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Consumer's Surplus: Measuring the Benefit to Consumers, Lecture notes of Calculus

The concept of consumer's surplus, which measures the difference between a consumer's willingness to pay for a good and the actual price they pay. discrete and continuous demand, calculations of gross and net surplus, and changes in consumer's surplus. It also introduces producer's surplus and discusses compensating and equivalent variation.

What you will learn

  • What is consumer's surplus and how is it calculated?
  • How does the concept of consumer's surplus apply to continuous demand?
  • What is the difference between gross and net consumer's surplus?

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2021/2022

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Consumer’s Surplus 93
Consumer’s Surplus
A. Basic idea of consumer’s surplus
1. want a measure of how much a person is willing to
pay for something. How much a person is willing
to sacrifice of one thing to get something else.
2. price measures marginal willingness to pay, so add
up over all different outputs to get total willingness
to pay.
3. total benefit (or gross consumer’s surplus), net
consumer’s surplus, change in consumer’s surplus.
See Figure 14.1.
B. Discrete demand
1. remember that the reservation prices measure the
‘‘marginal utility’’
2.
r
1
=
v
(1)
v
(0)
,
r
2
=
v
(2)
v
(1)
,
r
3
=
v
(3)
v
(2)
, etc.
3. hence,
r
1
+
r
2
+
r
3
=
v
(3)
v
(0) =
v
(3)
(since
v
(0) = 0
)
4. this is just the total area under the demand curve.
5. in general to get the ‘‘net’’ utility, or net
consumer’s surplus, have to subtract the amount
that the consumer has to spend to get these benefits
pf3
pf4
pf5

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Consumer’s Surplus

A. Basic idea of consumer’s surplus

1. want a measure of how much a person is willing to

pay for something. How much a person is willing

to sacrifice of one thing to get something else.

2. price measures marginal willingness to pay, so add

up over all different outputs to get total willingness

to pay.

3. total benefit (or gross consumer’s surplus), net

consumer’s surplus, change in consumer’s surplus.

See Figure 14.1.

B. Discrete demand

1. remember that the reservation prices measure the

‘‘marginal utility’’

2. r 1 = v (1) v (0), r 2 = v (2) v (1), r 3 =

v (3) v (2), etc.

3. hence, r 1 + r 2 + r 3 = v (3) v (0) = v (3) (since

v (0) = 0 )

4. this is just the total area under the demand curve.

5. in general to get the ‘‘net’’ utility, or net

consumer’s surplus, have to subtract the amount

that the consumer has to spend to get these benefits

r r r r r r 1 2 3 4 5 6

PRICE

1 2 3 4 5 6 QUANTITY A Gross surplus

r r r r r r 1 2 3 4 5 6

PRICE

1 2 3 4 5 6 QUANTITY B Net surplus

p

Figure 14.

C. Continuous demand. Figure 14.2.

1. suppose utility has form v (x) + y

2. then inverse demand curve has form p(x) = v

(x)

3. by fundamental theorem of calculus:

v (x) v (0) =

Z x

0

v

(t) dt =

Z x

0

p(t) dt

4. This is the generalization of discrete argument

Demand curve

Change in consumer's surplus

p

p"

p'

R

T

x" x' x

Figure 14.

F. This all works fine in the case of quasilinear utility,

but what do you do in general?

p

p *

p

x x

S S

x * x' x"

p'

p"

A B

Supply curve R

T

Change in producer's surplus

Supply curve

Producer's surplus

Figure 14.

G. Compensating and equivalent variation. See Figure

1. compensating: how much extra money would you

need after a price change to be as well off as you

were before the price change?

2. equivalent: how much extra money would you

need before the price change to be just as well off

as you would be after the price change?