + 22*$2 + 14*$3 = $96]
b.] For the fourth unit of activity Y, each dollar spent increases total benefit by
$ . The fourth unit of activity Y increases total benefit by $ . [ 10; TB = 10*$2 = $20]
c ]. Suppose the decision maker can spend a total of only $18 on the three activities.
What is the optimal level of X, Y, and Z? Why is this combination optimal? Why is
the combination 2X, 2Y, and 4Z not optimal? [1x, 4Y, 3Z; Px*X +Py*Y +Pz*Z = Taka 18; Mux/Px
=Muy/Py = Muz/Pz = 10; same benefit per $; 2X, 2Y, and 4Z not optimal because utility ratio are not
same; MUx/Px = 9; Muy/Py = 18; Muz/Pz = 9 ]
d.] Now suppose the decision maker has $33 to spend on the three activities. What is
the optimal level of X, Y, and Z? [ 5X, 5Y, 6Z : Px*X +Py*Y +Py*Z = Taka 33; for per Taka benefit = 4;

Chapter
3:
Consumer
Behavior
19 of 37
3.1
Ordinal versus Cardinal Utility
● Ordinal utility function Utility function that
generates a ranking of market baskets in order of
most to least preferred. [ A= 20 util, B = 35, C =15]
● Cardinal utility function Utility function
describing by how much one market basket is
preferred to another.

CONSUMER PREFERENCES: MEASURING UTILITY
 Indifference curve (IC):
Curve representing all
combinations of market
baskets that provide a
consumer with the same
level of satisfaction.
[ -20C/10F = MRS = -2; Slope (-) of IC is
known as MRS (Marginal rate of
substitution:
Rate at which we substitute one product
over another while keeping the
utility/satisfaction fixed);
at A & D: MRS = -10C/20F = -0.5
20
Managerial
Economics

UTILITY FUNCTION
 Formula that assigns a level of utility to individual
market basket. For example,
U(F, C) = F + 2C is the utility function
8 units food (F) and 3 units clothing (C) would provide
utility = 8 + 2(3) = 14 = UTIL
6 unit foods and 4 units clothing will provide the same
utility. [ UTIL = F+2C = 14]
But 4 units of food and 4 units of clothing do not yield
the same utility. [ UTIL = F+2C = 12; not same]
More is preferred to less: GOODs
Less is preferred over more: BADS
21
Managerial
Economics

INDIFFERENCE CURVE (IC)
 Features or characteristics of IC
1. IC is downward slopping (because, with the fixed
income, a consumer has to reduce consumption
of a product when consumption of another product
rises)
2. IC is convex to the origin (because of diminishing
marginal rate of substitution)
3. ICs can’t intersect each other (by doing so, it
violates transitivity rule)
4. Higher the indifference curve more is the
satisfaction (because in a higher IC, consumer
gets more products than a lower IC)
22
Managerial
Economics

THE THEORY OF CONSUMER CHOICE 23
Four Properties of Indifference Curves
Food
Cloth
A
I1
1. Indifference curves
are downward-
sloping.
B

Food
Cloth
I1
I2
I0
D
2. Higher indifference
curves are preferred
to lower ones.
C
A

Food
Cloth
I1
3. Indifference curves
cannot cross.
I1: B = A
I4: C = A
B =C [ not correct]
B
C
I4
A

Food
Cloth
4. Indifference curves are
bowed inward/ convex to
the origin.
Slope of IC = -Change of
Cloth/Change of Food
= - 6/1 = (Negative) slope
of IC = MRS = Marginal
Rate of Substitution
I1
1
1
6
2
A
B

5-27
Marginal Rate of Substitution
 MRS shows the rate at which one good can
be substituted for another while keeping
utility constant
 Negative of the slope of the indifference curve
 Diminishes along the indifference curve as X
increases & Y decreases
 Ratio of the marginal utilities of the goods
X
Y
MU
Y
MRS
X MU

  


Chapter
3:
Consumer
Behavior
28 of 37
An indifference map is a set of
indifference curves that
describes a person's
preferences.
An Indifference Map
3.1
Figure 3.3
Indifference Maps
● indifference map Graph containing a set of indifference curves
showing the market baskets among which a consumer is indifferent.
Any market basket on
indifference curve U3, such as
basket A, is preferred to any
basket on curve U2 (e.g.,
basket B), which in turn is
preferred to any basket on U1,
such as D.

