Chapter 14 Consumer

1
Chapter 14Consumers Surplus
2
Monetary Measures of Gains-to-Trade

• You can buy as much gasoline as you wish at 1
  per gallon once you enter the gasoline market.
• Q What is the most you would pay to enter the
  market?
• A You would pay up to the dollar value of the
  gains-to-trade you would enjoy once in the
  market.
• How can such gains-to-trade be measured?

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Monetary Measures of Gains-to-Trade

• Three such measures are
• Consumers Surplus
• Equivalent Variation, and
• Compensating Variation.
• Only in one special circumstance do these three
  measures coincide.

4
Equivalent Utility Gains

• Suppose gasoline can be bought only in lumps of
  one gallon.
• Use r1 to denote the most a consumer would pay
  for a 1st gallon -- call this her reservation
  price for the 1st gallon.
• r1 is the dollar equivalent of the marginal
  utility of the 1st gallon.

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Equivalent Utility Gains

• Now that she has one gallon, use r2 to denote the
  most she would pay for a 2nd gallon -- this is
  her reservation price for the 2nd gallon.
• r2 is the dollar equivalent of the marginal
  utility of the 2nd gallon.

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Equivalent Utility Gains

• Generally, if she already has n-1 gallons of
  gasoline then rn denotes the most she will pay
  for an nth gallon.
• rn is the dollar equivalent of the marginal
  utility of the nth gallon.

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Equivalent Utility Gains

• r1 rn will therefore be the dollar
  equivalent of the total change to utility from
  acquiring n gallons of gasoline at a price of 0.
• So r1 rn - pGn will be the dollar
  equivalent of the total change to utility from
  acquiring n gallons of gasoline at a price of pG
  each.

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Equivalent Utility Gains
r1
r2
r3
r4
r5
r6
1
2
3
4
5
6
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Equivalent Utility Gains

• What is the monetary value of our consumers
  gain-to-trading in the gasoline market at a price
  of pG?

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Equivalent Utility Gains

• The dollar equivalent net utility gain for the
  1st gallon is (r1 - pG)
• and is (r2 - pG) for the 2nd gallon,
• and so on, so the dollar value of the
  gain-to-trade is (r1 - pG) (r2
  - pG) for as long as rn - pG gt 0.

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Equivalent Utility Gains
value of net utility gains-to-trade
r1

• Consumers surplus or
• Net consumers surplus

r2
r3
r4
pG
r5
r6
2
4
6
1
3
5
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Equivalent Utility Gains

• If gasoline can be purchased in any quantity then
  ...

13
Equivalent Utility Gains
() Res.Prices
Reservation Price Curve for Gasoline
value of net utility gains-to-trade
pG
Gasoline
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Equivalent Utility Gains

• Unfortunately, estimating a consumers
  reservation-price curve is difficult,
• so, as an approximation, the reservation-price
  curve is replaced with the consumers ordinary
  demand curve.
• This approximation gives the Consumers Surplus
  measure of net utility gain.

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Quasi-Linear Utility

• One special case would be quasi-linear utility.
• With quasi-linear utility, calculating CS using
  the reservation-price curve will result in the
  same value with that using the ordinary demand
  curve.

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CS for Quasi-linear Utility
p1
Ordinary demand curve,
is exactly the consumers utility gain
from consuming x1 units of
commodity 1.
CS
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Change in CS

• Now, what if there is a change in one of the
  prices?
• How would a price change affect the consumers
  surplus?

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Consumers Surplus
p1
p1(x1), the inverse ordinary demand curve
for commodity 1
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Consumers Surplus
p1
p1(x1)
CS before
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Consumers Surplus
p1
p1(x1)
CS after
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Consumers Surplus
p1
p1(x1), inverse ordinary demand x1(p1), the
consumers ordinary demand for commodity 1.
Lost CS
measures the loss in Consumers Surplus.
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Compensating Variation and Equivalent Variation

• Two additional dollar measures of the total
  utility change caused by a price change are
  compensating variation (CV) and equivalent
  variation (EV).

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Compensating Variation

• p1 rises.
• Q What is the least extra income that, at the
  new prices, just restores the consumers original
  utility level?

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Compensating Variation

• p1 rises.
• Q What is the least extra income that, at the
  new prices, just restores the consumers original
  utility level?
• A The Compensating Variation.

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Compensating Variation
p1p1
p2 is fixed.
x2
u1
x1
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Compensating Variation
x2
p1p1p1p1
p2 is fixed.
u1
u2
x1
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Compensating Variation
x2
p1p1p1p1
p2 is fixed.
u1
u2
x1
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Compensating Variation
p2 is fixed.
p1p1p1p1
x2
u1
CV m2 - m1.
u2
x1
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Equivalent Variation

• p1 rises.
• Q How much money would have to be taken away
  from the consumer before the price change to
  leave him just as well off as he would be after
  the price change?
• A The Equivalent Variation.

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Equivalent Variation
p1p1
p2 is fixed.
x2
u1
x1
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Equivalent Variation
p2 is fixed.
p1p1p1p1
x2
u1
u2
x1
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Equivalent Variation
p1p1p1p1
p2 is fixed.
x2
u1
u2
x1
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Equivalent Variation
p1p1p1p1
p2 is fixed.
x2
u1
EV m1 - m2.
u2
x1
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CV and EV

• Both CV and EV measure how far apart two
  indifference curves are.
• Depend on the slope of the tangent line.
• CV does not equal EV in most cases.
• Only in quasilinear utility. Why?
• The distance of two indifference curves is the
  same no matter where it is measured.
• CV EV ? CS

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Producers Surplus

• Changes in a firms welfare can be measured in
  dollars much as for a consumer.

36
Producers Surplus
Output price (p)
Supply Curve
y
(output units)
37
Producers Surplus
Output price (p)
Supply Curve
y
(output units)
38
Producers Surplus
Output price (p)
ProducersSurplus.
Supply Curve
y
(output units)