Download Marginal Utility

Chapter 19 Demand for Goods
Consumer Choice, Behavior, Utility Maximization,
Income and Substitution Effect
We have covered this.
Price of good goes down… our real income
purchases more
Substitution Effect…. Willing to substitute dear
product for cheaper product if dear product
price goes up….
What is Utility?
Pleasure or satisfaction obtained from good or
service.
More pleasure… more we are willing to pay.
Favorite rock group… concert tickets are very
costly…
Willing to pay?
Willing to substitute?...
How many utils of satisfaction derived?
What is total utility?
Total utility= amount of satisfaction obtained
from entire consumption of a product.
Willing to sit through entire football game in the
pouring rain to watch your favorite team.
16oz steak good to last bite.
Marginal Utility?
 Marginal Utility= change in total utility obtained by
consuming one more additional (marginal) unit of a
good or service.
TU
Q
 Popcorn… each handful in a movie adds marginal
utility.
 Sometimes… each beer consumed adds marginal
utility. Some think total utility with each marginal
addition! 
Diminishing Marginal Utility
Law of Diminishing Marginal Utility = the
marginal utility of a good declines as more of
it is consumed in a given period of time.example is…….
As long as MU is increasing TU must be
increasing.
When MU is not increasing (diminishing) each
unit added yields less utility
Utility Theory (cont'd)
• Observations
– Marginal utility falls as more is consumed.
– Marginal utility equals zero when total utility is at
its maximum.
Diminishing Marginal Utility
As long as marginal utility > 0, total utility increases. When marginal
utility becomes negative, total utility maxes out and then decreases.
19-8
Example: Newspaper Vending Machines
versus Candy Vending Machines
• Newspaper machines do not prevent people from
taking more than one paper. Why not dispense candy
the same way?
• The answer is found in the concept of diminishing
marginal utility.
• Can you think of a circumstance under which a
substantial number of newspaper purchasers might
be inclined to take more than one newspaper from a
vending machine?
TU and MU
As more of a product is
consumed, Total utility
increases at a
Diminishing rate.
Tacos
consumed
in 1 meal
TU
0
1
0
10
2
18
8
3
24
6
4
28
4
5
30
2
6
30
0
7
28
-2
MU
TOTAL AND MARGINAL UTILITY
0
10
18
24
28
30
30
28
10
8
6
4
2
0
-2
30
Total Utility (utils)
0
1
2
3
4
5
6
7
TU
20
10
0
1
2
3
4
5
6
7
Units consumed per meal
Marginal Utility (utils)
Tacos
Total Marginal
consumed Utility, Utility,
per meal Utils
Utils
10
8
6
4
2
0
-2
MU
1
2
3
4
5
6
7
Units consumed per meal
TOTAL AND MARGINAL UTILITY
0
10
18
24
28
30
30
28
10
8
6
4
2
0
-2
30
Total Utility (utils)
0
1
2
3
4
5
6
7
TU
20
10
0
1
Observe
Diminishing
Marginal
Utility
2
3
4
5
6
7
Units consumed per meal
Marginal Utility (utils)
Tacos
Total Marginal
consumed Utility, Utility,
per meal Utils
Utils
10
8
6
4
2
0
-2
MU
1
2
3
4
5
6
7
Units consumed per meal
Marginal Utility, Demand and Elasticity
 How can law diminishing
MU explain demand curve
sloping downward?
 Ans: more units of good
yield smaller MU.. Have to
lower price to sell more.
 If MU drops quickly..
Demand is inelastic
 i.e. given decline in price
elicits small increase in QD.
 If MU drops more slowly,
the demand is elastic
 A small decline in price will
elicit larger amounts of QD.
Relationships
There is a relationship between price elasticity
and total revenue.
Total Revenue = price of a product multiplied by
the quantity sold in a given time period: PxQ.
TR= Price x Quantity sold
Price Elasticity and TR relationship
 Price hike increases TR if demand is inelastic
(this is usually something we can’t live without)
E< 1
 Price hike reduces TR if demand is elastic
(we can live without it)
E>1
 Price hike does not change TR if demand is unitary
elastic
E=1
Maximizing Utility
How would you maximize your utility?