EXCEPTIONS OF IC
 Perfect Substitute products: Two goods for which the
marginal rate of substitution [MRS] of one for the
other is a constant.
 perfect complements Two goods for which the
MRS is zero or infinite; the indifference curves are
shaped as right angles.
29
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Economics

COMPARE THESE 3 ICS [ COMPARE PERFECT COMPLEMENT AND
DOWNWARD SLOPING IC ( IMPERFECT SUBSTITUTE]
30
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Economics

MATHEMATICAL EXAMPLES. PAGE 120. EX. 5
 Suppose that Rahim and Karim spend their incomes on
two goods, food (F) and clothing (C). Rahim’s
preferences are represented by the utility function
U(F,C) = 10FC , while Karim’s preferences are
represented by the utility function U(F,C)= 0.20F2C2.
 With food on the horizontal axis and clothing on the
vertical axis, identify on a graph the set of points that
give Rahim the same level of utility as the bundle (10,5).
Do the same for Karim on a separate graph.
 On the same two graphs, identify the set of bundles that
give Rahim and Karim the same level of utility as the
bundle (15,8).
 Do you think Rahim and Karim have the same
preferences or different preferences? Explain.
31
Managerial
Economics

DRAWING OF INDIFFERENCE CURVE: MATH
EXAMPLE
 Suppose that Rahim and Karim spend their
incomes on two goods, food (F) and clothing (C).
Rahim’s preferences are represented by the utility
function U(F,C) = 10FC , while Karim’s preferences
are represented by the utility function U(F,C)=
0.20F2C2.
 With food on the horizontal axis and clothing on the
vertical axis, identify on a graph the set of points
that give Rahim the same level of utility as the
bundle (10,5). Do the same for Karim on a
separate graph.
32
Managerial
Economics

EX 5
For Rahim:
U(F,C) = 10FC = 10*10*5 = 500
10FC = 500
F*C = 50 [ Imperfect substitute:
you consume both product, at
different combinations
Indifference points
= (25,2), (10, 5), (5, 10), (2, 25)
Karim
U(F,C)= 0.20F2C2. =0.2*10^2*5^2
0.20F^2*C^2 = 500
F^2*C^2 = 500/ 0.2 = 2500 [ Take Root over]
F*C = 50 [ Imperfect Substitute]
Both Rahim and Karim has same preference for food and cloth when the bundle is
(10, 5)
33
Managerial
Economics
Food
Cloth

BUDGET LINE
[ INCOME, BUDGET, MONEY]
 It shows different combinations of goods and services
that an individual can buy with his/her income.
 Show the impact of change in income on budget line
34
Slope of the budget line is the
price ratio of two goods under
consideration: Slope = M/Pc /
M/Pf = Pf/Pc. [ I/Pf = 40; 40/Pf =
40; Pf = $1; I/Pc = 20, Pc = 2]
Income Change: Pf and Pc are
constant; Income increases,
Budget line shifts parallelly
rightwards (leftwards: income
goes down)

CHANGE IN BUDGET LINE WITH A CHANGE IN PRICE
35
Managerial
Economics
Price Changes A
change in the
price of one good (with
income unchanged) causes
the budget line
to rotate about one
intercept.
When the price of food falls
from $1.00 to $0.50, the
budget line
rotates outward from L1 to
L2.
However, when the price
increases
from $1.00 to $2.00, the line
rotates
inward from L1 to L3.
Price Change: Budget is
constant, One of the
product’s price may change (
increase/decrease)

MATHEMATICAL EXAMPLE. EX 10, PAGE 121
Samira buys five new college textbooks during his
first year at school at a cost of $80 each. Used
books cost only $50 each. When the bookstore
announces that there will be a 10 percent increase
in the price of new books and a 5 percent increase
in the price of used books, Samira’s father offers
her $40 extra.
A) What happens to Samira’s budget line?
Illustrate the change with new books on the
vertical axis.
B) Is Samira worse or better off after the price
change? Explain.
36
Managerial
Economics

LET US SOLVE:
Pn*n+ Pu*u = M = $ 400 = $80*5
80*n + 50*u = 400 [ Budget equation]
M = $ 400; u = $400/50 = 8; n = $400/80 = 5
Draw the Budget line.
Price of New Book = $80(1.10) = $88 = 80 + 80*10%
= 80 (1+0.1) = 80(1.1)
Used Book = $50(1.05) = $ 52.5
Her father gives her additional $ 40:
New Budget = $400+ $40 = $440;
Now New book = $440/$88 = 5 New book
Used Book = $440/$52.5 = 8.38 Used Books
Income Change or Price Change? Condition
improved with respect to used book.
37
Managerial
Economics

MATHEMATICAL EXAMPLE
 Sonia has a monthly income of $200 = M= Budget]
that she allocates among two goods: meat and
potatoes. Suppose meat costs $4 per pound and
potatoes $2 per pound. Draw her budget
constraint.
 Suppose also that her utility function is given by the
equation U(m, P) = 0.20m2P2. What combination of
meat and potatoes should she buy to maximize her
utility?
Pm/Pp =?
MUm = ? MUp =?
1) Pm/Pp = Mum/Mup
2) Pm*m+ Pp*P = M = $200
38

