### Willingness to Pay, MB and Consumer Surplus

```Consumer Surplus
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How many rectangles do you see here?
A
B
3, I hope. There is A, B, and A+B.
Some of what follows will require you to
work with rectangles. Why, you ask? Why
not! No, really it can make the job we have
to accomplish easier.
By the way, did you know that all squares
are rectangles, but not all rectangles are
square?
The area of a triangle is half of
the base times the height. Just
don’t use the hypotenuse. 2
Running a business has many challenges. One is figuring out
what to charge each customer. From the business point of view it
would be awesome if each person would pay the most they are
willing to pay for each unit.
As you might imagine, consumers probably do not like to reveal
the most they are willing to pay for each unit of the items they
purchase.
We mentioned before that the sports owner has some degree of
market power because of geographic territory distribution. This
suggests a downward slope to the demand that the team faces.
On the next slide I show a demand for a product from 1 person.
It is an ideal downward sloping demand and in economics we
think the demand curve is a representation of the true expression
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of willingness to pay.
The Demand curve again
P
Note the axes are not
drawn to the same scale.
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Another way to see the demand
curve
What is the amount the person is willing to pay for the first
unit on the demand curve one screen ago? Since the first unit
is not demanded until the price is 5, we say the person is
willing to pay \$5 for 1 unit of the good.
Note in the graph from before that the area made up of the part
b, c, d, e, and f is the \$5 the person is willing to pay for the
first unit. (Area of a rectangle is base times height – 1 times 5
here)
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Another way to see the demand
curve
Now, on the demand curve we see the person is willing to
pay \$3 for the second unit, but no more. This would be
represented by areas h, i, j, and k.
We could do this on and on for additional units. The point is
that the amount the consumer is willing to pay for each unit
is under the demand curve.
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Consumer surplus for a person
Say for the person we had before that they have to pay \$1 for
every unit they buy (only \$1 is being charged for each and every
unit). The consumer surplus the individual would get on each
unit would be:
Unit
willing to pay
have to pay
consumer surplus
1
5
1
4 b+c+d
2
3
1
2  h+i
3
1.5
1
.5  m
4
1
1
0
So the total consumer surplus for the individual is 6.5 This
consumer surplus is the difference between what the consumer is
willing to pay and what has to be paid. It represents money the
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consumer can use elsewhere.
Demand again, but now market
demand
P
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Market demand
The market demand curve is simply the summation, or
addition, of the demand each person has in a market.
To get the market demand
1) look at each price
2) at each price add up what each person is willing to buy at
that price.
The quantity demanded in the market is simply the quantities
added up at each price across the people in the market
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Consumer Surplus - CS
P
I am using the same example
I did before, but now think of
this as the market demand
curve.
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CS
On the previous screen someone is willing to pay \$5 for the
first unit. Note areas b, c, d, e and f add up to the \$5. This is
almost all the area under the demand curve out to one unit. If
we add in area a we can say all the area under the demand
curve out to a quantity is what the consumer is willing to pay
for the first unit. Of course area a should not be included, but
it makes life easy to add it in.
So, the willingness to pay for any quantity is the area under
the demand curve out to that quantity. When we have
thousands of consumers in a market it would be tedious to
look at each consumer separately and add up the surplus for
each.
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CS
P
A
P1
B
D1
Q
Q1
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CS
On the previous screen the price and quantity traded are P1
and Q1, respectively.
Consumer surplus is defined as what consumers are willing to
pay for a product minus what they have to pay.
At the market quantity of Q1 units
consumers are willing to pay A + B, and
consumers have to pay
B (really P1 times Q1), so
consumer surplus is A
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CS
Consumer surplus is a triangle in this example of looking at
the demand in the whole market. The area of a triangle is onehalf of the base times the height. Let’s see an example:
area = .5(10)(16-7) = 45
16
7
0
10
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CS
Say you are willing to pay \$50 for a ticket to the next ball
game. Let’s note that the \$50 you are willing to spend could
be spent on something else.
In economics we tend to say if you spend the \$50 on the ticket
then the game is at least as valuable, and maybe more
valuable, to you then what you would have used the \$50 for in
the alternative case.
In other words the ball game gives more utility than the next
best alternative with the \$50.
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CS
I like to think of the consumer surplus as money the consumer
has left over after buying the units. They would have paid
these dollars for the units, but did not have to. So these
dollars can be used somewhere else. So, if you can buy goods
that you want and pay less than you are willing to pay, then
you not only benefit from having the goods, you benefit from
the mechanism by which you buy the goods.
The consumer surplus from one item can be used elsewhere.
This is an addition to consumer welfare or standard of living.
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Summary ideas
Consumer surplus
for 1 consumer
Consumer surplus in a
market
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New example
Say demand has the form
P = 140 – 4A.
When you go to calculate consumer surplus you are likely to
need to know the value of a triangle that starts where the
demand curve intercepts the price (vertical) axis. You find this
by making A = 0 and solving for P. So, here P = 140 when A =
0.
If the actual price in this example is \$20 the attendance would
be 30 and the consumer surplus would be .5(30)(140 – 20) =
1800.
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