Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Basic Tools for General Equilibrium Analysis
Demand Side: Community Indifference Curve (CIC)
Shows various combinations of two goods with equivalent welfare
Downward sloping
And Convexity CI
Good X
Good Y
CI0
Y
X
Diminishing marginal rate of substitution
Since Y(MUy) = - X(MUx)
-Y/X = MUx/MUy
MRS = - =Y
X
MUx
MUy
Ordinal and Transitivity:
Farther out from origin point
Means higher welfare to
consumer
CI1
CI2
CI3
Good X
Good Y
CI0
Consumer demand is always satisfied with more goods
Good X
Good Y
CI0
B
A
C
Non-intersecting Community Indifference Curve
CI1 > CI0 D > C contradiction
A = B = C = DCI1: A = D
CI0: B = A = C
D
CI1
These are the wrong
Portions of CIC.
Why?
Good X
Good Y
C0
Consumer equilibrium:
Maximize welfare subject to the income constraint (Budget constraint)
Slope of budget line:
Y/X = (0y)/(-0x)
= (I1/Py)/(-I1)Px)
= - Px/Py = MRS
At point A:
(Px)(0x1) + (Py)(0y1) = I1
y1 = (I1)/(Py) – (Px/Py)X1
Y = (I1)/(Py) – (Px/Py)X
Y/X = – Px/Py
Good X
Good Y
CI0
y1
x10 x
y
A
I1
I2
Supply side: Production possibility frontier (PPF)
Isoquent concept:
Show various combinations of two inputs that produce same level output
Capital
Labor0
Q1
K1
L1
K1’
L1’
P
P’
K
L
Marginal rate of technical substitution
(K)x(MPPK) = - (L)x(MPPL)
K/L = - MPPL/MPPK
K/L = MRTS
Downward sloping and
Convexity for possible substitution
Q2
Q3
Q4
Non-intersecting
Farther out from origin point
Means greater quantities of outputs
Capital
Labor0
Q1
K1
L1
K1’
L1’
P
P’
K
L
Constant return to scale: a given percentage increase in all inputs
will lead the same percentage increase in output
Capital
Labor0
Q1=10
K1
2L1
2K1
PQ2=20
4L1
Labor intensive output
expansion path
G
Capital intensive output expansion path
4K1
P’
L1
G’
Producer Equilibrium:At the point the isoquant is tangent to the isocost.
Firm maximizes output for the given cost (i.e., most efficient production),
Or firm minimizes its factor cost for the given level of output.
The slope of isocost (or the factor price line)
K/L = 0K/-0L
= - (B1/r)/(B1/w)
= w/r where r is labor wage,
w is capital rental rate
= MPPL/MPPK = MRTS
At point P:
B1 = rK + wL
rK = B1 – wL
K = (B1/r) – (w/r)L
K/L = - w/r
Capital
Labor0
Q1
K1
L1
P
K
L
K’
L’
B1
B2
P’
Q2
H
OcLc
Kc
Incr
easi
ng K
L
K
OcLc
Kc
Incr
easi
ng K
L
K
C-Isoquant
(K/L)c
S-Isoquant (K/L)s
Ks
Ls
S is capital-intensive
(K/L)s > (K/L)c or
(L/K)s < (L/K)c
C is labor-intensive
(L/K)s < (L/K)c or
(K/L)s > (K/L)c
Resources allocation in two goods within a country
OcLc
Kc
Incr
easi
ng K
(K/L)c
L
K
OcLc
Kc
Incr
easi
ng K
(K/L)c
L
K
Isoquant
Os
(K/L)s
Ls
Ks
The Edgeworth Box:
K
0cL
C1
C2C3
C4C5
V
Not Pareto
Efficiency
Contract curve: production efficiency locus
with increasing opportunity cost
L
0sK
S1S2
S3S4
S5
The Edgeworth Box:
K
0cL
C1
C2C3
C4
C5
L
0sK
S1
S2S3S4
S5
Not Pareto
EfficiencyV
Contract curve: production efficiency locus
with constant opportunity cost
Country II: Capital abundant country
K2
L2
Steel
Clothes
S3
S2
S1
S0
C3
C2
C1
C0
Country I: Labor-abundant country
KI
LI
Clothes
Steel
S3
S2
S1
S0
C3
C2
C1
C0
Good Y
Good X0
PPF (or contract curve)
with constant opportunity cost
Constant increase
Increasing Opportunity Cost
PPF (or contract curve)
Decreasing increase
Constant vs. Increasing Opportunity Cost on the PPF
General equilibrium: domestic demand = domestic supply
Good Y
Good X
PPF & budget curve
CI0
A0
(Px/Py)
CI1
CI2
Production at point A0 is satisfied and
consumed by consumers demand within
a country with constant opportunity cost.
(Classical case)
XYY
X
Y
X
Y
XXY MRS
MU
MU
P
P
MC
MCMRT
Marginal rate of transformation(MRT)
Marginal rateOf substitution(MRS)
CI0
CI1
CI2
B
A
PX
PY
E
(autarky price)
0X -Cloth
Y-Steel
PPF
General equilibrium: domestic demand = domestic supply
Good Y
Good X
PPF
CI0
A0
(Px/Py)
CI1
CI2
Budget curve
Production at point A0 is satisfied and
consumed by consumers demand within
a country with increasing opportunity
cost. (Neo-classical case)
CI0
CI1
CI2
Community
Indifferent curves
0X -Cloth
Y-Steel
PPF
B
A
PX
PY
E
(autarky price)
XYY
X
Y
X
Y
XXY MRS
MU
MU
P
P
MC
MCMRT
Marginal rate of transformation
(MRT)
Marginal rateOf substitution
(MRS)
LA
aX
0 Good X
Good Y
LA
ay PX
PY
Country AGiven labor endowment is fixed with L
yaxa
LLL
yx
yx
+
+
Solving for
xay
ax
aL
Yy-
the slope is
- ax
ay=
- Px
Py
Unit cost in producing X is ax or (w x ax) |w –wage in money term
Total cost in producing X is axx
xxX a)xa(X
MC
Then
xxXX aPMCP >
yyyy aP MCP
In perfect competition:
Similarly:
Y ofunit 1 produce to required units labor
Xofunit 1 produce to required unitslabor
a
a
P
P
y
x
y
x
Thus:
Trade Triangle Concept
From the export country view of point:
exports 10 units
imports
5 units
PT =1/2 =Terms of trade becomes worse
exports 10 units
imports
10 units
PT = 1 = terms of trade or relative price
Trade Triangle Concept
exports 10 units
imports
15 units
PT = 3/2 = Terms of trade better off for
export country
Related Documents
