7/27/2019 Eaton Micro 6e Ch13
1/32
7/27/2019 Eaton Micro 6e Ch13
2/32
2005 Pearson Education Canada Inc.13.2
General Equilibrium
Earlier chapters dealt with a partial equilibriumframework (characterized by a market-tomarket equilibrium).
This chapter widens the perspective by fittingall the analytical pieces together into one largepicture of efficiency in an economy widecontext.
This framework considers all markets in theeconomy simultaneously and is known as ageneral equilibrium analysis.
7/27/2019 Eaton Micro 6e Ch13
3/32
2005 Pearson Education Canada Inc.13.3
Preference Assumptions
1. Indifference curves are convex tothe appropriate origin.
2. Indifference curves are smooth.
3. Both goods are essential for allconsumers.
4. The thing that affects well-beingare the quantities of the two goodsconsumed.
7/27/2019 Eaton Micro 6e Ch13
4/32
2005 Pearson Education Canada Inc.13.4
Figure 13.1 The Edgeworth box diagram
7/27/2019 Eaton Micro 6e Ch13
5/32
7/27/2019 Eaton Micro 6e Ch13
6/32
2005 Pearson Education Canada Inc.13.6
Efficiency in Consumption
Given the assumptions previouslystated:
An allocation of goods is Pareto-optimal in a many person exchangeeconomy if MRS is identical for allindividuals.
7/27/2019 Eaton Micro 6e Ch13
7/32
7/27/2019 Eaton Micro 6e Ch13
8/32
2005 Pearson Education Canada Inc.13.8
Figure 13.2 The contract curve
7/27/2019 Eaton Micro 6e Ch13
9/32
2005 Pearson Education Canada Inc.13.9
Figure 13.3 Budget lines in an exchange economy
7/27/2019 Eaton Micro 6e Ch13
10/32
2005 Pearson Education Canada Inc.13.10
Figure 13.4 Competitive equilibrium in
an exchange economy
7/27/2019 Eaton Micro 6e Ch13
11/32
2005 Pearson Education Canada Inc.13.11
From Figure 13.4
The initial allocation is at point A.
Given the announced price, line AE* isthe budget line for Shelly and Marvin.
Since they will both choose E*, theannounced price is a competitiveequilibrium price and E* is a competitive
allocation.Since E* is on the contract curve, the
competitive equilibrium is Pareto-optimal.
7/27/2019 Eaton Micro 6e Ch13
12/32
2005 Pearson Education Canada Inc.13.12
Walras Law
When there are n markets in ageneral equilibrium model, Walraslaw states that if demand is equal to
supply in n-1 markets, then thedemand is equal to supply in the nthmarket as well.
7/27/2019 Eaton Micro 6e Ch13
13/32
2005 Pearson Education Canada Inc.13.13
First Theorem of Welfare
Economics
Given the assumptions made, thecompetitive equilibrium allocation ofa many person exchange economy is
Pareto-optimal.
In other words, all gains from tradeare realized in a competitive
equilibrium.
7/27/2019 Eaton Micro 6e Ch13
14/32
2005 Pearson Education Canada Inc.13.14
Second Theorem of Welfare
Economics
With the assumed preferences, given anyPareto-optimal allocation, there is an initialallocation such that, given the initial
allocation, the Pareto-optimal allocation isthe competitive equilibrium allocation.
(From Figure 13.4, this says that anyallocation on the budget line will produce E*,
the competitive equilibrium).
7/27/2019 Eaton Micro 6e Ch13
15/32
2005 Pearson Education Canada Inc.13.15
Efficiency in General Equilibrium
with Production
Production Assumptions:
1. Isoquants are smooth and convex.
2. Both inputs are essential inproducing both goods.
3. Production functions exhibit
constant returns to scale.4. Production involves no externalities.
7/27/2019 Eaton Micro 6e Ch13
16/32
2005 Pearson Education Canada Inc.13.16
Efficiency in Consumption
Condition
Efficiency in consumption requiresthat MRS is identical for allindividuals.
In other words, the allocation toindividual consumers of the goodsproduced in an economy must be
Pareto-optimal.
7/27/2019 Eaton Micro 6e Ch13
17/32
2005 Pearson Education Canada Inc.13.17
Figure 13.5 The production possibilities set
7/27/2019 Eaton Micro 6e Ch13
18/32
2005 Pearson Education Canada Inc.13.18
Efficiency In Production
Efficiency in production requires thatthe combination of goods actuallyproduced must be on the production
possibility frontier (PPF).
Efficiency in production Condition:
Efficiency in production requires thatthe MRTS must be identical for allfirms.
7/27/2019 Eaton Micro 6e Ch13
19/32
2005 Pearson Education Canada Inc.13.19
Figure 13.6 An Edgeworth box for production
7/27/2019 Eaton Micro 6e Ch13
20/32
2005 Pearson Education Canada Inc.13.20
Efficiency in the Product Mix
This condition concerns the interfacebetween production and consumption.
The absolute value of the slope of the PPF
is known as the marginal rate oftransformation (MRT).
The MRTmeasures the opportunity cost
of the economy as a whole for a smallincrease in the amount of good 1 relativeto good 2.
7/27/2019 Eaton Micro 6e Ch13
21/32
2005 Pearson Education Canada Inc.13.21
Figure 13.7 The marginal rate of transformation
7/27/2019 Eaton Micro 6e Ch13
22/32
2005 Pearson Education Canada Inc.13.22
Marginal Rate of Transformation
The marginal rate of transformationcan be expressed in terms of themarginal products in two different
but equivalent ways:
MRTS=MP12/MP1
1 = MP22/MP2
1
7/27/2019 Eaton Micro 6e Ch13
23/32
2005 Pearson Education Canada Inc.13.23
Efficiency in the Product Mix
Efficiency in the Product Mix Condition:
Efficiency in the product mix requiresthat each consumers MRS be identicalto the economys MRT.
7/27/2019 Eaton Micro 6e Ch13
24/32
2005 Pearson Education Canada Inc.13.24
Figure 13.8 Efficiency in product mix
7/27/2019 Eaton Micro 6e Ch13
25/32
2005 Pearson Education Canada Inc.13.25
Efficient Allocation of resources
Each of the three efficiency conditions isnecessary for an efficient allocation ofresources:
1.
Efficiency in consumption requires that MRS isidentical for all individuals.
2. Efficiency in production requires that theMRTS must be identical for all firms.
3. Efficiency in the product mix requires thateach consumers MRS be identical to theeconomys MRT.
7/27/2019 Eaton Micro 6e Ch13
26/32
7/27/2019 Eaton Micro 6e Ch13
27/32
2005 Pearson Education Canada Inc.13.27
Figure 13.9 Efficiency in product mix for
general competitive equilibrium
7/27/2019 Eaton Micro 6e Ch13
28/32
7/27/2019 Eaton Micro 6e Ch13
29/32
2005 Pearson Education Canada Inc.13.29
Figure 13.10 Trade between Two Countries
7/27/2019 Eaton Micro 6e Ch13
30/32
2005 Pearson Education Canada Inc.13.30
Sources of Inefficiency
What produces an inefficient allocationof resources?
There are many potential sources ofinefficiencies, one is a monopoly.
7/27/2019 Eaton Micro 6e Ch13
31/32
7/27/2019 Eaton Micro 6e Ch13
32/32
2005 Pearson Education Canada Inc.13 32
Monopoly and Inefficiency
For a monopoly the inefficiencyarises from a distortion of theproduct mix.
The inefficiency arises because theprofit maximizing monopolistproduces where MRMRT and the allocation ofresources is inefficient.