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GENERAL EQUILIBRIUM
(under construction)
- how to link individual consumer, firm and market to economy
as a whole
- Partial Equilibrium Analyses investigate changes in one
market assuming that conditions in other markets do not change.
- General Equilibrium Analyses investigate changes in ways
that include interrelationships with other markets and changes that might
occur there.
- basic assumption: perfect competition
1. GENERAL
(M&Y 10th
Fig. 16.1; M&Y 11th Fig. 16.1; B&B Fig. 16.4; B&Z not displayed)
All factors of production are owned by consumers and each consumer supplies inputs
of capital (K) and labour (L) according to their preference.
All output (x, y) is produced by firms according to their profit
maximization possibilities.
The quantity of K & L is fixed. The
maximum amount of x or y that can be produced using K & L is fixed with all
possible combinations of x & y that can be produced defining a production
possibility frontier (see point 7 below).
Consumers choose preferred market baskets subject
budget constraint. It is assumed that an initial distribution of
income exists and prices are fixed. Conditions for consumer
equilibrium:
-
the Marginal Rate of Substitution (MRS = MUy/MUx) equals the
slope of the Budget Line ;
-
the MRS also equals -1/(/Px/Py); and,
-
a 'rationale' consumer will equate the MU per dollar of each
commodity consumed, i.e. MUx/Px = MUy/Py .
Every firm maximizes profits subject to constraints fixed
by technology, demand for product and price of inputs.
Conditions:
Long Run Economic Profits are zero for every firm.
The quantity demanded equals the quantity supplied for all
products and inputs.
2. EXISTENCE
The Existence of General Equilibrium has been proven -
theoretically.
This existence can be illustrated by counting equations and
variables that characterize equilibrium.
This counting procedure is not, however, the proof.
3. EDGEWORTH
BOX FOR CONSUMPTION (M&Y 10th Fig.
16.2;
M&Y 11th Fig. 16.2; B&B Fig. 16.3; B&Z not displayed)
Edgeworth Box for consumption reflects allocation of fixed supplies of
goods between consumers (M&Y 10th Fig.
16.4, M&Y 11th Fig. 16.3; B&B Fig. 16.15; B&Z not displayed) assuming initial income distribution
Exchange between consumers represented by movement within Edgeworth
Box
4. CONTRACT CURVE
IN CONSUMPTION (M&Y 10th Fig.
16.2;
M&Y 11th Fig. 16.2; B&B Fig. 16.3; B&Z not displayed)
-
Gven initial income distribution (at P) off contract curve,
MRS for consumer different allows for Pareto optimum change making one
person better off without making the other worse off; outcome depends on
bargaining power of the parties
-
Exchange equilibrium where there is equality in the
Marginal Rates of Substitution, i.e., MRS of consumer 1 = MRS of consumer 2
(or more)
-
The Contract Curve highlights all points within an Edgeworth Box that can serve as Exchange Equilibria, i.e., all points for which the MRS of both people are equal or all points for which the indifference curves of both people
are tangent to one another.
5. EDGEWORTH
BOXES FOR PRODUCTION (M&Y
10th
Fig. 16.3; not displayed M&Y 11th, B&B, B&Z)
-
Given inital endowment of factors off contract curve (z),
MRTS for producers different allows for Pareto optimum exchange making one
producers output higher without lowering output of the other
-
Edgeworth Boxes illustrates allocation of fixed
supplies of inputs between the production of two types of goods.
-
Equilibrium in Production is achieved when the Marginal Rates of
Technical Substitution in the production of the goods are equal (M&Y 10th
Fig. 16.5; M&Y 11th Fig. 16.5; B&B Fig. 16.17; B&Z not displayed).
6. CONTRACT
CURVE IN PRODUCTION
The Contract Curve in a Production Edgeworth Box highlights
all points that can serve as Exchange Equilibria between the production of
two goods, i.e., all points for which the MRTS in the production of both
goods are equal or all points for which the isoquants of both goods are
tangent to one another (M&Y 10th
Fig. 16.5; M&Y 11th Fig. 16.5; B&B Fig. 16.17; B&Z not displayed).
7. CONTRACT CURVE AND THE PRODUCTION POSSIBILITY FRONTIER
Points on this Contract Curve identify combinations of
outputs for two goods that support a Production Possibility Frontier (M&Y
10th Fig.
16.6; M&Y 11th Fig. 16.6; B&B Fig. 16.18; B&Z not displayed).
8.
MARGINAL RATE OF PRODUCT TRANSFORMATION
The Marginal Rate of Product Transformation reflects the
rate at which an economy can transform one good into another by reallocating
inputs along a contract curve (M&Y 10th Fig.
16.7, M&Y 11th Fig. 16.7; B&B & B&Z not displayed).
The MRPT is the slope of a Production Possibility Frontier
at a specific point.
9. OPTIMALITY
The optimal allocation of inputs picks a point of the
Frontier for which the underlying Exchange Equilibrium can support a common MRS for consumption that equals the MRPT, i.e., the Marginal Rate of Product
Transformation.
10. SUMMARY
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general equilibrium occurs when there is a simultaneous
equilibrium in all markets assuming perfect competition
-
in production, exchange equilibrium (between inputs) exists
where producers of different goods share the same MRTS (contract curve in
production)
-
from the contract curve in production, the PPC can be
derived
-
in consumption, exchange equilibrium (between goods) exists
where consumers share the same MRS (contract curve in consumption)
-
from the contract curve in consumption, the point of
production on the PPC will be where the MRPT (slope of PPC) equals
consumer MRS between goods (contract curve in consumption) assuming an
initial distribution of income (goods) between consumers
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