Post on 13-Dec-2015
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Utility
Like elasticity, Utility is another fancy name for satisfaction or happiness
Utility refers to satisfaction derived from consumption of goods and services.
To understand consumer behavior, we must know the difference between Total Utility and Marginal Utility 7-2
Total Utility
Cumulative satisfaction derived from consumption of a specific quantity of goods or services.
Example: Lets look at Bob’s satisfaction
schedule from ice cream consumption.
7-3
Total Utility
Number of Ice Cream Total Utility
0 0 util
1 10 util
2 18 util
3 24 util
4 28 util
7-4
Total Utility
Ice Cream
Total Utility
0 0 util
1 10 util
2 18 util
3 24 util
4 28 util
Note: No consumption
provides no utility. Higher
consumption implies higher utility.
Total utility is always rising.
7-5
Marginal Utility
Marginal utility Extra satisfaction from the
consumption one additional unit. It is not the total cumulative
satisfaction from consumption of all previous units.
It is rather the satisfaction of just one (the last) unit consumed.
Lets look at Bob’s marginal utility.
7-6
Marginal Utility
Number of Ice Cream
Total Utility
0 0 util
1 10 util
2 18 util
3 24 util
4 28 util
Undefined
7-7
10 util
8 util
6 util
4 util
Marginal
Utility
Marginal Utility
Ice Cream
Marginal Utility
0 Undefined
1 10 util
2 8 util
3 6 util
4 4 util
Note: Needs two units to
compare marginal utility.
Marginal utility falls with consumption.
Can be even negative.
When MU is negative, TU must fall from previous TU
7-8
Law of Diminishing Marginal Utility
Bob’s marginal utility is falling with higher unit consumed.
This is not an accident. This is in fact a behavioral
assumption that economists make and call it:
The Law of Diminishing Marginal Utility
7-9
Utility Graphically
0
10
20
30
1086420
-2
1 2 3 4 5 6 7
1 2 3 4 5 6 7
TU
(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
Q
7-10
MU
Q
Theory of Consumer Behavior
This theory tells us how consumers maximize utility.
It tells us how much of each goods or services consumer should buy to maximize total utility.
It finds utility maximizing: Quantities (or Q*)When Income (or M) is fixedWhen Prices (or P) are fixed
7-11
Theory of Consumer Behavior
Assume that A consumer’s income M=40 Wants to purchase pizza and
Video rental, where Price of Pizza, Pp =$8 Price of Video Rental, Pv =$4
TU and MU for good Pizza and Video rental are known
This theory tells us how much of Pizza and video rental this consumer should purchase
Theory of Consumer Behavior
We need a stable preference for Pizza This preference is expressed by TU and
MU Pizza
(1)Consumed
per week
(2)TotalUtility
(3)MarginalUtility
0 0
1 56
2 88
3 112
4 130
5 142
6 150
Theory of Consumer Behavior
Pizza
(1)Consumed
per week
(2)TotalUtility
(3)MarginalUtility
0 0
1 56 56
2 88 32
3 112 24
4 130 18
5 142 12
6 150 8
Theory of Consumer Behavior
Similarly we need a stable Preference for Video Rental expressed by TU and MU
Video Rental
(1)Viewed
per week
(2)TotalUtility
(3)Marginal
Utility
0 0
1 40
2 68
3 88
4 100
5 108
6 114
Theory of Consumer Behavior
Video Rental
(1)Viewed
per week
(2)TotalUtility
(3)Marginal
Utility
0 0
1 40 40
2 68 28
3 88 20
4 100 12
5 108 8
6 114 6
Theory of Consumer Behavior
Which one would you consume first? Is it your first pizza (with 56 MU)?
