From Individual Demand to Consumer Surplus

1
From Individual Demand to Consumer Surplus

• Today Deriving market demand from individual
  demand using reservation prices to derive
  consumer surplus

2
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

3
Example Individual to market demand
Price Shannons quantity demanded Pats quantity demanded
6 0 0
5 2 0
4 4 0
3 6 0
2 8 3
1 10 6
0 12 9

• Suppose Pat and Shannon have the following demand
  schedules for apples

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Example Individual to market demand

• How do we get the market demand from individual
  demands?
• We add them up

Price Shannons quantity demanded Pats quantity demanded Total demand
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
5
Some graphing reminders

• Some reminders of graphs
• Label axes
• Label dollar amounts, quantities, etc.
• To save space, all quantity numbers here are
  apples

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Graphing demandsShannon (left) Pat (right)
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Total demand
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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

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Price greater than 3

• When price is greater than 3, Shannon is the
  only person demanding a positive quantity
• Thus, the top half of Shannons demand curve is
  the same as the markets

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At 3, 6 0 units are demanded
11
At 0, 12 9 units are demanded
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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)

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Reservation price and consumer surplus

• How well off are we when we buy something?
• Calculate consumer surplus by using demand curve
  and reservation price

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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

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Lets return to part of Shannons demand

• Shannons reservation price for 6th apple is 3

Price Shannons quantity demanded
6 0
5 2
4 4
3 6
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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

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Back to Shannon
Price Shannons 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
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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
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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
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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
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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
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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
• On your own Read Ch. 5 appendix
• Indifference curves are important in Econ 100A