Chapter 2: Fundamentals of Welfare Economics

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Chapter 2 Fundamentals of Welfare Economics

• -In order to evaluate government policies, we
  need a starting point
• -Welfare Economics the branch of economic
  theory concerned with the social desirability of
  alternate economic states and policies

2
Chapter 2 Fundamentals of Welfare Economics

• Welfare Economics
• First Fundamental Theorem of Welfare Economics
• Second Fundamental Theorem of Welfare Economics

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Theory - Starting Point Pure Exchange Economy

• We start with a simple model
• 2 people
• 2 goods, each of fixed quantity
• Determine good allocation
• The important results of this simple, 2-person
  model hold in more real-world cases of many
  people and many commodities

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Pure Exchange Economy Example

• Two people Maka and Susan
• Two goods Food (f) Video Games (V)
• We put Maka on the origin, with the y-axis
  representing food and the x axis representing
  video games
• If we connect a flipped graph of Susans goods,
  we get an EDGEWORTH BOX, where y is all the food
  available and x is all the video games

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Makas Goods Graph
Ou is Makas food, and Ox is Makas Video Games
u
Food
O
x
Video Games
Maka
6
Edgeworth Box
Susan
y
O
Ow is Susans food, and Oy is Susans Video
Games
r
Total food in the market is Or(Os) and total
Video Games is Os (Or)
u
Food
w
Each point in the Edgeworth Box represents one
possible good allocation
O
s
x
Video Games
Maka
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Edgeworth and utility

• We can then add INDIFFERENCE curves to Makas
  graph (each curve indicating all combinations of
  goods with the same utility)
• Curves farther from O have a greater utility
• (For a review of indifference curves, refer to
  Intermediate Microeconomics)
• We can then superimpose Susans utility curves
• Curves farther from O have a greater utility

8
Makas Utility Curves
Makas utility is greatest at M3
Food
M3
M2
M1
O
Video Games
Maka
9
Edgeworth Box and Utility
Susan
O
Susan has the highest utility at S3
r
S1
A
S2
At point A, Maka has utility of M3 and Susan has
Utility of S2
S3
Food
M3
M2
M1
O
s
Video Games
Maka
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Edgeworth Box and Utility
Susan
O
If consumption is at A, Maka has utility M1 while
Susan has utility S3
r
A
B
S3
By moving to point B and then point C, Makas
utility increases while Susans remains constant
C
Food
M3
M2
M1
O
s
Video Games
Maka
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Pareto Efficiency
Susan
O
Point C, where the indifference curves barely
touch is called PARETO EFFICIENT, as one person
cant be made better off without harming the
other.
r
S3
C
Food
M3
M2
M1
O
s
Video Games
Maka
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Pareto Efficiency

• When an allocation is NOT pareto efficient, it is
  wasteful (at least one person could be made
  better off)
• Pareto efficiency evaluates the desirability of
  an allocation
• A PARETO IMPROVEMENT makes one person better off
  without making anyone else worth off (like the
  move from A to C)
• However, there may be more than one pareto
  improvement

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Pareto Efficiency
Susan
O
If we start at point A -C is a pareto
improvement that makes Maka better off -D is a
pareto improvement that makes Susan better off -E
is a pareto improvement that makes both better off
r
A
S3
C
S4
Food
S5
E
M3
M2
D
M1
O
s
Video Games
Maka
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The Contract Curve

• Assuming all possible starting points, we can
  find all possible pareto efficient points and
  join them to create a CONTRACT CURVE
• All along the contract curve, opposing
  indifferent curves are TANGENT to each other
• Since the slope of the indifference curve is the
  willingness to trade, or MARGINAL RATE OF
  SUBSTITUTION (x for y) (MRSxy), along this
  contract curve

Pareto Efficiency Condition
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The Contract Curve
Susan
O
r
Food
O
s
Video Games
Maka
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MATH House and Chase

• Assume that house and Chase have the following
  utilities and MRS for books and coffee

The Pareto Efficiency Condition therefore becomes
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MATH House and Chase

• If there are 10 books, and 4 cups of coffee, then
  the contract curve is expressed as

If House has 6 books, a pareto efficient
allocation would be
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MATH House and Chase

• Therefore, House would have 6 books and 2.4 cups
  of coffee, and Chase would have 4 (10-6) books
  and 1.6 (4-2.4) cups of coffee, for utilities of

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Theory - Starting PointEconomy with production

• A production economy can be analyzed using the
  PRODUCTION POSSIBILITIES CURVE/FRONTIER
• The PPC shows all combinations of 2 goods that
  can be produced using available inputs
• The slope of the PPC shows how much of one good
  must be sacrificed to produce more of the other
  good, or MARGINAL RATE OF TRANSFORMATION (x for
  y) (MRTxy)
• Note that although the slope is negative, the
  negative is assumed and rarely shown in simple
  calculations

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Production Possibilities Curve
Here the MRTSpr is equal to (7-5)/(2-1)-2, or
two robots must be given up for an extra pizza.
10
9
8
The marginal cost of the 3rd pizza, or MCp2
robots
7
6
The marginal cost of the 6th and 7th robots, or
MCr1 pizza
Robots
5
4
Therefore, MRTxyMCx/MCy
3
2
Therefore, MRTpr2/12
1
1
2
3
4
5
6
7
8
Pizzas
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Efficiency and Production

• If production is possible in an economy, the
  Pareto efficiency condition becomes