Pizza Video Rental
(1)Consumed
per week
(2)TotalUtility
(3)MarginalUtility
(1)Viewed
per week
(2)TotalUtility
(3)Marginal
Utility
0 0 0 0
1 56 56 1 40 40
2 88 32 2 68 28
3 112 24 3 88 20
4 130 18 4 100 12
5 142 12 5 108 8
6 150 8 6 114 6
Theory of Consumer Behavior
We can’t say that yet because pizza provides higher MU, but it is more expensive
We need to take price into account, some how
Pizza (PP=$8) Video Rental (PV=$4)
(1)Consumed
per week
(2)TotalUtility
(3)MarginalUtility
(1)Viewed
per week
(2)TotalUtility
(3)Marginal
Utility
0 0 0 0
1 56 56 1 40 40
2 88 32 2 68 28
3 112 24 3 88 20
4 130 18 4 100 12
5 142 12 5 108 8
6 150 8 6 114 6
Theory of Consumer Behavior
Pizza (PP=$8) Video Rental (PV=$4)
(1)Consume
d per
week
(2)TotalUtility
(3)Margin
alUtility
(4)Marginal
Utility per $
MUP
(1)Viewed
per week
(2)TotalUtility
(3)Margina
lUtility
(4)Margina
lUtility per $
MUP
0 0 --- --- 0 0 --- ---
1 56 56 7 1 40 40 10
2 88 32 4 2 68 28 7
3 112 24 3 3 88 20 5
4 130 18 2.25 4 100 12 3
5 142 12 1.5 5 108 8 2
6 150 8 1 6 114 6 1.5
Theory of Consumer Behavior
Comparing Per dollar MU or MUP
This consumer should consume in the following sequence:
1. First Video rental 2. First Pizza and Second
Video rental (one of each)3. Third video rental4. Second Pizza5. Third Pizza and Fourth
Video Rental (one of each)6. And no more, why?
Pizza (PP=$8) Video Rental (PV=$4)
(1)Consume
d per
week
(4)Marginal
Utility per $
MUP
(1)Viewed
per week
(4)Margina
lUtility per $
MUP
0 --- 0 ---
1 7 1 10
2 4 2 7
3 3 3 5
4 2.25 4 3
5 1.5 5 2
6 1 6 1.5
Theory of Consumer Behavior
This consumption sequence indicates that to maximize utility you must consume in a
way that
MU for the last pizza consumed P
is exactly equal to MU for the last video rentals P
In this case, MUPizza MUVideo rental
Ppizza PVideo rental
3= =
Utility Maximizing Condition MUPizza MUVideo rental
PPizza PVideo rental
This condition simply means that the last dollar spent on each good must provide the same marginal utility
This constitutes the condition for utility maximization
=
Utility Maximizing Condition MUPizza MUVideo rental
PPizza PVideo rental =
However note that the above condition is fulfilled at three quantity combinations:1 pizza and 2 video
[per $ MU is 7]3 pizza and 4 video
[per $ MU is 3]5 pizza and 6 video
[per $ MU
is 1.5]
Pizza (PP=$8) Video Rental (PV=$4)
(1)Quantity of Pizza
(4)MUP
(1)Quantity of
Video Rental
(4)MUP
0 --- 0 ---
1 7 1 10
2 4 2 7
3 3 3 5
4 2.25 4 3
5 1.5 5 2
6 1 6 1.5
Utility Maximizing ConditionAmong these three combinations, which
one is really utility maximizing:A. 1 pizza and 2 video [per $ MU is 7]B. 3 pizza and 4 video [per $ MU is 3]C. 5 pizza and 6 video [per $ MU is 1.5]To know that we need think about the BudgetComb. A cost [1x$8 + 2x$4] $16 (Money left)Comb. B cost [3x$8 + 4x$4] $40 (Exactly)Comb. C cost [5x$8 + 6x$4] $64 (Unaffordable)
Equilibrium Quantity When the last dollar spent on each
good yields the same marginal utility, there is no way to increase utility by reallocating the budget to buy some other quantity combination
This is why quantity choice at which the utility maximized is also called Equilibrium quantity
Equilibrium Quantity
How do we check that equilibrium quantity indeed provided highest level of utility possible
To see that we need to go back to the total utility table
Let’s compare another bundle that also costs $4o in the utility table
Equilibrium Quantity
At the equilibrium combination TU is 212Equilibrium Quantity suggests that no other affordable quantity choice will yield higher TUNote, 2 pizza and 6 video also cost $40But the TU is 202
Pizza (PP=$8) Video Rental (PV=$4)
(1)Quanti
ty
(2)TU
(4)MUP
(1)Quanti
ty
(2)TU
(4)MUP
0 0 --- 0 0 ---
1 56 7 1 40 10
2 88 4 2 68 7
3 112 3 3 88 5
4 130 2.25 4 100 3
5 142 1.5 5 108 2
6 150 1 6 114 1.5
Violation of Utility Max. Condition
The utility maximizing condition is violated when at the current quantity choice one of the following happens:
MUPizza MUVideo rental
PPizza PVideo rental
MUPizza MUVideo rental
PPizza PVideo rental <
>
Violation of Utility Max. Condition
When Utility maximization condition is violated: Clearly the consumer is not maximizing
satisfaction Therefore, not consuming equilibrium
quantities Which means, by reallocating budget
across pizza and video or buying a different combination consumer can increase satisfaction
Violation of Utility Max. Condition
Assume that at the current level of pizza and video consumption, we have
MUP MUV
PP PV
What specifically would you suggest this consumer to increase satisfaction?
