C H AP T E R
T h eo r e t i ca l
S E V E N
m o d e l s
o f
b e h a vi o r
Developing Models of Rational
Consumer Behavior
and a Theory of the Firm
A Model Of The Rational Consumer
Individual consumers actively attempt to placate their desires through the act of
consumption. We seek satisfaction, which when achieved, leaves us with a pleasurable
feeling. How can we theoretically demonstrate this phenomena, in general terms, for all
consumers? This presents us with a problem because we must discover a way to
circumvent the subjective nature of personal consumption.
Consider for a moment your individual measurement of satisfaction. When you
walk through the local retail mall you face many products you desire, but unfortunately
you cannot buy them all because of your limited income. How do you decide what to
buy? Well we take into account our budget, our present mood, the time of the year, and,
subliminal forces, all come into play. Given the existence of all these forces we finally
purchase one pair of neutral slacks and three shirts. This we find to be satisfying.
Now suppose that your income has instantly increased, which enables you to
purchase more. In this case you purchase 2 pairs of slacks and 6 shirts which you find to
be more satisfying than the former case. But how much more satisfying is it? Do we
normally conclude that since we have purchased twice as much that now we have
doubled our levels of satisfaction? No! Generally, we conclude that one situation
pleases us more than the other. As consumers we tend to rank our individual preferences
in some kind of order. But remember that this is all dependent upon our individual
subjectivity.
Now let’s take those observations of consumer behavior and construct a model
that depicts what every consumer would do (in the same situation). The first problem we
confront here is measuring satisfaction. We have already observed that this depends on
each individual’s personal preferences, and what we need here is some way to
standardize this measurement. Suppose that a meter could be made to measure the levels
of satisfaction people get from consuming various combinations of goods. Let’s just say
that this machine, when strapped to one’s arm, can detect different levels of tension in the
skin that correspond to the amount of satisfaction the individual is demonstrating from
that purchase. This machine is perfect for us because it converts every one’s satisfaction
to measurable units called utils. Thus the util is a standard measurement of satisfaction
received by consumption. The greater the utils measured the higher the level of
satisfaction.
This is of course very hypothetical, but suppose such a utility meter does exist and
furthermore suppose that it has shown the following:
Coffee
Bagels
Utils
2
2
5
3
1
5
2
4
10
5
1
10
4
2
10
8
1
15
6
2
15
3
5
15
Typically economists would seek thousands of bits of information to construct
their model and then plot a “scatter diagram” to establish relationships. A scatter
diagram is simply a graph of individual points which the analyst studies for relationships.
Here is an example:
•
•
•
• •
•
• •
• •
• •
• • •
•
•
Bagels
Coffee
By connecting the points that have identical util values we can demonstrate a
particular combination of goods that we prefer (at that time) or to which we are
indifferent.
•
•
•
• •
•
• •
• •
• •
• • •
•
•
Bagels
Coffee
Every point on each of these lines provides the same level of satisfaction. Each
curve by itself is called an indifference curve, collectively an indifference curve map.
An indifference curve is a particular combination of goods that consumers prefer (at that
time) or to which they are indifferent. The existence of one indifference curve suggests
the existence of an infinite number of curves on that plane.
Indifference curves have certain implications and peculiarities. They are
downward sloping and convex to the origin. This shape provides for substitution and
explains the rate at which substitution takes place. Constructing a tangent to an
indifference curve and calculating its slope will reveal the rate at which substitution
occurs at that point on the curve. A second feature is that by definition each specific
indifference curve represents a given level of utility throughout its range. Using standard
graphing relationships the closer to the origin the lower the level of satisfaction being
depicted along that curve. Therefore curves further to the right are associated with higher
levels of satisfaction and are therefore always preferred. One last observation is that
indifference curves cannot intersect. Since each point on a curve represents a specific
level of utils, intersecting points would, in theory, represent different values at that point.
since no two identical points on a grpah can have different values we say indifference
curves cannot intersect.
Finally we can symbolize all this mathematically with the following equation: U
= f(q1,q2) + b. This simple identity says there is a functional relationship between two
goods (q1,q2) along with outside forces (b) that determine utility.
We have also observed that the consumers ability to consume is being constrained
by the scarcity of available resources. Ideally we would like to move to higher and
higher indifference curves. Realistically, however, scarcity is constraining us. This
constraint can be depicted by constructing a budget constraint in our graphical model of
an indifference curve map.
Bagels
y
•
•
•
• •
•
• •
• •
•
•
• • •
•
•
Budget
Constraint
x
Coffee
Indifference curves help us demonstrate how consumers are always attempting to
maximize their satisfaction. One constraint imposed was limited resources, and so a
production possibilities curve can be constructed to demonstrate this. While consumers
are indeed forced to make choices due to limited resources, we normally do not attribute
that choice to scarcity. Instead, it is our limited income that really limits our
consumption. Using the same logic as when we constructed production possibilities
curves can lead to the construction of our budget constraints.
