Consumer Behavior - Utility Theory
At this point we want to start examining the economic decision-making of individual
entities in the economy. That is, individual consumers, households, firms, and industries. This is
really the start of Microeconomics.
Although it takes both D & S to make a market and to determine a price level, it is often felt
that it is consumers, those entities whose decisions are reflected by demand, who are the major
driving force in the market. This belief tends to have some validity since if you consider it for a
moment you'll realize that we tend to focus more on consumption at various stages in our lives
than we do on production. When you are very young and very old you are more of a consumer
than a producer. It is during that middle part of your life that you are, in general, the most
productive. Therefore we'll start by looking at the demand side of the market. We will examine
Consumer Behavior and develop a model that shows:
1.) How consumers make consumption decisions;
that is, how they determine what portion of their income to spend on various G/Ss.
2.) Why the demand for some G/Ss is more elastic than the demand for other G/Ss.
Essentially, we will be developing a model of behavior that explains DEMAND and the rationale
behind the downward sloping D curve. This is termed utility theory.
Utility is a somewhat abstract concept. What you buy/consume depends partly upon your
preferences/tastes (and also on resource constraints).
You want what a G/S provides - the satisfaction of some want - not the actual G/S itself.
Utility is simply a method of ranking/ordering your preferences. Preferences are themselves an
intangible concept, but in general wouldn't you agree that your preference for a certain good is
linked in a positive way to the amount of satisfaction that you derive from the consumption of that
good?
Earlier we used the term utility to denote the satisfaction of wants. Additionally, we made the
assumption that:
"man is a rational self-interested utility maximizer".
Basically then, what we are going to do is examine how you expend your resources so that your
Utility is maximized. This discussion assumes that you can't affect prices!
And, since earlier we noted that because of scarcity consumers can't have everything that they
want we'll have to maximize Utility subject to constraints. These constraints are our budget and
prices. This model then is going to take into consideration 3 things:
Income, Prices and consumer preferences ( given by utility comparisons).
Most discussions of utility at this level use a numerical measure of utility. This is fine as a
pedagogical tool but there are a lot of caveats that should be mentioned.
1.) UTILITY CANNOT BE MEASURED IN AN ABSOLUTE SENSE!
That is, you cannot measure it quantitatively/numerically.
How much satisfaction/benefit do you get from the consumption of some good such as your
favorite beverage? Can you give me some numerical magnitude that has meaning? I can't.
You can indicate the order of your preference, i.e. you can state that goodx P goody. You can
measure it in an ordinal sense such as 1st., 2nd. etc. So why do we express utility
quantitatively?
Because it facilitates the explanation of the concept of MU.
But remember that any numbers used here are essentially plucked out of the air. They are
only examples.
2.) UTILITY IS SUBJECTIVE AND CAN CHANGE OVER TIME.
What gives one person a lot of satisfaction may not give another person the same
satisfaction. And you may not get the same amount of satisfaction in the future as you do
now.
EXAMPLE: CLOTHES; They go in and out of fashion.
There are 2 measures of Utility that we need to define and examine.
TOTAL UTILITY (TU) - The total amount of satisfaction received from all units consumed of a
good.
MARGINAL UTILITY (MU) - The change in total utility from consuming one more unit of a good.
Marginal is used here in the same sense as additional.
MU =
∆T U
∆Q TU =
Let's take an example:
Assume that you are given:
# of diet Coke Consumed 0
1
2
3
!
MU
Utility of each then you have
-
10 15 8 TU 0
10 25 33 &
MU
10
15
8
Clearly you would not consume the 2nd. Diet coke which has 15 units of satisfaction after the first
which only has 10 units thus the order of consumption is relevant or the ranking of preferences.
Does the additional utility of another unit consumed, be it the 2nd., 3rd., 4th., or whatever, have to be
>, <, or the same as the utility of the previous unit?
Normally, if a good can be used to satisfy more than 1 want, you would use the first unit to satisfy
the greatest want first and any successive units to satisfy lesser wants. For example: You are
stranded in the desert, you are filthy and you are dying of thirst. A rescuer arrives and gives you
water. Would you drink or wash first? You would probably drink the first few units until you were no
longer thirsty and then if there were any remaining units you would then wash! The implication is
that succeeding units satisfy lesser wants or that you get lesser utility from succeeding units.
This gives us the:
LAW OF DIMINISHING MARGINAL UTILITY
- the MU gained by consuming equal and successive units of a G will eventually decline
as the amount of a G consumed increases - all other things held constant.
Several things to note about MU and TU:
1.) as long as MU > 0, then TU is increasing;
2.) when MU < 0, then TU is decreasing. Does it make sense to stop consuming then when MU =
0 unless you are constrained prior to this point? YES!!
One of our goals here is to determine how we maximize utility subject to our income and price
constraints and in the process see if we can determine a general rule for this that will also tell us
how much of a particular good a consumer will buy.
To develop this let's again take an example:
Assume that there are only two goods to which we allocate our budget.
Slices of Pizza (P) and Gyros (G).
Pp = price of pizza slice;
Pg = price of a gyro;
Assume that the budget is entirely spent.
Thus we want to max U s.t. Budget = P(Pp) + G(Pg). What do we need to know?
Budget = $10; Pp = $2/slice; Pg = $2 each And we'll need some MU schedules.
# of pizza slice
MUp
# gyro
MUg
1
10
1
12
2
8
2
8
3
6
3
3
4
4
4
2
5
2
5
1
TUpizza = 30
Note that this is a
schedule of MUs and
thus it gives MU of that
particular unit and not of
that NUMBER of units!!
