Tutorial 6: Consumer and Market Demand
One of the principle reasons for studying the
consumer choice model is to discover what it tells us about
the shape of an individual consumer's demand curve. After
all, we can use the consumer choice model to vary the price
of a good and watch what happens to the quantity of that
good consumed. Well, that's all the information we need
to construct a demand schedule -- two prices and the associated
quantities demanded.
Individual Demand
Let's manipulate the consumer choice model and see how
we can generate an individual consumer's demand curve. Figure
1 below shows the consumer choice model, with food and clothing
as the two goods, where Pf = $2 per unit, Pc = $2 per unit,
and income = $80 per period. The consumer has attained the
highest satisfaction possible given her preferences, the
prices of the two goods, and her income, with F* = 20 units,
C* = 20 units, and u(F*, C*) = 400 "utils".
Figure 1
From its initial rate of $2 per unit,
we'll raise the price of food to $8 per unit.
Because the law of demand states that quantity demanded
varies inversely with price, cæteris paribus,
we must hold the other variables constant. So we'll freeze
preferences (i.e., no change in a or b in the utility function),
keep PC at $2 per unit, and keep income at $80 per period.
Figure 2 below shows the new budget constraint this consumer
faces.
Figure 2
Now let the consumer adjust to this new budget reality.
In Tutorial 5c we
learned that the consumer's objective is to maximize
utility subject to a budget constraint. Graphically,
this means that the consumer's utility-maximizing choice
must meet two conditions:
- The market basket chosen must place the consumer on
the highest indifference curve attainable;
- That same market basket must be located on the budget
line (i.e., no "saving").
To reach this objective, the consumer chooses a combination
of the two goods such that the budget line and indifference
curve are tangent.
Figure 3 shows the result. Drawing a new indifference curve
(U1) just tangent to the new budget constraint (B1) shows
the consumer's new optimum choice of food (F* = 5 units)
and clothing (C* = 20 units), with U1(F*, C*) = 200 "utils".
Figure 3
We now have just enough information to derive the consumer's
individual demand curve. Table 1 summarizes this information.
Table 1
Pf |
QfD |
u(F*, C*) |
PC |
Income |
Pref's
a & b |
$2/unit |
20 units/t |
400 "utils" |
$2/unit |
$80/pd |
0.5 |
0.5 |
$8/unit |
5 units/t |
200 "utils" |
$2/unit |
$80/pd |
0.5 |
0.5 |
Draw a graph with Price on the vertical axis (in $/unit)
and quantity on the horizontal axis (units of food/t).
- Plot the first price-quantity combination (Pf = $2/unit
and Qfd = 20 units/t).
- Plot the second price-quantity combination (Pf = $8/unit
and Qfd = 5 units/t).
- Connect the two points and you have a line representing
the consumer's demand for food!
Your graph should look like the one
in Figure 4.
Figure 4
Let's examine the properties of this demand line.
- An increase in price, P, from $2 to $8 per unit, causes
a decrease in the quantity demanded, Q, from 20 to 5 units
per time period. Similarly, a decrease in price would
cause an increase in the quantity demanded.
- The level of utility that can be attained changes as
we move along the demand curve -- an increase in P (from
$2 to $8) causes a decrease in the maximum indifference
curve attainable, which implies a decrease in satisfaction
(from 400 "utils" to 200 "utils").
Similarly, a decrease in P causes an increase in the maximum
indifference curve attainable, which implies an increase
in satisfaction.
- At every point on the consumer's demand curve, the consumer
is maximizing U by satisfying the condition that MRS -
Px/Py = 0, subject to the constraint that Income = Px*X
+ Py*Y.
There are two implications that may be derived from this
last point.
- The MRS varies along D (the relative value of Food
falls as one buys more).
- How much one is willing to pay for a good varies along
an individual's demand curve(the more Food one has the
less one is willing to pay for another unit of it), i.e.,
the consumer's reservation price falls as the quantity
already consumed per period increases.
Continues...
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Individual Demand