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FUNDAMENTALS OF WELFARE ECONOMICS
2. Market efficiency
2.1. The invisible hand of competitive markets
2.2. Welfare economics and Pareto efficiency
2.3. Analyzing economic efficiency
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Market efficiencywelfare economics and Pareto efficiency
WELFARE ECONOMICS is the branch of economics that focuses on normativeissues:
what should be produced,
how it should be produced,
for whom,
who should make these decisions.
PARETO EFFICIENCY:Resource allocations that have the property that no one can be made better
off without someone being made worse off are said to be Paretoefficient, or Pareto optimal.
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Market efficiencywelfare economics and Pareto efficiency
Pareto efficiency and individualism:
The criterion of Pareto efficiency is concerned only with each individualswelfare, not with the relative well-being of different individuals.
It is each individuals perception of her own welfare function that counts.This is consistent with the general principle of CONSUMER SOVEREIGNTY,which holds that individuals are the best judge of their own needs andwants, of what is in their best interest.
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Market efficiencywelfare economics and Pareto efficiency
FUNDAMENTAL THEOREMS
OF WELFARE ECONOMICS:
Every competitive economy is Pareto efficient
Every Pareto efficient resource allocation can be attained
through a competitive market mechanism, with the
appropriate initial redistributions.
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Market efficiencywelfare economics and Pareto efficiency
EFFICIENCY FROM THE
PERSPECTIVE OD A SINGLEMARKET
In deciding how much to demand,individuals equate the marginalbenefit they receive fromconsuming an extra unit with the
marginal cost, the price they haveto pay.
In deciding how much to supply, firmsequate the marginal benefit theyreceive, which is just the price,with the marginal cost.
At the market equilibrium, wheresupply equals demand, themarginal benefit (to consumers) isequal to the marginal cost to firms
and each equals the price
Price
Quantity
E
Supply
curve
Demand
curve
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Market efficiencyanalyzing economic efficiency
EXCHANGE EFFICIENCY
concerns the distribution of goods,
means that, given the set of goods available in the economy,no one can be made better off without someone else being
made worse off.
It requires that there is no scope for trades, or exchanges thatwould make both parties better off.
It requires that all individuals have the same marginal rate ofsubstitution between any pair of commodities.
Competitive markets in which all individuals face the sameprices always have exchange efficiency.
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Market efficiencyanalyzing economic efficiency
Robinsons Budget Constraint
Given income of $100, the price of oranges of
$2, and the price of apples of $1, an
individual can purchase any combinationof apples and oranges along or to the left
the budget constraint.
The slope of the budget constraint is based
on the relative price of oranges andapples.
Apples
Oranges
Budgetconstraint
100
50
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Market efficiencyanalyzing economic efficiency
THE CONSUMERSCHOICE PROBLEM
The budget constraint gives thecombinations of apples & orangesthat Robinson can buy, given hisincome & given the price of apples& oranges.
The indifference curve gives thosecombinations of apples & orangesamong which Robinson isindifferent.
Robinson chooses the point along thebudget constraint which he mostprefers, that is, the point wherethe indifference curve I0is tangentto the budget constraint (point E).
E
B
A
D C
F
I0
I1
100
50 59 6017 18
18
17
89
80
Apples
Oranges
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Exchange
Two consumers, A and B. Their endowments of goods 1 and 2 are
E.g.
The total quantities available
A A A ( , )1 2
B B B ( , ).1 2
and
A ( , )6 4 B ( , ) .2 2and
1 1 6 2 8A B 2 2 4 2 6
A B
units of good 1
units of good 2.and
are
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Exchange
Edgeworth and Bowley devised a diagram,
called an Edgeworth box, to show all possible
allocations of the available quantities of goods
1 and 2 between the two consumers.
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Starting an Edgeworth Box
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Starting an Edgeworth Box
Width =1 1 6 2 8A B
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Starting an Edgeworth Box
Width =1 1 6 2 8A B
Height =
2 24 2
6
A B
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Starting an Edgeworth Box
Width =1 1 6 2 8A B
Height =
2 24 2
6
A B
The dimensions of
the box are the
quantities available
of the goods.
