General Equilibrium (()Welfare Economics) General Equilibrium
Partial Equilibrium: Neglects the way in which changes in one market affect other (product/factor) markets. General E quilib ri um: A nal yses th e way in which the choices of economic agents are co-ordinated across all product and factor markets. Agenda
Exchange Economy – 2 individuals/consumers (A and B) – 2 products (X and Y) Production Economy – 2 products (X and Y) – 2 factors (L and K) General Equilibrium – 2 individuals/consumers (A and B) – 2 products (X and Y) – 2 factors (L and K) Exchange Economy
2 Individuals: A and B
2 Products: X and Y AiiAssume a world with no production and with fixed endowments of X and Y (hence thlihe line on top of fX X an dY)d Y). Edgeworth Box
1. Look at the world from Individual AAs’s perspective 2. Look at the world from Individual B’s perspective 3. Combine A and BBs’s worlds to form an Edgeworth box Edgeworth Box
Total amount of Y A U 2 A U 1 Individual A Total amount of X Edgeworth Box Total amount of X IdiidlIndividual B U 1 B B U 2 Total amount of Y
Individual A Edgeworth Box Total amount of X IdiidlIndividual B
Total amount of Y
Individual A Each ppppoint within the box represents a particular allocation of the two products between the two individuals Pareto Efficient Allocation
Pareto Efficient Allocation: Each individual is on the highest possible indifference curve, given the indifference curve of the other individual. Edgeworth Box
IdiidlIndividual B Total amount of Y
YB
Individual A XA Total X amount of Pareto Inefficient Allocation
and are Pareto inefficient allocations. Why? Because there exists changes illiin allocations, starti ifng from or that would make at least one individual better off without making the other individual worse off. Edgeworth Box
IdiidlIndividual B Total amount of is a pareto Y efficient point
Individual A Total X amount of Pareto Efficient Allocation
• At point/allocation • Individual A is on the higher possible indifference curve given B’s indifference curve an d • Individual B is on the highest possible indifference curve given As A’s indifference curve. • Theref ore, is a paret o effi c ient all ocati on • Note: The two indifference curves are tangential to each other Pareto Efficient Allocations
IdiidlIndividual B Total amount of and are Y also Pareto efficient allocations Individual A Total X amount of Contract Curve
IdiidlIndividual B Total amount of Joining up these Y Pareto efficient points yields the Individual contract A Total curve X amount of Contract Curve
The curve connecting all Pareto efficient allocations is known as the contract curve. AhihAt each point on the contract curve, the MRS’s for A and B are equal, i.e. A B MRS xy = MRS xy Market Place
An “auc tioneer” adj ust s th e
product prices (Px and Py) until the following three conditions hoodld:
P B PX (1)MRS A X (2) MRS P PY Y
(3) Demand for X X Demand for Y Y Market Place: Exchange Economy E quilib ri um IdiidlIndividual B Total UA amount of
Y UB PX
PY
Individual A Total X amount of Exchange Edgeworth Box: Summary
XB IdiidlIndividual B Total amount of Y
YB YA PX
Individual PY A XA Total X amount of Production Economy
Two firms produce two products (X and Y) The firms use two factors of producti on, capi tal (K) and l ab our (L) Assume fixed endowments of K and L. (()gProduction) Edgeworth Box
Firm Y Producing Total 0 Good Y amount of X 1 At the Y1 K tangency points: X X 0 MRTS LK= Y MRTS LK Firm Producing Total GdXGood X L amount of (()gProduction) Edgeworth Box
Firm Producing Total Y0 Good Y amount of X1 You can Y K 1 jijoin up all these Y* (Pare to ) X0 efficient Firm poitints t o Producing form the Total GdXGood X contttract L amount of curve. Market Place: Production Economy Equilibrium An “auc tioneer” adj ust s th e
factor prices (Pl = w and Pk = r) until the following three cocodtonditions ho odld:
w Y w (1)MRTS X (2) MRTS r r
(3) Demand for L L Demand for K K Production Possibility Curve
Each point on y the production possibility curve is (Pareto) efficient
x Production Possibility Curve
y X Y MRTS LK = MRTS LK
x Production Possibility Curve
y Points lie inssdeteide the curve are (()Pareto) inefficient
x Production Possibility Curve
y Where on the PPC? How much X andhd how much Y shldbhould be produced?
x Production Possibility Curve
Slope of the y PPC = y/x How many units of Y that have to given up in order to produce one more unit of X
Marginal rate of product transformation (MRPT or MRT) General Equilibrium
Claim: In equilibrium, firms will produce at the ppppyoint on the production possibility
curve at which MRPT = Px/Py
If MRPT < Px/Py produce more X and less Y
If MRPT > Px/Py produce less X and more Y
[As ide: MRSxy = Px/Py MRPTxy = MRSxy] General Equilibrium y The slope of the PPF = P x/Py
Px/Py
x General Equilibrium y At this point we can draw in the amount of x and y produced
Px/Py
x General Equilibrium y This is the amount of x produced
Px/Py
X x General Equilibrium y This is the amount of y produced Y
Px/Py
x General Equilibrium y Recall the Edgeworth box Y
Px/Py
X x General Equilibrium
y
Individual B Y
Px/Py
Individual A X x General Equilibrium
y
Individual B Y
Px/Py
Individual A X x General Equilibrium
Recall that y MRSxy= Px/Py
Individual B Y
Px/Py
Individual A X x General Equilibrium
y MRS = MRPT = Px/Py
Y
UA Px/Py P /P x y UB
X x General Equilibrium Three Conditions for General Equilibrium:
A B PX (1) MRS XY MRS XY PY
X Y PL w (()2) MRTSLK MRTSLK PK r
PX (3) MRPTXY MRS XY PY Welfare Economics 1st Fundamental Theorem of Welfare Economics: If all markets are perfectly competitive, the allocation of resources will be Pareto efficient. 2nd Fundamental Theorem of Welfare Economics: Any Pareto efficient allocation can be obtained as the outcome of competitive marktket processes, prov iddthtthided that the economy's initial endowment of resources can be redistributed , via lump sum taxes and subsidies, among agents.