LET US SOLVE
Utility Maximization Principle:
MUx/MUy = Px/Py [ slope of Indifference curve = Slope of Budget
Line]
Or: MUx/Px = MUy/Py
……………………………………………………………...
U(m, P) = 0.20m2P2
dU/dm = MUm = 0.2*2m2-1 p^2 = 0.4mp^2
dU/dP = MPp = 0.2m^2*2*P2-1 = 04m^2p
Slope of IC = MUm/MUp = 0.4mp^2 / 04m^2p = p/m
Slope of Budget line = Pm/Pp = Taka 4/Taka 2 = 2
39
Managerial
Economics

CONT.
2 Step Approach:
1) MUm/MUp = Pm/Pp [ utility maximization rule]
p/m = 2; P = 2m
2) Write the budget equation: Pm*m+ Pp*P = M = Taka 200
4m + 2*2m = 200; 8m = 200; m = 25; P = 2m = 50
M = Taka 200; Pm = Taka 4, Pp = Taka 2
U(m, P) = 0.20m2P2
= 0.2*25^2*50^2 = 312500 = UTIL ( UTIL is the unit of account of
utility)
Utility Maximum Bundle :
Meat = 25 Unit
Potato = 50 Units
U(m, P) = 0.20m2P2= 0.2*25^2*50^2 = 312500 = UTIL
I = Income ; M = Money; B = Budget 40
Managerial
Economics

EXAMPLE
41
Suppose a consumer has the indifference map shown below. The relevant budget line
is LZ. The price of good Y is $10.
a. What is the consumer’s income? [ M/Py = 50, M = Taka 500= Income]
b. What is the price of X? [ M/Px = 40, Px = 12.5]
c. Write the equation for the budget line LZ. [ PxX+PyY= 12.5X+ 10Y= M = Taka500]
d. What combination of X and Y will the consumer choose? Why? [20X = Taka 12.5* 20 =
Taka 250, Y = Taka 250/10 = 25Y]
e. What is the marginal rate of substitution at this combination? [ MRS = MUx/MUy = Px/Py
= 12.5/10 = 1.25]
f. Explain in terms of the MRS why the consumer would not choose combinations
designated by A or B. [ At A, MUx/Muy< Px/Py; at B; Mux/Muy> Px/Py
g. Suppose the budget line pivots to LM, income remaining constant. What is the new
price of X? What combination of X and Y is now chosen?
h. What is the new MRS?

BUDGET LINE LM , WHAT IS PX =? [M/PX = 80; 500/PX = 80; PX =
TAKA 6.25 ; MRS = PX/PY = TAKA 6.25/TAKA 10 = 0.625
42
Managerial
Economics

CHAPTER 4: PAGE 120, PROVE THAT PRICE EFFECT = SUBSTITUTION
EFFECT + INCOME EFFECT
INCOME AND SUBSTITUTION EFFECT
 When price of a product [ Normal product] declines,
it has two important effects
1) People can get that product at a cheaper price
thus the ability or purchasing power rises
2) People may not increase the consumption of the
product to maximum thus there is an income gain.
43

PRICE, INCOME AND SUBSTITUTION EFFECT: NORMAL
GOODS [ PLEASE SEE TEXT BOOK: P. 120]
 Substitution effect: It
shows the change in
consumption of a product
(whose price has
changed) while keeping
the utility constant. For
example, even if the
consumer can consume
F1F2 extra, they will
actually consume F2E.
Thus EF2 is income gain.
44
Economics
for
Managers

Giffen Goods

PRICE CHANGE AND INDIVIDUAL
DEMAND CURVE
 Effect of price change:
When price of one
product decreases,
that will rotate the
budget line, hence the
demand curve of the
product can be drawn.
 Price consumption
curve: curve tracking
the utility maximizing
combinations.
46
Economics
for
Managers

INCOME CHANGE AND CONSUMER’S
RESPONSE
 If income increases
with price constant,
the consumers will
demand more of a
normal product
47
Economics
for
Managers

ENGEL CURVE
 Curve relating the
quantity of a good
consumed to income.
 In (a), food is a
normal good and the
Engel curve is upward
sloping. In (b),
however, rotten rice
is inferior good after
a certain income
level.
48
Economics
for
Managers

NETWORK EXTERNALITIES
4.5
The Bandwagon Effect
● network externality When each individual’s
demand depends on the purchases of other
individuals.
A positive network externality exists if the quantity of a
good demanded by a typical consumer increases in
response to the growth in purchases of other
consumers. If the quantity demanded decreases, there
is a negative network externality.
●bandwagon effect Positive network externality
in which a consumer wishes to possess a good in
part because others do.

Is a cash subsidy better than a Food stamps

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