From Individual Demand to Consumer Surplus Today: Deriving market demand from individual demand; using reservation prices to derive 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 to market demand Suppose Pat and Shannon have the following demand schedules for apples PriceShannon’s quantity demanded Pat’s quantity demanded $600 $520 $440 $360 $283 $1106 $0129

Example: Individual to market demand How do we get the market demand from individual demands? We add them up PriceShannon’s quantity demanded Pat’s quantity demanded Total demand $6000 $5202 $4404 $3606 $28311 $ $012921

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, units are demanded

At $0, 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 n th unit corresponds to a particular point of a demand curve

Let’s return to part of Shannon’s demand Shannon’s reservation price for 6 th apple is $3 PriceShannon’s quantity demanded $60 $52 $44 $36

Calculating consumer surplus Consumer surplus (CS) for the n th 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 Shannon PriceShannon’s quantity demanded $60 $52 $44 $36 QuantityReservation price 1 st unit$ nd unit$5 3 rd unit$ th unit$4 5 th unit$ th 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 QuantityReservation price CS 1 st unit$5.50$ nd unit$5.00$ rd unit$4.50$ th unit$4.00$ th unit$3.50$ th 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 QuantityReservation price CS 1 st unit$5.50$ nd unit$5.00$ rd unit$4.50$ th unit$4.00$ th unit$3.50$ th 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 On your own: Read Ch. 5 appendix Indifference curves are important in Econ 100A