>
Utility-Maximizing Conditions
Note, this situation implies that per $ MU for pizza is higher
MUP MUV
PP PV
Which means, pizza has a bigger bang for the buck
Therefore, this consumer should buy more pizza and less video
>
Utility-Maximizing Conditions
MUP MUV
PP PV
How does buying more pizza and less video restore utility maximizing condition
What happens to MUP when more pizza is consumed?
What happens to MUV when less video is consumed?
Therefore, by reallocating this way consumer will reach equilibrium
>
It goes up!
It goes down!
Where does Demand Curve Come From
Recall, demand is a relationship between: Price and Quantity demanded at that price Keeping all else constant
The law of demand says that this relationship is inverse or negative
Which means: Quantity demanded is lower at higher price
and Quantity demanded is higher at lower price
Utility theory explains why that is so
Where does Demand Curve Come From
Utility Theory or Consumer Behavior says that higher quantity demanded at lower price is an equilibrium choice
The law of demand comes from consumers’ utility maximizing behavior
In other words, what we will observe in few slides that when price changes MU per $ changes as well
When that happens consumers’ utility maximizing bundles changes
Where does Demand Curve Come From
The utility maximizing bundle changes in such a way that price and quantity choice becomes negatively related
Let’s see that using an example that we already are familiar with
Theory of Consumer Behavior
Pizza (PP=$8) Video Rental (PV=$4)
(1)Consume
d per
week
(2)TotalUtility
(3)Margin
alUtility
(4)Marginal
Utility per $
MUP
(1)Viewed
per week
(2)TotalUtility
(3)Margina
lUtility
(4)Margina
lUtility per $
MUP
0 0 --- --- 0 0 --- ---
1 56 56 7 1 40 40 10
2 88 32 4 2 64 24 7
3 112 24 3 3 84 20 5
4 130 18 2.25 4 96 12 3
5 142 12 1.5 5 106 10 2
6 150 8 1 6 114 8 1.5
Where does Demand Curve Come From
Based on this table, from our previous analysis we know that this consumer will choose 3 pizza and 4 video rental
This is because that choice is utility maximizing equilibrium quantity choice
Now, if I want to draw the demand curve for video rental for this consumer, I will have one point of his demand curve
That is PV=4 and Q*V=4
Where does Demand curve come from
We can plot that point (4, 4)as follows: Price
4
4 Quantity Demanded
Where does Demand curve come from
However one point is not enough even for a linear demand curve. We need at least another point
To get that point, let’s increase the price of video rental from $4 to $8
If we do so, we need to update our MU table. Especially the MU/p column
Theory of Consumer Behavior
Pizza (PP=$8) Video Rental (PV=$4)
(1)
Quantity
(2)
TU
(3)
MU
(4)
MUP
(1)
Quantity
(2)
TU
(3)
MU
(4)
MUP
When P=4
(5)
MUP
When P=8
0 0 --- --- 0 0 --- --- ---
1 56 56 7 1 40 40 10 5
2 88 32 4 2 64 24 6 3
3 112 24 3 3 84 20 5 2.5
4 130 18 2.25 4 96 12 3 1.5
5 142 12 1.5 5 108 8 2 1.25
6 150 8 1 6 114 6 1.5 1
Where does Demand curve come from
Consumer utility maximization rule tells us that this consumer will choose a different quantity combination under new price
Specifically, based on his preference table (TU and MU) the consumer will choose
3 pizza and 2 video rental This gives us another point on the demand
curve for video rental of this consumer Which is PV=8 and Q*V=2