Welfare Analysis

1
Welfare Analysis
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Agenda

• Welfare Economics and Analysis Defined
• Positive Versus Normative Economics
• Willingness-to-Pay (WTP) Welfare Measures
• Pareto Optimality
• Edgeworth-Bowley and Pareto Optimum
• First and Second Fundamental Theorem of Welfare

3
Agenda Cont.

• Measuring Consumer and Producer Welfare
• Graphical Welfare Analysis

4
Welfare Economics

• Its a branch of economics that examines resource
  allocation and the policies that govern these
  allocation in terms of societal and/or individual
  costs and benefits.
• One of its objective is to help society make
  better decisions that maximizes its well-being.

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Welfare Analysis

• It is a method used to analyze different resource
  allocations and how these allocations affect
  different groups.
• It is meant to answer the following questions
• Is an allocation of resources economically
  efficient?
• What effect does a particular resource allocation
  have on different groups?

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Positive Economics

• This branch of economics focuses on predicting
  behavior of economic agents by using a set of
  axioms or assumptions.
• Positive economics objectively tries to answer
  what will happen given a set of economic
  circumstances.
• It concerns itself with what is.
• E.g., What happens to price and quantity if you
  put a per unit tax on it?

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Normative Economics

• It is a branch of economics that incorporates
  value judgments in the analysis of resource
  allocation.
• It focuses on what should be.
• What should be the appropriate policy?
• What should the economy be like?
• Welfare economics tends to fall under normative
  economics in terms of analysis.
• E.g., What is the best policy to help producers
  due to a freeze that damaged a majority of their
  crop?

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Positive Versus Normative Economics

• The key difference between positive and normative
  economics is that the assumptions that Positive
  Economics rely upon tend to have no morality or
  ethical implications, while the assumptions of
  Normative Economics have some sort of value
  judgment as their basis.

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Willingness-to-Pay (WTP) Welfare Measures

• There are two primary ways of measuring welfare
  changes due to a change in a policy.
• Compensating Variation
• Equivalent Variation
• The difference between the two is dependent upon
  whether a change occurs or not.

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Compensating Variation

• This compensation represents the amount of money
  taken away from an individual/firm after an
  economic change that leaves the individual/firm
  just as well off as before the change occurred.
• Welfare gains implies that this amount represents
  the maximum amount that the individual/firm would
  be willing-to-pay for the change to occur.
• Welfare losses imply that this amount is the
  negative of the minimum amount that a
  individual/firm would require as compensation for
  the change to occur.

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Equivalent Variation

• This compensation represents the amount of money
  paid to an individual/firm which, if an economic
  change does not happen, leaves the individual
  just as well off as if the change occurred.
• If a welfare gain would occur, it is the minimum
  compensation that the person would need to forgo
  the change to occur.
• If a welfare loss would occur, it is the negative
  of the maximum amount that the individual/firm
  would be willing to pay to avoid the change to
  occur.

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Pareto Optimality

• A resource allocation is said to be Pareto
  optimal if there is no reallocation of resources
  that can make one person better-off with out
  harming some other person.
• A Pareto optimal allocation does not have to be
  unique and may even be judged unfair.
• Pareto optimality usually is the preferred
  criterion for economist when practicing normative
  economics.

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More on Pareto

• A Pareto improvement is said to exist if you can
  reallocate resources and make at least one person
  better-off without harming any other person.
• A Pareto dominated allocation of resources is an
  allocation where a transfer of resources will
  make at least one person better-off without
  harming another.

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Examining Pareto Optimum
Consumer B
Consumer A
x2
x2
UB
UA
x1
x1
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Edgeworth-Bowley Box

• An Edgeworth-Bowley Box allows you to represent
  two consumers and there decisions in a single
  graph.
• It represents two different consumers consumption
  of two different goods and the corresponding
  utility of each.

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Edgeworth-Bowley Box Example
x2A
Consumer B
OB
x1B
UB
UA
x1A
OA
x2B
Consumer A
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Edgeworth-Bowley Box and Pareto

• Suppose Consumer A and B can consume wheat and
  chickens.
• Assume that Consumer A has 180 bushels of wheat
  and 5 chickens.
• Assume that Consumer B has 20 bushels of wheat
  and 15 chickens.
• Call Consumer A and B initial allocations
  endowment 1.
• Let UA and UB represent respectively A and Bs
  initial indifference curves that intersect with
  endowment 1.
• Can either producer be made better-off through
  reallocation of goods.

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Edgeworth-Bowley Box and Pareto Cont.
WheatA
Consumer B
ChickensB
15
OB
UB
20
Endowment 1
180
Endowment 2
Contract Curve
Endowment 3
UA
ChickensA
OA
5
WheatB
Consumer A
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Edgeworth-Bowley Box and Pareto Cont.