TUgyro = 26
We could spend our entire budget purchasing just pizza slices or just gyros since either would
completely deplete our budget. However a rational consumer would not choose to purchase just 5
gyros because the TU of 5 gyros = 26 < 30 = TU of 5 pizza slices. The question is then whether
there is some other alternative that would provide an even greater amount of TU. Is there some
other combination of units or possible choice that would improve our situation. One way to do this
is to start with the good that has the highest MU for the 1st. unit and then continue
selecting that unit of whichever good has the highest MU until we've exhausted our budget. That
is:
BUY
MU
AMT. SPENT
AMT. LEFT
gyro-1st.unit
12
2
8
pizza-1st.unit
10
2
6
2nd. pizza (or G)
8
2
4
2nd G (or P)
8
2
2
3rd. pizza
6
2
Totals
44
10
0
Since our budget is exhausted and TU = 44 we have clearly improved our position and maximized
TU by choosing a rule that says simply select that unit that has the highest MU and repeat this
until the income is exhausted.
Will this work in all cases? What happens if prices aren't equal?
What if Pg = $1? MUs haven't changed. However, if we buy the combination that maximized our
utility when Pg = $2, we'll have TU = 44 and we'll have $2 left. According to the decision rule we
used above we would then select the 4th. slice of pizza, giving us TU = 48 and depleting our
budget.
Is TU maximized now? And clearly the answer is no since we could expend the $2
on the consumption of the 3rd. and 4th. gyros and we would get 5 additional units of utility instead
of 4 units. Thus in this case with Pp = $2/slice and Pg = $1 each, we would maximize TU at 49 by
consuming 3 slices of pizza and 4 gyros.
Thus using a decision rule of simply picking the next unit based upon which unit has the highest
MU will not always lead us to TU maximization.
What is the source of the problem? It is the fact of unequal prices. We really aren’t comparing
similar units. To put everything on an equal footing we need to express them in equal units
so let's do it as MU per $ spent. That is divide MU by Price to get MU per $; i.e. MU/P. So now let
us add a MU/P column to our above table and we get:
# of pizza slice
MUp
MUp/Pp
# gyro
MUg
MUg/Pg
1
10
5
1
12
12
2
8
4
2
8
8
3
6
3
3
3
3
4
4
2
4
2
2
5
2
1
5
1
1
Now let the decision rule be to select the next unit that has the highest MU per $. In this case we
would select them in the following order:
BUY
MU
AMT. SPENT
AMT. LEFT
gyro-1st.unit
12
1
9
gyro-2nd.unit
8
1
8
1st. pizza
10
2
6
2nd pizza
8
2
4
3rd. pizza
6
2
2
3rd. gyro
3
1
1
4th. gyro
2
1
0
Totals
49
10
Using this method and the original prices what would be the outcome?
The same solution that we originally had.
Can we use this information to develop a general rule? YES!!
How are we making our selection? We are comparing MU/P (MU per dollar).
At the last unit consumed - when you have exhausted your budget - there are 3 possible situations
that could exist. Between any 2 goods A and B you could have:
Case #1 M Ua
Pa
>
M Ub
Pb OR
Case # 2 =
OR
M Ua
Pa
M Ub
Pb Case #3
M Ua
Pa
<
M Ub
Pb
In the first case you get greater utility per $ by consuming good A. So to maximize your utility you
would want to buy another unit of A which would mean that:
A.) you would have to buy less of B since the budget is exhausted.
B.) the next unit of A would have a lower MU/P and the previous unit of B would have a higher
MU/P.
Case # 3 is essentially the reverse of this with B providing the higher MU/P; you are getting less
utility per $ by consuming A so you would want to buy less of A. In either situation you want to
consume more of that good that has the higher MU/P (and thus less of the good that has the lower
MU/P) until this situation no longer exists.
That is, to maximize total utility, you consume that combination of G/Ss such that it is impossible
to get more TU by consuming more of one good and less of another.
Where does that leave you? At the point where MU/P are equalized across all goods. Thus we can
state our general rule for TU maximization as:
TU is maximized when: MPU2 1 =
all income is spent and while
M U2
P2 = . . . .
M U1
M U2
P1 > P 2
=
M Un
Pn
and all income is spent. Or, when
, buying more of good 1 and less of good 2 will
not increase TU.
This entire statement is what we refer to as Consumer Equilibrium. Clearly we need the last part
of this statement to cover situations like our last example where TU is maximized and MU/P isn’t
equalized. This demonstrates several things:
1.) the concept of marginal analysis; although we were maximizing TOTAL UTILITY it was the
marginal aspects of the situation that led to the important generalization about TU
maximization.
2.) it shows why DEMAND is downward sloping and also how you can derive a demand curve.
At equilibrium you have one point on the demand curve for each good.
If Px decreases then MUx /Px increases. To restore equilibrium, the MUx must also
decrease. For MU to decline you have to consume more. Thus as P decreases, Qd
increases. And you have the downward sloping demand curve.
Essentially, you are substituting that good that has a higher MU/P for the good that has a
lower MU/P. The substitution effect is due to the change in MU/P. The P change affects your
willingness (substitution effect) to buy and your ability (income effect) to buy.
The size of the income effect depends upon the part of your budget that the good occupies.
The size of the substitution effect depends on the # of/ quality of substitutes available.
If demand is inelastic then MU decreases relatively fast and the income effect is relatively small. If
demand is elastic then MU decreases relatively slowly and the income effect is relatively large.
Note that you are maximizing U subject to constraints at each point on the Demand Curve.