Download Efficiency in production

Chapter 13
Competitive General Equilibrium
13.1
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General Equilibrium
Earlier chapters dealt with a partial equilibrium
framework (characterized by a market-to
market equilibrium).
 This chapter widens the perspective by fitting
all the analytical pieces together into one large
picture of efficiency in an economy wide
context.
 This framework considers all markets in the
economy simultaneously and is known as a
general equilibrium analysis.

13.2
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Preference Assumptions
1.
2.
3.
4.
13.3
Indifference curves are convex to
the appropriate origin.
Indifference curves are smooth.
Both goods are essential for all
consumers.
The thing that affects well-being
are the quantities of the two goods
consumed.
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Figure 13.1 The Edgeworth box diagram
13.4
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The Edgeworth Box
 When
indifference curves are smooth
and convex, if two are tangent at a
point in an Edgeworth Box, that point
is a Pareto-optimal allocation.
 Given smooth indifference curves, if
MRS at some allocation is identical
for two individuals then that
allocation is Pareto-optimal.
13.5
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Efficiency in Consumption
 Given
the assumptions previously
stated:
An allocation of goods is Paretooptimal in a many person exchange
economy if MRS is identical for all
individuals.
13.6
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The Contract Curve
 All
the points in the Edgeworth box
where the indifference curves are
tangent describes the entire set of
Pareto-optimal allocations.
 A line connecting all these points of
tangency is call the contract curve.
13.7
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Figure 13.2 The contract curve
13.8
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Figure 13.3 Budget lines in an exchange economy
13.9
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Figure 13.4 Competitive equilibrium in
an exchange economy
13.10
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From Figure 13.4
 The
initial allocation is at point A.
 Given the announced price, line AE* is
the budget line for Shelly and Marvin.
 Since they will both choose E*, the
announced price is a competitive
equilibrium price and E* is a competitive
allocation.
 Since E* is on the contract curve, the
competitive equilibrium is Pareto-optimal.
13.11
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Walras’ Law
 When
there are n markets in a
general equilibrium model, Walras’
law states that if demand is equal to
supply in n-1 markets, then the
demand is equal to supply in the nth
market as well.
13.12
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First Theorem of Welfare
Economics
 Given
the assumptions made, the
competitive equilibrium allocation of
a many person exchange economy is
Pareto-optimal.
 In other words, all gains from trade
are realized in a competitive
equilibrium.
13.13
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Second Theorem of Welfare
Economics
With the assumed preferences, given any
Pareto-optimal allocation, there is an initial
allocation such that, given the initial
allocation, the Pareto-optimal allocation is
the competitive equilibrium allocation.
 (From Figure 13.4, this says that any
allocation on the budget line will produce E*,
the competitive equilibrium).

13.14
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Efficiency in General Equilibrium
with Production
Production Assumptions:
1. Isoquants are smooth and convex.
2. Both inputs are essential in
producing both goods.
3. Production functions exhibit
constant returns to scale.
4. Production involves no externalities.
13.15
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Efficiency in Consumption
Condition
 Efficiency
in consumption requires
that MRS is identical for all
individuals.
 In other words, the allocation to
individual consumers of the goods
produced in an economy must be
Pareto-optimal.
13.16
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Figure 13.5 The production possibilities set
13.17
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Efficiency In Production
 Efficiency
in production requires that
the combination of goods actually
produced must be on the production
possibility frontier (PPF).
 Efficiency in production Condition:
Efficiency in production requires that
the MRTS must be identical for all
firms.
13.18
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Figure 13.6 An Edgeworth box for production
13.19
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Efficiency in the Product Mix
 This
condition concerns the interface
between production and consumption.
 The absolute value of the slope of the PPF
is known as the marginal rate of
transformation (MRT).
 The MRT measures the opportunity cost
of the economy as a whole for a small
increase in the amount of good 1 relative
to good 2.
13.20
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Figure 13.7 The marginal rate of transformation
13.21
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Marginal Rate of Transformation
 The
marginal rate of transformation
can be expressed in terms of the
marginal products in two different
but equivalent ways:
MRTS=MP12/MP11 = MP22/MP21
13.22
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Efficiency in the Product Mix
 Efficiency
in the Product Mix Condition:
Efficiency in the product mix requires
that each consumer’s MRS be identical
to the economy’s MRT.
13.23
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Figure 13.8 Efficiency in product mix
13.24
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Efficient Allocation of resources

1.
2.
3.
Each of the three efficiency conditions is
necessary for an efficient allocation of
resources:
Efficiency in consumption requires that MRS is
identical for all individuals.
Efficiency in production requires that the
MRTS must be identical for all firms.
Efficiency in the product mix requires that
each consumer’s MRS be identical to the
economy’s MRT.
13.25
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Efficiency and General Competitive
Equilibrium
 First
Theorem of Welfare Economics:
Given the assumptions made, the
competitive equilibrium of this
general equilibrium model with
production is efficient.
13.26
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Figure 13.9 Efficiency in product mix for
general competitive equilibrium
13.27
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Second Theorem of Welfare
Economics
Given the assumed preferences, given any
Pareto-optimal allocation (POA) of goods,
that is attainable in the model, there is a
distribution of ownership of inputs (DOI)
such that POA is a competitive equilibrium
allocation associated with DOI.
 In other words, to achieve equity,
redistribute the ownership of inputs; to
achieve efficiency, use competitive markets.

13.28
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Figure 13.10 Trade between Two Countries
13.29
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Sources of Inefficiency
 What
produces an inefficient allocation
of resources?
 There are many potential sources of
inefficiencies, one is a monopoly.
13.30
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Monopoly and Inefficiency

1.
2.
13.31
For a monopoly the first 2 efficiency
conditions still hold:
Because all firms face the same
input prices, each chooses an input
bundle so that MRTS=w1e/w2e
Because all consumers face the
same product prices, each chooses
a bundle at which the MRS=p1e/p2e
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Monopoly and Inefficiency



13.32
For a monopoly the inefficiency
arises from a distortion of the
product mix.
The inefficiency arises because the
profit maximizing monopolist
produces where MR<P.
Therefore for all consumers, the
MRS>MRT and the allocation of
resources is inefficient.
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