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Chapter 14
NAME
Consumer’s Surplus
Introduction.
In this chapter you will study ways to measure a con
sumer’s valuation of a good given the consumer’s demand curve for it.
The basic logic is as follows: The height of the demand curve measures
how much the consumer is willing to pay for the last unit of the good
purchased—the willingness to pay for the marginal unit. Therefore the
sum of the willingnessestopay for each unit gives us the total willingness
to pay for the consumption of the good.
In geometric terms, the total willingness to pay to consume some
amount of the good is just the area under the demand curve up to that
amount. This area is called
gross consumer’s surplus
or
total beneft
of the consumption of the good. If the consumer has to pay some amount
in order to purchase the good, then we must subtract this expenditure in
order to calculate the
(net) consumer’s surplus
.
When the utility function takes the quasilinear form,
u
(
x
)+
m
,the
area under the demand curve measures
u
(
x
), and the area under the
demand curve minus the expenditure on the other good measures
u
(
x
m
. Thus in this case, consumer’s surplus serves as an exact measure of
utility, and the change in consumer’s surplus is a monetary measure of a
change in utility.
If the utility function has a diFerent form, consumer’s surplus will not
be an exact measure of utility, but it will often be a good approximation.
However, if we want more exact measures, we can use the ideas of the
compensating variation
and the
equivalent variation.
Recall that the compensating variation is the amount of extra income
that the consumer would need at the
new
prices to be as well oF as she
was facing the old prices; the equivalent variation is the amount of money
that it would be necessary to take away from the consumer at the old
prices to make her as well oF as she would be, facing the new prices.
Although diFerent in general, the change in consumer’s surplus and the
compensating and equivalent variations will be the same if preferences are
quasilinear.
In this chapter you will practice:
•
Calculating consumer’s surplus and the change in consumer’s surplus
•
Calculating compensating and equivalent variations
Example:
Suppose that the inverse demand curve is given by
P
(
q
)=
100
−
10
q
and that the consumer currently has 5 units of the good. How
much money would you have to pay him to compensate him for reducing
his consumption of the good to zero?
Answer: The inverse demand curve has a height of 100 when
q
=0
and a height of 50 when
q
= 5. The area under the demand curve is a
trapezoid with a base of 5 and heights of 100 and 50. We can calculate
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CONSUMER’S SURPLUS
(Ch. 14)
the area of this trapezoid by applying the formula
Area of a trapezoid
=
base
×
1
2
(height
1
+height
2
)
.
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