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Feasible Allocations
What allocations of the 8 units of good 1and the 6 units of good 2 are feasible?
How can all of the feasible allocations be
depicted by the Edgeworth box diagram?
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Feasible Allocations
What allocations of the 8 units of good 1and the 6 units of good 2 are feasible?
How can all of the feasible allocations be
depicted by the Edgeworth box diagram? One feasible allocation is the before-trade
allocation; i.e. the endowment allocation.
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Width =1 1 6 2 8A B
Height =
2 24 2
6
A B
The endowment
allocation is
A ( , )6 4
B ( , ) .2 2
and
The Endowment Allocation
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Width =1 1 6 2 8A B
Height =
2 24 2
6
A B
A ( , )6 4 B ( , )2 2
The Endowment Allocation
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A ( , )6 4OA
OB
6
8
B ( , )2 2
The Endowment Allocation
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A ( , )6 4OA
OB
6
8
4
6
The Endowment Allocation
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B ( , )2 2
OA
OB
6
8
4
6
2
2The Endowment Allocation
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A ( , )6 4 B ( , )2 2
OA
OB
6
8
4
6
2
2
The
endowment
allocation
The Endowment Allocation
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More generally,
The Endowment Allocation
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The Endowment Allocation
OA
OB
The
endowment
allocation
1 1
A B
2A
2
2
A
B
1A
1B
2B
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Other Feasible Allocations
denotes an allocation to consumerA.
denotes an allocation to consumer
B. An allocation is feasibleif and only if
( , )x xA A1 2
( , )x xB B1 2
x xA B A B1 1 1 1x xA B A B2 2 2 2 .and
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Feasible Reallocations
OA
OB
1 1
A B
xA
2
2
2
A
B
xA1
xB1
xB2
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Feasible Reallocations
OA
OB
1 1
A B
xA2
2
2
A
B
xA1
xB1
xB2
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Feasible Reallocations
All points in the box, including the boundary,
represent feasible allocations of the combined
endowments.
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Feasible Reallocations
All points in the box, including the boundary,
represent feasible allocations of the combined
endowments.
Which allocations will be blocked by one or
both consumers?
Which allocations make both consumers
better off?
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Adding Preferences to the Box
2A
1A
xA
2
xA1
OA
For consumer A.
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Adding Preferences to the Box
2A
1A
xA
2
xA1
For consumer A.
OA
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Adding Preferences to the Box
2B
1B
xB
2
xB1
For consumer B.
OB
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Adding Preferences to the Box
xB
2
xB1
For consumer B.
OB
2B
1B
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Adding Preferences to the Box
2B
1B
xB
1
xB2
For consumer B.OB
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Adding Preferences to the Box
2A
1A
xA
2
xA1
OA
For consumer A.
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Adding Preferences to the Box
2A
1A
xA
2
xA1
OA
2B
1BxB1
xB2
OB
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Edgeworths Box
2
A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
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Pareto-Improvement
An allocation of the endowment that
improves the welfare of a consumer without
reducing the welfare of another is a Pareto-
improving allocation.
Where are the Pareto-improving allocations?
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Edgeworths Box
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
P t I t
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Pareto-Improvements
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The set of Pareto-
improving allocations
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Pareto-Improvements
Since each consumer can refuse to trade, the
only possible outcomes from exchange are
Pareto-improving allocations.
But which particular Pareto-improving
allocation will be the outcome of trade?
P t I t
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Pareto-Improvements
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The set of Pareto-
improving reallocations
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Pareto-Improvements
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Pareto-Improvements
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Pareto-Improvements
Trade
improves both
As and Bs welfares.
This is a Pareto-improvementover the endowment allocation.
P t I t
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Pareto-ImprovementsNew mutual gains-to-trade region
is the set of all further Pareto-
improving
reallocations.
Trade
improves both
As and Bs welfares.
This is a Pareto-improvementover the endowment allocation.
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Pareto-ImprovementsFurther trade cannot improve
both A and Bs
welfares.