• Endowment 1 represents a Pareto dominated
  allocation.
• Endowment 2 represents a Pareto improvement
  allocation.
• Endowment 3 represents a Pareto optimum
  allocation.
• The Contract Curve represents all of the Pareto
  optimal allocations.

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First Fundamental Theorem of Welfare

• This theorem states that under the competitive
  setting market economies will achieve a Pareto
  optimal point as long as consumers maximize
  utility and producers maximize profits.

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Second Fundamental Theorem of Welfare

• Any Pareto optimum allocation can be sustained by
  perfect competition with a suitable lump-sum
  transfer of resources.

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Measuring Producers Welfare

• There are two primary ways to measure the welfare
  of producers
• Profit (p)
• ?TR TVC TFC
• Quasirent/Producer Surplus (PS)
• PS TR TVC ? TFC
• Note In general the compensating and equivalent
  variation is the same for both measures.

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Profit, Quasirent, and Producer Surplus
Graphically
P
MC
P1
ATC
A
AVC
PATC
B
PAVC
Q
Area A Profit Area A Area B
Quasirent/Producer Surplus
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Why use producer surplus over profit as a welfare
measure?

• Profit tends to underestimate the benefit to the
  producer because it does not take into account
  the benefit of producing even though the producer
  may be making a loss but minimizing that loss by
  still producing.

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Measuring Consumer Welfare

• Since a persons utility is not directly
  observable, a proxy for their utility is
  necessary.
• One such proxy is consumer surplus which is the
  area under their demand curve and above the price
  paid.
• There are many complex aspects to consider about
  measuring consumer welfare because the
  compensating and equivalent variations tend not
  to be the same.
• Due to these complexities, we will assume that
  consumer surplus is a good enough measure relying
  on work done by Willig (1976).

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Consumer Surplus Graphically
P
A
P0
Demand
Q
Area A Consumer Surplus
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Graphical Welfare Analysis Steps

• Step 1 Set-up an original supply and demand
  scenario for the policy being examined
• Step 2 Graphically determine the initial
  equilibrium price, equilibrium quantity,
  producers surplus (PS), and consumers surplus
  (CS)
• Step 3 Analyze how the policy will affect
  consumer price and/or demand and demonstrate it
  on the graph
• Step 4 Break-up the graph using the initial and
  new prices and quantities

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Graphical Welfare Analysis Steps Cont.

• Step 5 Calculate the new producer and consumer
  surpluses
• Step 6 Sum up the change in areas of producer
  and consumer surplus changes
• Step 7 Calculate any taxpayer gains or losses if
  appropriate
• Step 8 Calculate the total welfare change due to
  the policy

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Welfare Analysis of Technological Change

• Suppose you have a change in technology that
  causes you supply curve to rotate clockwise from
  its intersection with the price axis.
• E.g., Government sets a policy to allow biotech
  research
• Define the following
• S0 is the original supply curve
• S1 is the new supply curve
• D is the demand curve
• p0,q0 is the initial quantity and price
  equilibrium
• p1,q1 is the new quantity and price equilibrium

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Graphical Welfare Analysis of Technological Change
P
S0
a
p0
S1
b
d
c
p1
g
e
f
D
q1
q0
Q
Change in PS fg-b
Change in CS bcd
Change in TS cdfg
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Summary of Results for Technological Change

• Consumers definitely gain under this situation
• Producers will gain if areas f g gt area b
• Producers will lose if areas f g lt area b
• Total surplus increases

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Welfare Analysis of a Quota or Market Rationing

• Suppose the government decides to subsidize a
  particular commodity to help producers.
• Define the following
• S is the supply curve
• D is the demand curve
• q1 is the quota set by the government
• p0,q0 is the initial quantity and price
  equilibrium
• p1 is the price that producers are willing to
  supply at q1
• p2 is the price that consumers pay at q2

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Graphical Welfare Analysis of a Quota or Market
Rationing
P
S
a
p2
b
c
p0
e
d
p1
f
D
q0
q1
Q
Change in PS b e
Change in TS c e
Change in CS b c
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Summary of Results for a Quota or Market Rationing

• Consumers definitely lose under this situation
• Producers gain if area b gt area e
• Producers lose if area b lt area e
• Total surplus decreases by area c e

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Welfare Analysis of a Price Ceiling

• Suppose you have a policy that requires a price
  ceiling, i.e., a maximum price that can be
  charged for a good.
• E.g., Government sets a price ceiling on how much
  can be paid for a staple good like milk.
• Define the following
• S is the supply curve
• D is the demand curve
• p0,q0 is the initial quantity and price
  equilibrium
• p1 is the new price given the ceiling
• p2 is the price that consumers would be willing
  to pay for output q1
• q1 is the quantity supplied by producers at the
  price ceiling
• q2 is the quantity demanded by consumers at the
  price ceiling

