From Individual Demand to Consumer Surplus

Today: Deriving market demand from individual demand; using

reservation prices to derive consumer surplus

Previously…

7 core principles Thinking like economists Introduction to supply and demand Equilibrium A route choice experiment and its

equilibrium Deriving individual demand

Today

Using individual demands to derive market demand

Reservation price Consumer surplus

Recall individual demand

Last time, we went through the assumptions that gave us a downward-sloping individual demand curve

We will use “horizontal addition” to derive market demand from all individual demands

Example: Individual demand to market demand Suppose Pat

and Shannon have the following demand schedules for apples

Price

Shannon’s quantity demande

d

Pat’s quantity demande

d

$6 0 0

$5 2 0

$4 4 0

$3 6 0

$2 8 3

$1 10 6

$0 12 9

Example: Individual demand to market demand

How do we get the market demand from individual demands?

We add them up

Price

Shannon’s

quantity demand

ed

Pat’s quantity demand

ed

Total deman

d

$6 0 0 0

$5 2 0 2

$4 4 0 4

$3 6 0 6

$2 8 3 11

$1 10 6 16

$0 12 9 21

Some graphing reminders Some reminders

of graphs Label axes Label dollar

amounts, quantities, etc.

To save space, all quantity numbers here are apples

Graphing demands:Shannon (left) & Pat (right)

Total demand

How can we graph demand with only the graphs?

Another method of graphing total demand from individual demand is a method called horizontal addition

We horizontally add quantities demanded from each person AT A GIVEN PRICE

Price greater than $3 When price is

greater than $3, Shannon is the only person demanding a positive quantity

Thus, the top half of Shannon’s demand curve is the same as the market’s

At $3, 6 + 0 units are demanded

At $0, 12 + 9 units are demanded

Bottom half of the demand curve At $3, 6 units are

demanded At $0, 21 units

are demanded Bottom half of

demand curve connects (6, $3) and (21, $0)

Reservation price and consumer surplus

How “well off” are we when we buy something?

Calculate consumer surplus by using demand curve and reservation price

Reservation price

Reservation price is the highest price a person is willing to pay for a good or service

Note that reservation price for the nth unit corresponds to a particular point of a demand curve

Let’s return to part of Shannon’s demand Shannon’s

reservation price for 6th apple is $3

Price Shannon’s quantity

demanded

$6 0

$5 2

$4 4

$3 6

Core principle: Efficiency

Today, we calculate consumer surplus to help on our quest to efficiency

Calculating consumer surplus

Consumer surplus (CS) for the nth unit is the vertical difference between the demand curve and the price paid

We will calculate CS two ways Discretely Approximate using area under

demand curve

Back to ShannonPrice Shannon’s

quantity demanded

$6 0

$5 2

$4 4

$3 6

Quantity

Reservation price

1st unit $5.50

2nd unit $5

3rd unit $4.50

4th unit $4

5th unit $3.50

6th unit $3

If P = $3… At P = $3,

Shannon demands 6 apples

To calculate total consumer surplus for Shannon, we simply add CS for each unit purchased

Quantity

Reservation price

CS

1st unit $5.50 $2.50

2nd unit $5.00 $2.00

3rd unit $4.50 $1.50

4th unit $4.00 $1.00

5th unit $3.50 $0.50

6th unit $3.00 $0.00

CS for 6 units purchased CS is the sum of

the six dollar amounts in the right column, or $7.50

Quantity

Reservation price

CS

1st unit $5.50 $2.50

2nd unit $5.00 $2.00

3rd unit $4.50 $1.50

4th unit $4.00 $1.00

5th unit $3.50 $0.50

6th unit $3.00 $0.00

CS from demand curves CS can be

approximated by calculating the area under the demand curve and above the price

The area of this triangle is a good approximation of CS

CS from demand curves Height of triangle

is ($6 – $3), or $3. Length of triangle

is (6 – 0), or 6 Area of triangle is

one-half times length times height

CS = $9

The area of this triangle is a good approximation of CS

This concludes demand

What have we learned? How individual demand is derived Utility The rational spending rule Deriving market demand from

individual demand Consumer surplus