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Pareto-Optimality
Better for
consumer B
Better for
consumer A
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Pareto-OptimalityA is strictly better off
but B is strictly worseoff
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Pareto-OptimalityA is strictly better off
but B is strictly worseoff
B is strictly betteroff but A is strictly
worse off
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Pareto-OptimalityA is strictly better off
but B is strictly worseoff
B is strictly betteroff but A is strictly
worse off
Both A and
B are worse
off
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Pareto-OptimalityA is strictly better off
but B is strictly worseoff
B is strictly betteroff but A is strictly
worse off
Both Aand B are
worse
off
Both A and
B are worse
off
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Pareto-Optimality
The allocation is
Pareto-optimalsince the
only way one consumers
welfare can be increased is to
decrease the welfare of the other
consumer.
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Pareto-Optimality
The allocation is
Pareto-optimal since the
only way one consumers
welfare can be increased is to
decrease the welfare of the other
consumer.
An allocation where convex
indifference curves are only
just back-to-back is
Pareto-optimal.
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Pareto-Optimality
Where are all of the Pareto-optimal
allocations of the endowment?
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Pareto-Optimality
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Pareto-Optimality
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
All the allocations marked by
a are Pareto-optimal.
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Pareto-Optimality
The contract curveis the set of all Pareto-
optimal allocations.
Pareto-Optimality
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Pareto-Optimality
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
All the allocations marked by
a are Pareto-optimal.
The contract curve
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Pareto-Optimality
But to which of the many allocations on the
contract curve will consumers trade?
That depends upon how trade is conducted.
In perfectly competitive markets? By one-on-
one bargaining?
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The Core
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The set of Pareto-
improving reallocations
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The Core
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The Core
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The Core
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Pareto-optimal trades blocked
by B
Pareto-optimal trades blocked
by A
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The Core
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The Core
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Pareto-optimal trades not blocked
by A or B are the core.
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The Core
But which core allocation?
Again, that depends upon the manner in
which trade is conducted.
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Trade in Competitive Markets
Consider trade in perfectly competitive
markets.
Each consumer is a price-taker trying to
maximize her own utility given p1, p2and herown endowment. That is, ...
Trade in Competitive Markets
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Trade in Competitive Markets
2
A
1A
xA2
xA1
OA
For consumer A.
p x p x p pA A A A1 1 2 2 1 1 2 2
x A2*
x A1*
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Trade in Competitive Markets
So given p1and p2, consumer As net demands
for commodities 1 and 2 are
x A A1 1* x A A2 2* .and
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Trade in Competitive Markets
And, similarly, for consumer B
Trade in Competitive Markets
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Trade in Competitive Markets
2B
1B
xB2
xB1
For consumer B.
OB
x B1*
x B2*
p x p x p pB B B B1 1 2 2 1 1 2 2
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Trade in Competitive Markets
So given p1and p2, consumer Bs net demands
for commodities 1 and 2 are
x B B1 1* x B B2 2* .and
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Trade in Competitive Markets
A general equilibriumoccurs when prices p1and p2cause both the markets for
commodities 1 and 2 to clear; i.e.
x xA B A B1 1 1 1* *
x xA B A B
2 2 2 2* *
.and
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Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Can this PO allocation be
achieved?
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
x A2*
x A1*
Trade in Competitive Markets
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A2*
x A1*
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A2*
x A1*
x B
1
*
x B2*
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A2*
x A1*
x B
1
*
x B2*
But
x xA B A B
1 1 1 1* *
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A2*
x A1*
x B
1
*
x B2*
and
x xA B A B
2 2 2 2* *
T d i C i i M k
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Trade in Competitive Markets
So at the given prices p1and p2there is an
excess supply of commodity 1
excess demand for commodity 2.
Neither market clears so the prices p1and p2do not cause a general equilibrium.
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
So this PO allocation cannot be
achieved by competitive trading.
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Which PO allocations can be
achieved by competitive trading?
T d i C titi M k t
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Trade in Competitive Markets
Since there is an excess demand forcommodity 2, p2will rise.