• Assume MRTpr3/4 and MRSpr2/4.
• -Therefore Maka could get 3 more robots by
  transforming 4 pizzas
• -BUT Maka only needs to get 2 robots for 4 pizzas
  to maintain utility
• -Therefore his utility increases from the extra
  robot, Pareto efficiency isnt achieved

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Efficiency Production Example

• From the PPC, we know that

• We can therefore reinterpret Pareto efficiency
  as

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Theory - First Fundamental Theorem Of Welfare
Economics

• IF
• All consumers and producers act as perfect
  competitors (no one has market power)
• and
• 2) A market exists for each and every commodity
• Then
• Resource allocation is Pareto Efficient

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First Fundamental Theorem of Welfare Economics
Origins

• From microeconomic consumer theory, we know that

• Since prices are the same for all people

• Therefore economic theory gives us the first part
  of Pareto efficiency

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First Fundamental Theorem of Welfare Economics
Origins

• From basic economic theory, a perfect competitive
  firm produces where PMC, therefore

• But we know that MRT is the ratio of MCs,
  therefore

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First Fundamental Theorem of Welfare Economics
Origins

• Again from microeconomic consumer theory, this
  changes to

• Which satisfies the second requirement of Pareto
  Efficiency
• Therefore, we can expand Pareto Efficiency to
  imply that

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Efficiency?Fairness

• If Pareto Efficiency was the only concern,
  competitive markets automatically achieve it and
  there would be very little need for government
• Government would exist to protect property rights
• Laws, Courts, and National Defense
• But Pareto Efficiency doesnt consider
  distribution. One person could get all societys
  resources while everyone else starves. This
  isnt typically socially optimal.

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Fairness
Susan
O
r
Points A and B are Pareto efficient, but either
Susan or Maka get almost all societys resources
B
C
Food
A
Many would argue C is better for society, even
though it is not Pareto efficient
O
s
Video Games
Maka
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Fairness

• For each utility level of one person, there is a
  maximum utility of the other
• Graphing each utility against the other gives us
  the UTILITY POSSIBILITIES CURVE
• Just as typical utility is a function of goods
  consumed Uf(x,y), societal utility can be seen
  as a function of individual utilities Wf(U1,U2)
• This is referred to as the SOCIAL WELFARE
  FUNCTION, and can produce SOCIAL INDIFFERENCE
  CURVES

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Utility Possibilities Curve
All points on the curve are Pareto efficient,
while all points below the curve are not. Any
point above the curve is unobtainable
B
Makas Utility
C
A
O
Susans Utility
Maka
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Typical Social Indifference Curves
An indifference curve farther from the origin
represents a higher level of social welfare.
Makas Utility
O
Susans Utility
Maka
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Fairness

• If we superimpose social indifference curves on
  top of the utilities possibilities curve, we can
  find the Pareto efficient point that maximizes
  social welfare
• This leads us to the SECOND FUNDAMENTAL THEOREM
  OF WELFARE ECONOMICS

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Maximizing Social Welfare
ii is preferred to i, even though ii is not
Pareto efficient
i
ii
The highest possible social welfare, iii, is
Pareto efficient
Makas Utility
iii
O
Susans Utility
Maka
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Second Fundamental Theorem of Welfare Economics

• The SECOND FUNDAMENTAL THEOREM OF WELFARE
  ECONOMICS states that society can attain any
  Pareto efficient allocation of resources by
  making a suitable assignments of original
  endowments, and then letting people trade
• -Roughly, by redistributing income, society can
  pick the starting point in the Edgeworth box,
  therefore obtaining a desired point on the
  Utility Possibility Frontier

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Second Fundamental Theorem of Welfare Economics
Susan
O
r
Starting Point
Goal
Food
O
s
Video Games
Maka
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Why Income Redistribution?

• Why achieve equity through income redistribution
  instead of taxes/penalties and subsidies/incentive
  s?
• Taxes and penalties punish income-enhancing
  behavior, encouraging people to work less.
• Subsidies and incentives give an incentive to
  stay in a negative state to keep receiving
  subsidies and incentives.
• Lump sum transfers have the least distortion.

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Why Is Government so Big?

• Government has to ensure property laws are
  protected. (1st Theorem)
• Government has to redistribute income to achieve
  equity. (2nd Theorem)
• Often the assumptions of the First Welfare
  Theorem do not hold (Chapter 3)

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Welfare Economics Limitations

• We Assume Government exists to maximize the
  utility of its citizens.
• Government could aim to Be a global power,
  achieve cultural goals, achieve religious goals,
  etc.
• Pluswhat if people want to sit on the couch all
  day, watching the Biggest Loser?
• Should the government support this activity?

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Merit Goods

• Merit Good commodities that should be provided
  even if society
• doesnt want them ie police/fluorine in water
• And/Or
• b) is unwilling to cover their cost in the free
  market
• ie Canadian Broadcast Corporation (CBC)

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Welfare Economics Evaluation

• -Welfare Economics is concerned with RESULTS, not
  PROCESS
• -is the HOW important?
• -contract law?
• -Old Testament law?
• -Lottery?
• -Free-for-all wrestling match?

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Welfare Economics Evaluation

• Welfare Economics asks 3 questions of every
  government action
• Will it have desirable distributional
  consequences?
• Will it enhance efficiency?
• Is the cost reasonable?
• -Although these questions may be difficult to
  answer, they provide direction, and if they are
  all no, the government shouldnt interfere