Select that good which delivers the most
marginal utility/dollar even for last dollar
spent.
Optimizing Consumption
• Consider the following:
– Consumers have limited incomes (budgets)
– We must make choices of how to allocate our income
– We can use utils to measure the marginal utility
additional consumption gives us
– Consumers will be able to optimize consumption by
spending dollars on goods that give the highest
marginal utility per dollar (most “bang for your buck”)
• Consumer optimum
– Combination of goods and services
that maximizes utility for a given income
Deciding What to Buy
• In a simplified setting, we can narrow our
consumption choice to two goods, X and Y
• We can spend each dollar optimally by asking
MUX
Price X
Which is larger?
MUY
Price Y
• In other words:
– Which good will give us the highest marginal utility per
dollar spent?
– This is the “bang for your buck” question
Deciding What to Buy
MU X
Price X
Which is larger?
MU Y
Price Y
• Why do we divide by the price?
– Must account for price differences in goods
– Some goods may give high MU, but are more
expensive!
• If the X side is larger, what do we do?
– Spend next dollar on good X
– X will give us more happiness per dollar
– Important: after this consumption, MUX will fall!
Example: Pizza and Pepsi
• Two goods, pizza and Pepsi
– Pizza is $2 per slice
– Pepsi is $1 per can
– You have $10 to spend
• Consumption of pizza and Pepsi both exhibit
diminishing marginal utility
– If I consume pizza, MUpizza falls
– If I consume Pepsi, MUPepsi falls
Pizza and Pepsi Optimum
Pizza is $2.00/slice; Pepsi is $1.00/can
Budget = $10.00
Pizza and Pepsi Optimum
Activity Problem
Total and Marginal Utility per Dollar from Pizza and Wall
Climbing
Budget: $50
Pizza costs $10 a piece; Wall Climbing is $20/hour or
$10/half hour
Quantity
TU
MU
0
1
2
3
4
5
0
70
130
180
220
250
0
50
Mu/$
pizza
Quantity
TU
MU
00
0.5
1.0
1.5
2.0
2.5
0
90
170
230
260
270
0
Mu/$
Wall
climbing
Answer to Activity Problem
Total and Marginal Utility per Dollar from Pizza and Wall Climbing
Budget: $50
Pizza costs $10 a piece; Wall Climbing is $20/hour or $10/half hour
MU/pizza =
P
MU/Wall Climbing
P
Quantity
TU
MU
0
1
2
3
4
5
0
70
130
180
220
250
0
70
60
50
40
30
Mu/$
Pizza
7
6
5
4
3
2 Pizza’s = $20 ($10 each)
1.5 Hours Wall Climbing = $20 + $10 = $30
Total= $50 budget
Quantity
TU
MU
00
0.5
1.0
1.5
2.0
2.5
0
90
170
230
260
270
0
90
80
60
30
10
Mu/$
Wall
Climbing
9
8
6
3
1
$10.00 to spend for pizza and beer
Maximize total utility between two goods
Take my $10.00 spend it on good that yields most utility.
Slice
Pizza
TU
MU
MU/$
$2.00
Pt Beer
TU
MU
MU/P
$2.00
1
2
3
4
20
36
50
58
20
16
14
8
10
1
20
20
10
8
2
38
18
9
7
3
54
16
8
4
68
14
7
4
$10.00 = 2 slices pizza and 3 pints beer. Total Utility = 56 pizza,
112 for beer.
Price
QD
$2.75
1
$2.00
2
$1.00
3
$.25
4
$2.75
$.25
Because MU declines, lower price is needed to lure the customer
to buy more.
Mathematical Version… (assumes no savings.. Spend last $)
MU of product A
= MU of product B
Price of A
Price of B
IF utility maximization occurs these ratios should be equal algebraically.
Last check on knowledge!
Units
Consumed
TU
0
1
2
3
4
5
6
0
10
MU
10
8
25
30
3
34
Last check on knowledge!
Units
Consumed
TU
0
1
2
3
4
5
6
0
10
MU
10
8
25
30
3
34
Units
Consumed
TU
MU
0
1
2
3
4
5
6
0
10
18
25
30
33
34
10
8
7
5
3
1