1. Molly W. Dahl Georgetown University Econ 101 – Spring 2009
Consumer’s Surplus
Molly W. Dahl
Georgetown University
Econ 101 – Spring 2009

2. Inverse Demand Functions
Taking quantity demanded as given and then asking what the price must be describes the inverse demand function of a commodity.
Usually we ask “Given p1 what is the quantity demanded of x1?”
But we could also ask the inverse question “Given that the quantity demanded is x1, what must p1 be?”

3. Inverse Demand Functionsp1
Given p1’, what quantity is demanded of commodity 1? Answer: x1’ units.
p1’
x1’
x1*

4. Inverse Demand Functionsp1
Given p1’, what quantity is demanded of commodity 1? Answer: x1’ units.
The inverse question is: Given x1’ units are demanded, what is the price of commodity 1?
Answer: p1’
p1’
x1’
x1*

5. Consumer’s Surplus p1 CS
Consumer’s surplus is the consumer’s utility gain from consuming x1’ units of commodity 1. CS

6. Change in Consumer’s Surplus
The change to a consumer’s total utility due to a change to p1 is approximately the change in her Consumer’s Surplus.

7. Change in Consumer’s Surplus
p1(x1), the inverse ordinary demand curve for commodity 1

8. Change in Consumer’s Surplus
p1(x1)
CS before

9. Change in Consumer’s Surplus
p1(x1)
CS after

10. Change in Consumer’s Surplus
p1(x1)
Lost CS

11. In Class: Calculating Consumer Surplus

12. Producer’s Surplus
Changes in a firm’s welfare can be measured in dollars much as for a consumer.

13. Producer’s Surplus
Output price (p)
S = Marginal Cost y
(output units)

14. Producer’s Surplus
Output price (p)
S = Marginal Cost y
(output units)

15. Producer’s Surplus y Output price (p) S = Marginal Cost Revenue =
(output units)

16. Producer’s Surplus y Output price (p) S = Marginal Cost
Variable Cost of producing y’ units is the sum of the marginal costs y
(output units)

17. Producer’s Surplus y Output price (p)
Revenue less VC is the Producer’s Surplus.
S = Marginal Cost
Variable Cost of producing y’ units is the sum of the marginal costs y
(output units)

18. Cost-Benefit Analysis
Can we measure in money units the net gain, or loss, caused by a market intervention; e.g., the imposition or the removal of a market regulation?
Yes, by using measures such as the Consumer’s Surplus and the Producer’s Surplus.

19. Cost-Benefit Analysis
Price
The free-market equilibrium
Supply p0
Demand q0
QD, QS

20. Cost-Benefit Analysis
Price
The free-market equilibrium and the gains from trade generated by it. CS
Supply p0 PS
Demand q0
QD, QS

21. Cost-Benefit Analysis
Price
The gain from freely trading the q1th unit. CS
Supply
Consumer’s gain p0 PS
Producer’s gain
Demand q1 q0
QD, QS

22. Cost-Benefit Analysis
Price
The gains from freely trading the units from q1 to q0. CS
Supply
Consumer’s gains p0 PS
Producer’s gains
Demand q1 q0
QD, QS

23. Cost-Benefit Analysis
Price
The gains from freely trading the units from q1 to q0. CS
Supply
Consumer’s gains p0 PS
Producer’s gains
Demand q1 q0
QD, QS

24. Cost-Benefit Analysis
Price CS
Any regulation that causes the units from q1 to q0 to be not traded destroys these gains. This loss is the net cost of the regulation.
Consumer’s gains p0 PS
Producer’s gains q1 q0
QD, QS

25. Cost-Benefit Analysis
Price
An excise tax imposed at a rate of $t per traded unit destroys these gains.
Deadweight Loss CS pb t
Tax Revenue ps PS q1 q0
QD, QS

26. Cost-Benefit Analysis
Price
An excise tax imposed at a rate of $t per traded unit destroys these gains.
Deadweight Loss
So does a floor price set at pf CS pf PS q1 q0
QD, QS

27. Cost-Benefit Analysis
Price
An excise tax imposed at a rate of $t per traded unit destroys these gains.
Deadweight Loss
So does a floor price set at pf, a ceiling price set at pc CS pc PS q1 q0
QD, QS

28. Cost-Benefit Analysis
Price
An excise tax imposed at a rate of $t per traded unit destroys these gains.
Deadweight Loss
So does a floor price set at pf, a ceiling price set at pc, and a ration scheme that allows only q1 units to be traded. CS pe pc PS q1 q0
QD, QS
Revenue received by holders of ration coupons.

29. Compensating Variation and Equivalent Variation
Two additional dollar measures of the total utility change caused by a price change are Compensating Variation and Equivalent Variation.

30. Compensating Variation
p1 rises.
Q: What is the extra income that, at the new prices, just restores the consumer’s original utility level?
Or, after the policy has been implemented, how much must you be compensated to reach the same utility as before the policy?
A: The Compensating Variation.

31. Compensating Variation
p1=p1’
p2 is fixed. x2 u1 x1

32. Compensating Variation
p1=p1’ p1=p1”
p2 is fixed. x2 u1 u2 x1

33. Compensating Variation
p1=p1’ p1=p1”
p2 is fixed. x2 u1 u2 x1

34. Compensating Variation
p1=p1’ p1=p1”
p2 is fixed. x2 u1
CV = m2 - m1. u2 x1

35. Equivalent Variation p1 rises.
Q: What is the extra income that, at the original prices, just restores the consumer’s original utility level?
Or, how much would you pay to avoid moving to the new policy?
A: The Equivalent Variation.

36. Equivalent Variation
p1=p1’
p2 is fixed. x2 u1 x1

37. Equivalent Variation
p1=p1’ p1=p1”
p2 is fixed. x2 u1 u2 x1

38. Equivalent Variation
p1=p1’ p1=p1”
p2 is fixed. x2 u1 u2 x1

39. Equivalent Variation EV = m1 - m2. p1=p1’ p1=p1” p2 is fixed. x2 u1 u2

40. Consumer’s Surplus, Compensating Variation and Equivalent Variation
When the consumer has quasilinear utility,
CV = EV = DCS.
Why? There are no income effects with quasilinear utility.
Otherwise, EV < DCS < CV.