If you put all your income into the consumption of coffee and only coffee you
would be at point “x” on the graph. On the other hand if you put all your income into the
consumption of bagels and only bagels you would be at point “y” on the graph.
Connecting points “x” and “y” leads to a line known as a budget constraint.
Bagels
y
all bagels &
no coffee
all coffee &
no bagels
x
Coffee
Connecting points x & y yields a budget constraint.
Bagels
y
Budget
Constraint
x
Coffee
Budget constraints reveal not only the total amount of money available for
consumption but also how much we can consume. In addition, relative prices are
implied.
Calculating the area of the triangle formed by the budget constraint and the axis of
the graph indicates either total dollars or amounts (of bagels and coffee) available.
To determine relative prices examine where the budget constraint intersects the
axis and compare the amount of one good that income can purchase relative to the other.
A relative price is simply the price of one good expressed in terms of the price of another
good. In the graph below, coffee is relatively more expensive than bagels because the
total income purchases fewer units of coffee than bagels.
y
Bagels
Coffee is more expensive than
bagels because the total income
purchases fewer units of coffee
relative to the units of bagels
that can be purchased.
x
Coffee
Notice that when point “x” shifts, while point “y” remains constant, the price of
coffee relative to bagels falls.
y
Bagels
x
x'
x''
Coffee
This graph shows the price of bagels changing relative to bagels.
B
a
g
e
l
s
y''
y'
y
x
Coffee
Using all this information let’s now add indifference curves to the budget
constraints to complete our model of the rational consumer.
B
a
g a
e
l a''
s
z
y
x
b'' b
Coffee
Once again the above graph shows the familiar indifference curve map with a
series of budget constraints. This particular map says that with income level a’’ b’’ I will
maximize my satisfaction at point “x” , which represents some combination of coffee and
bagels. If my income rises to ab my satisfaction increases because now I can consume
more of both. And finally if my income falls back to a’’b’’ my satisfaction diminishes
because now I am consuming smaller quantities of both coffee and bagels.
This simple little graph is great because it implies a lot. For example the area to
the left of line a’’b’’ represents both total income available, and the total amount of
bagels and coffee. Point “x” therefore represents an equilibrium between the goods we
are purchasing and our income. Similarly, points y & z represent equilibriums associated
with higher levels of income.
If we now connect these equilibrium points we construct yet another curve called
an income-consumption curve. An income-consumption curve is the locus of
equilibrium budgets resulting from various levels of money income and constant money
prices.
B
a
g
a
e
l a''
s
Income-consumption
Curve
b'' b
Coffee
The income-consumption curve simply says that as your income rises so will
consumption (assuming prices remain constant). But are prices always constant? No!
Almost everyday we see them fluctuate. One day Tab is selling for $1.99/64 oz. and the
next day for $.99/64 oz. These fluctuations in price affect our choices because often our
decisions are based on relative prices between products.
If prices of one product fall in relation to another product then it is like getting an
increase in income if you buy the less expensive good because more money is available
for additional consumption. For example if the price of coffee falls we then have more
income left to purchase other goods. Here is a graph of such a case:
B a
a
g
e
l
s
b
b'
Coffee
b''
Connecting the equilibrium points yields a new curve called the priceconsumption curve. A price-consumption curve is simply the locus of equilibrium
budgets resulting from variations in the price ratio, money income remaining constant.
B a
a
g
e
l
s
Price-consumption curve
b
b'
Coffee
b''
This curve shows that as the price of one good falls relative to another,
consumption of the less expensive good will rise. Awareness of price sensitivity is
revealed in the types of goods we purchase. Goods are considered to be substitutes,
complements, inferior, and superior. Substitutes are products that are related such that
an increase in the price of one will cause an increase in demand for the other (i.e. coffee
& tea). Complements are products that are usually consumed jointly (peanut butter &
jelly). An increase in the price of one will cause the demand for the other to fall.
Inferior goods are those who consumers buy less of as their incomes rise. While normal
or superior goods consumers tend to buy more of as their incomes rise.
Now we can use the price-consumption curve to derive the individual consumer’s
demand curve. Dropping a perpendicular from each equilibrium point on the graph
below will show how much coffee will be consumed at that price. The quantity shown
by point x1 is the amount of coffee purchased at the highest price. Notice that as the
price of coffee falls, our willingness and ability to buy more increases (points x2 and x3).
B a
a
g
e
l
s
x1 x2
x3
Coffee
Plotting the price and quantity of coffee from the above graph yields a demand
curve for coffee.
P
D
x1
x2
x3
Q
While consumers are conscious of relative prices they are also interested in the
demand that exists for the products they want. Knowledge of demand is important
because it helps consumers analyze their own behavior providing them with ways to
consider how economic changes affect them. Producers are interested so they can predict
how changes will affect markets for their products. Government is also interested
because of its obligation to provide stability in our market.
Changes in relative prices that encourage us to substitute one good for another
causes what is known as a substitution effect. In the process a reduction in the price of
one good is like receiving an increase in income. Therefore, as a result of a substitution
effect an income effect is realized.