Since there is an excess supply of commodity
1, p1will fall.
The slope of the budget constraints is - p1/p2
so the budget constraints will pivot about the
endowment point and become less steep.
Trade in Competitive Markets
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Which PO allocations can be
achieved by competitive trading?
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Which PO allocations can be
achieved by competitive trading?
Trade in Competitive Markets
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p
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Which PO allocations can be
achieved by competitive trading?
Trade in Competitive Markets
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
x A
2
*
x A1*
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A
2
*
x A1*
Trade in Competitive Markets
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A
2
*
x A1*
x B1*
x
B
2
*
Trade in Competitive Markets
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A
2
*
x A1*
x B1*
x
B
2
*
So
x xA B A B
1 1 1 1
* *
Trade in Competitive Markets
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2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A
2
*
x A1*
x B1*
x
B
2
*
and
x xA B A B
2 2 2 2
* *
Trade in Competitive Markets
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Trade in Competitive Markets
At the new prices p1
and p2
both markets
clear; there is a general equilibrium.
Trading in competitive markets achieves a
particular Pareto-optimal allocation of the
endowments.
This is an example of the First Fundamental
Theorem of Welfare Economics.
Market efficiencyanalyzing economic efficiency
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PRODUCTION EFFICIENCY
It requires that, given the set of resources, the economy not be able toproduce more of one commodity without reducing the output of someother commodity.
The economy must be operating along its production possibility curve.
It requires that all firms have the same marginal rate of technicalsubstitution (MRTS) between any pair of inputs.
Competitive markets in which firms face the same prices always haveproduction efficiency.
Market efficiencyanalyzing economic efficiency
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PRODUCTION EFFICIENCY &THE PRODUCTION POSSIBILITIESFRONTIER
Points inside the frontier areattainable but inefficient.
Points along the frontier are feasible& efficient.
Points outside the frontier areunattainable, given the resources
of the economy.
Apples
Oranges
Production
Possibilities
Frontier
Market efficiencyanalyzing economic efficiency
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ISOQUANTS & ISOCOST LINES
An isoquant gives combinations of inputs(land & labor) which yeald the same
output.
The slope of the isoquant is the MRTS.
The isocost line gives those combinations ofinputs which cost the same amount.
The slope of the isocost line is given by therelative prices of the two inputs.
The firm maximizes its output, given aparticular level of expenditures oninputs, at the point where the isoquant istangent to the isocost line.
At that point, the MRTS equals the relativeprice.
Land
Labor
Q1
Q0
Isoquants
Isocost line
Labor input into apples
A 0
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PRODUCTION EFFICIENCY
The sides of this Edgeworth-Bowley Box give the available supplies ofresourcesland & labor.
It requires the tangency of the isoquants.
At tangency points (such as E) MRTS of land for labor is the same in theproduction of apples & oranges.
Apple
isoquants
E
Orangeisoquant
Apple
isoquants
D C
Land input
into oranges
Labor input into oranges
Land inputinto apples
Land
Labor
A
B
0
0
B
A
Q1
Q0
Q2
Market efficiencyanalyzing economic efficiency
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PRODUCT MIX EFFICIENCY
It requires that the marginal rate of transformation (MRT)the
slope of the production possibilities curveequal
individuals marginal rate of substitution (MRS)
Competitive markets have product mix efficiency.
Market efficiencyanalyzing economic efficiency
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PRODUCT MIX EFFICIENCYrequires that MRT equal
consumers MRS
In order to reach the highest level ofconsumers utility, the
indifference curve & the
production possibilities schedule
must be tangent (point E).
E
Indifference curves
Production
Possibilities Curve
Apples
Oranges
E
Market efficiencyanalyzing economic efficiency
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Basic conditions for Pareto efficiency:
1. EXCHANGE EFFICIENCY: MRS between any two goodsmust be the same for all individuals.
2. PRODUCTION EFICIENCY: MRTS between any two inputsmust be the same for all firms.
3. PRODUCT MIX EFFICIENCY: MRT must equal MRS.
Competitive economies satisfy all three conditions