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Graphical Welfare Analysis of a Price Ceiling
P
S
a
p2
b
c
p0
d
e
f
g
p1
h
D
q0
q1
q2
Q
Change in PS - d - e
Change in TS -c- e
Change in CS d c
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Summary of Results for Price Ceiling

• Producers definitely lose under this situation
• Consumers will gain if area d gt area c
• Consumers will lose if area d lt area c
• Total surplus decreases
• q2 q1 represents the excess demand for the
  product with a price ceiling

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Welfare Analysis of a Price Floor

• Suppose you have a policy that requires a price
  floor, i.e., a minimum price that can be charged
  for a good.
• E.g., Government sets a price floor for what a
  producer can get for a commodity.
• Define the following
• S is the supply curve
• D is the demand curve
• p0,q0 is the initial quantity and price
  equilibrium
• p1 is the new price given the floor
• p2 is the price that producers would be willing
  to sell output q1
• q1 is the quantity demanded by consumers at the
  price floor
• q2 is the quantity supplied by producers at the
  price floor

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Graphical Welfare Analysis of a Price Floor
P
S
a
p1
b
d
c
p0
f
e
g
h
p2
D
q0
q1
q2
Q
Change in PS b f
Change in TS -c- f
Change in CS b c
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Summary of Results for Price Floor

• Consumers definitely lose under this situation
• Producers will gain if area b gt area f
• Producers will lose if area b lt area f
• Total surplus decreases
• q2 q1 represents the excess supply for the
  product with a price floor

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Welfare Analysis of a Price Support

• Suppose you have a price support policy where the
  government buys the surplus.
• E.g., Government sets a price support for corn.
• Define the following
• S is the supply curve
• D is the demand curve
• p0,q0 is the initial quantity and price
  equilibrium
• p1 is the new price given the price support
• p2 is the price that producers would be willing
  to sell output q1
• q1 is the quantity demanded by consumers at the
  price support
• q2 is the quantity supplied by producers at the
  price support

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Graphical Welfare Analysis of a Price Support
P
S
a
p1
b
d
c
p0
i
f
e
g
h
p2
j
l
k
D
q0
q1
q2
Q
Change in PS b c d
Change in TS d
Change in CS b c
Tax Payers Cost c d f g h i k l
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Summary of Results for Price Support

• Consumers definitely lose under this situation
• Producers will gain areas b c d
• Total surplus increases to d at a large taxpayer
  expense
• The taxpayer expense may not be a sunk cost
  because they could sell the surplus production to
  foreign countries or save it for low yield years.

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Welfare Analysis of an Ad Valorem Tax

• Suppose the government decides to put an ad
  valorem tax, i.e., a tax paid per unit of
  quantity, on cigarettes.
• Define the following
• S is the supply curve
• D is the demand curve
• D1 is the new demand curve faced by consumers
• t is the tax
• p0,q0 is the initial quantity and price
  equilibrium
• p1 is the new price that producers receive after
  the tax
• p2 is the price that consumers pay with the tax
• The difference between p1 and p2 is the tax
• q1 is the quantity demanded by consumers and
  supplied by producers

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Graphical Welfare Analysis of an Ad Valorem Tax
P
S
t
a
p2
c
b
d
p0
f
g
e
p1
h
D1
D
q0
q1
Q
Change in PS e f g
Change in TS d g
Change in CS b c d
Tax Payers gain b c e f
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Summary of Results for an Ad Valorem Tax

• Consumers and producers definitely lose under
  this situation
• The taxpayer gains areas b c g f in tax
  revenue.
• Total surplus decreases by areas b

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Welfare Analysis of a Subsidy to Consumers

• Suppose the government decides to subsidize a
  particular commodity to help producers.
• Define the following
• S is the supply curve
• D is the demand curve
• D1 is the new demand curve faced by consumers
• s is the subsidy
• p0,q0 is the initial quantity and price
  equilibrium
• p1 is the new price that producers receive after
  the tax
• p2 is the price that consumers pay with the tax
• The difference between p1 and p2 is the tax
• q1 is the quantity demanded by consumers and
  supplied by producers

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Graphical Welfare Analysis of a Subsidy to
Consumers
P
s
S
a
p2
c
b
d
p0
e
g
f
p1
h
D1
D
q0
q1
Q
Change in PS b c
Change in TS d
Change in CS e f g
Tax Payers lose b c d e f g
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Summary of Results for a Subsidy to Consumers

• Consumers and producers definitely gain under
  this situation
• The taxpayer lose areas b c d e f g in
  tax revenue.
• Total surplus decreases by area d

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Notes on Welfare Analysis

• Many different policies can be used to achieve
  the same goal.
• The key to policy welfare analysis is to
  understand how each party is affected by each
  policy.
• While not done at this point comparative welfare
  analysis of different policies can be done using
  a single graph.