Download General equilibrium

Institute of Economic Theories - University of Miskolc
Microeconomics
General equilibrium
Mónika Kis-Orloczki
Assistant lecturer
Subject of the examination
• Can a general equilibrium evolve, that could mean
equilibrium in all markets, if all the economic agents
would like to enforce their interests
• If the resources are the same, and they have fixed
amounts, and we produce only two goods from them,
what allocation does ensure the Pareto-optimal inputemployment which ensures the profit-maximization.
Conditions of the examination
• Economic agents aim at optimization
• Convex indifference curves and isoquant curves 
Law of diminishing marginal utility and of diminishing
returns
• No externalities
• The conditions of the pure competition are fulfilled
The general equilibrium of PRODUCTION
without prices
• 2 inputs (L, K) and 2 outputs (x, y)
• Fixed quantity of input
• Examination in the Edgeworth box: a graphical tool
that shows the isoquant map of two products turned
opposite to each other. The size of the box is determined
by the quantity of the available inputs.
Edgeworth-box of production
Starting from Point D
• From the point of view of the production of X, all the
allocations are more efficient that are on higher
isoquant curves (above D)
• Same is true for Y (under D)
• The area marked with blue lines: Shows allocations that
are advantageous for both products  Pareto-efficient
combinations
• There is an endless number of isoquants in the isoquant
map, so when the marked area becomes only one
pointthe 2 isoquants are tangents Pareto-optimal
point, the final allocation
• In the Pareto-optimal point the slope of the tangents of
the isoquant curves are equal, MRTSX = MRTSY  the
relative productivity of the inputs are equal in the two
sectors
• In a Edgeworth box there is an endless number of
Pareto-optimal points
• Contract curve of production(CC): Points that
represent the final,Pareto-efficient input allocations, at
a given quantity of input and technology. (set of all
Pareto-efficient points in the Edgeworth box)
• Shape of the curve is determined by the number of
inputs available and by the isoquant that expresses the
technology of the production.
Contract Curve of production(CC)
Production-possibility Frontier
• Production-possibility Frontier (PPF) or Production
possibility Curve a graph in the system of coordinates of
two goods that represents the Pareto-optimal output levels
at a Pareto-efficient employment of resources.
Y
A: Maximum output at an efficient
input employment
B
A
B: This production can’t be realized
at a fixed number of inputs
C: Not efficient input use or not all
the inputs are employed
C
PPF
X
Marginal Rate of Transformation
• The slope of the production-possibility frontier (PPF) at any
given point is called the Marginal Rate of Transformation
(MRT). It shows by how many we must decrease the
production of Y in order to increase the production of X by
one unit.
dy
MRT  
Y
dx
•The reason for the negative slope
of MRT is the scarcity of resources
MRT
PPF
1
2
3
X
•The PPF is concavethe MRT is
getting steeper and
steeperincreasing alternative
costs = Law of diminishing returns
The general equilibrium of CONSUMPTION
without prices
• 2 consumers: A, B and 2 products: X, Y
• Without pricesBarter
• Examination in the Edgeworth box of exchange: a
graphical tool that is used to analyse the exchange of 2
goods between 2 people. It shows the indifference map of
two products turned opposite to each other. The size is
determined by the total quantity of available products.
• During the exchange non of the actors should get on lower
indifference curve, exchange that are advantageous for both
consumers.
Contract Curve of exchange(CC)
Pareto efficient allocation
• A Pareto efficient allocation can be described as an
allocation where: there is no way to make all people better
off or to make some individual better off without making
someone else worse off. All the gains from trade have been
exhausted or there are no mutually advantageous trades to
be made.
• In this point, the Marginal Rates of Substitution for both
consumers are the same  MRSA=MRSB .
• The Pareto- efficient allocations make up the Contract
Curve of the exchange. (CC)
General equilibrium of the production and
exchange without prices
• The same allocation is determined in two ways:
– By the CC of production by input-vectors
– By the PPF by output-vectors
• All the points on PPF is equivalent of the points of CC, even
the non-efficient points can be depicted under the PPF.
• In the Edgeworth box of exchange in a Pareto-optimal point
no further advantages can be gained by exchange. But by
the production it can be changed: By the rearranging of the
resources the amount of the available products can be
changed.
• The rearranging of resources can be continued until the
MRS of the consumers is not equivalent to the MRT of the
production.  until MRS≠MRT
Y
MRT
MRT
PPF
X
A final allocation of goods is Paretoefficient
if the next conditions are true at the same time:
• The exchange is effective: MRSA=MRSB
• The production is effective: MRTSX =MRTSY
• The criteria of the effectiveness in general:
MRT= MRSA=MRSB
Prices in the model
• We assume perfect competition  actors are pricetakers
• Income:
 IA=PX*WXA+PY*WYA
 IB=PX*WXB+PY*WYB (W=inicial endowment point)
 ILLUSTRATION
 The budget line of the cosumers are equivalent
because their real income is determined by W and
by the rate of prices
• The coordinates of the optimal points show the total demand
of the consumer for the two goods  Gross Demand: the
amount of the products that the consumers would like to
consume taking into account their budget constraint
• The consumer possesses one part of the Gross demand and
wants to get the other part by exchange. This latter is called
the Net Demand.
• The market is not in the state of equilibrium, as the demand
≠supply at this chosen rate of prices, and the amount of the
products that the consumers want to consume is not equal
with the total amount of products available
• New prices will evolve on the market:
– Excess demand: P
– Excess supply: P
• At the new price rate the amount A is willing to buy
equals with the amount B is willing to sell and vice
versa the sum of their Net Demand is 0.
• The MRS of both consumers are equal to the
market price rate, that is called equilibrium price
rate: PX/PY= MRSA=MRSB
• This relation can be deduced from the point of view
of production as well
• The market is in the state of equilibrium:
» Walrasian Equilibrium
» Competitive Equilibrium
» Market Equilibrium
Market equilibrium
• In this state in all the markets of the economy
the equilibrium prices are equal with the
Marginal Costs of the products. The
producers’ surplus is Zero and the Consumers’
surplus is maximal.
• S=D