Part IIA, Paper 1 Consumer and Producer Theory

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Part IIA, Paper 1Consumer and Producer Theory

• Lecture 5
• Compensating and Equivalent Variation
• Flavio Toxvaerd

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Todays Outline

• Welfare
• Consumer surplus
• Equivalent variation
• Compensating variation
• Slutsky vs Hicksian substitution

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Consumer Surplus and Welfare
Following a price change,
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Consumer Surplus and Welfare
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Evaluating Welfare Changes

• Consider the situation where the price of good 1
  takes one of two values, p1 p01 or p1 p11,
  while the price of good 2 remains unchanged.
• When p1 p01 a consumer with income m will
  maximise utility subject to her budget
  constraint, and achieve a level of utility u0
  v(p01, p2 , m) (the indirect utility function)

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Evaluating Welfare Changes

• From duality, and the expenditure function, we
  also know that e(p01, p2 , u0) m
• Similarly, when p1 p11 we can write
• u1 v(p11,p2 ,m) and e(p11,p2 ,u1) m
• Now consider e(p01, p2 , u1) this gives the
  expenditure required to achieve the new level of
  utility, u1 , at the original set of prices, p01.
  

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Equivalent Variation
EV e(p01, p2 , u1) - m

• This gives the equivalent change in income that
  would have altered the utility of the consumer by
  the same amount as the price movement

x2
Evaluated at original prices
u1
EV
u0
b
a
x1
m/p11
m/p01
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Example 1

• Energy assistance for the elderly
• The Government is concerned about high energy
  prices facing the elderly over the winter months
• Two forms of assistance are proposed
• A subsidy of s percent of the price of energy
• A lump sum energy rebate paid to all pensioners

Which policy should the government adopt?
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Example 1
The price subsidy will reduce the effective price
of electricity, and so increase demand for
electricity from x1(p1,p2,m) to x1(p1(1-s),p2,m).
x2
u1
The overall cost of the subsidy will be
S(sp1) x1(p1(1-s),p2,m).
EV
u0
EV gives the size of a lump sum rebate required
to make the pensioner indifferent between the
rebate and the subsidy
x1
m/p1
m/p1(1-s)
x1(p1)
x1(p1(1-s))
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Example 1
So we need to compare the relative magnitudes of
S and EV
EV is area under Hicksian demand curve at u1
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Example 1
p
EV CS if income effect equals zero. EV gt CS
for price fall of normal good.
Hicksian demand
p1
Marshallian demand
p1(1-s)
Recall Slutsky Eqn
x1
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Example 1 Subsidy
A lump sum rebate is more cost effective than a
price subsidy
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Example 1 Subsidy
p
Hicksian demand
p1
sp1
subsidy
Marshallian demand
p1(1-s)
x1
x1(p1(1-s),p2,m)
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Example 1 Warning!

• There are many other important aspects of the
  problem not addressed in this analysis
• This is a partial equilibrium analysis. We have
  not considered
• impact of increased electricity demand on the
  market price of electricity
• impact of any substitution away from alternative
  heating source
• whether or not the government wants to encourage
  electricity usage by the elderly, and so reduce
  winter medical care
• We have assumed that all consumers are identical
  - so no consideration of distribution aspects
  given

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Compensating Variation
x2
Evaluated at new prices
Consider the amount of income a consumer would
willingly forsake in exchange for a change in
prices.
u1
u0
CV
CV lt 0, positive compensation required
CV measures the income effect of a price change
x1
m/p10
m/p11
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Example 2

• Fixed meal charges
• A Cambridge College is considering abandoning the
  fixed meal charge imposed on students, in
  favour of charging higher food prices in hall

Should the student union support this proposal?
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Example 2
The proposal will increase food prices from p10
to p11. Without any change in student income this
will lead to a consumption point, x(p11,p2,m) and
utility level u1.
x2
The level of income required to compensate the
consumer for this price rise will be determined
by
u0
CV
u1
a
The student union should support the change if
and only if the fixed meal charge is greater than
the compensating variation.
b
x1
m/p11
m/p10
x11
x10
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Evaluation

• The practical difficulty with this analysis is
  the measurement of
• e(p11,p2,u0)
• the amount a consumer needs to spend to achieve
  the original level of utility at the new vector
  of prices

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Passive Expenditure
Indirect Effect
Actual Expenditure
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Slutsky vs Hicksian Substitution
Hicksian substitution keeps utility constant.
x2
Slutsky substitution keeps real income
constant, that is - keeps original consumption
bundle affordable.
u0
u1
Difference is the indirect effect
x1
x11
m/p10
x10
S.S.
H.S.
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Example 2, continued
The student union can use the present levels of
consumption to estimate the compensating
variation
Thus, the student union should support the
proposal if
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Example 2
h(p1,p2,u0)
p
CV area under Hicksian demand curve at u0
h(p1,p2,u1)
p1
Marshallian demand
p1(1-s)
x1
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Readings

• Varian, Intermediate Microeconomics, chapter 14
• Varian, Microeconomic Analysis, chapter 10