1. General Equilibrium Analyses in Trade Model
2. Basic Tools for
General Equilibrium Analyses in Trade Model

2. Diminishing marginal rate of substitution
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
Since Y(MUy) = - X(MUx)
 -Y/X = MUx/MUy
Good X
Good Y
CI0 Y X
Diminishing marginal rate of substitution
MRS = = Y X
MUx
MUy

3. Consumer demand is always satisfied with more goods
Ordinal and Transitivity:
Farther out from origin point
Means higher welfare to
consumer
CI1
CI2
CI3
Good X
Good Y
CI0

4. Non-intersecting Community Indifference Curve
CI0: B = A = C
A = B = C = D
CI1: A = D
Good X
Good Y
CI0 B A C
CI1 > CI0  D > C
contradiction D
CI1

5. These are the wrong
Portions of CIC.
Why?
Good X
Good Y C0

6. 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
Good X
Good Y
CI0 y1 x1 x y A I1 I2
At point A:
(Px)(0x1) + (Py)(0y1) = I1
y1 = (I1)/(Py) – (Px/Py)X1
Y = (I1)/(Py) – (Px/Py)X
 Y/X = – Px/Py

7. Supply side: Production possibility frontier (PPF)
Isoquent concept:
Show various combinations of two inputs that produce same level output
Downward sloping and
Convexity for possible substitution
Capital
Labor 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

8. Q2 Q3 Q4
Non-intersecting
Farther out from origin point
Means greater quantities of outputs
Capital
Labor Q1 K1 L1
K1’
L1’ P P’ K L

9. Capital intensive output expansion path
Constant return to scale: a given percentage increase in all inputs
will lead the same percentage increase in output
Capital intensive output expansion path
4K1 P’ L1 G’
Capital
Labor
Q1=10 K1
2L1
2K1 P
Q2=20
4L1
Labor intensive output
expansion path G

10. 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
Capital
Labor Q1 K1 L1 P K L K’ L’ B1 B2 P’ Q2 H
At point P:
B1 = rK + wL
rK = B1 – wL
K = (B1/r) – (w/r)L
K/L = - w/r

11. 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
S-Isoquant
(K/L)s Ks Ls Oc Lc Kc
Increasing K
Increasing L L K
C-Isoquant
(K/L)c

12. Resources allocation in two goods within a countryOs
(K/L)s Ls Ks
Increasing L
Increasing K Oc Lc Kc
Increasing K
Increasing L
(K/L)c L K
Isoquant

13. The Edgeworth Box: L 0s K S1 S2 S3 S4 S5 K 0c L C1 C2 C3 C4 C5 V
Not Pareto Efficiency
Contract curve: production efficiency locus
with increasing opportunity cost

14. The Edgeworth Box: L 0s K S1 S2 S3 S4 S5 K 0c L C1 C2 C3 C4 C5
Not Pareto Efficiency V
Contract curve: production efficiency locus
with constant opportunity cost

15. Country II: Capital abundant country
Steel
Clothes S3 S2 S1 S0 C3 C2 C1 C0
Country II: Capital abundant country K2 L2

16. Country I: Labor-abundant country
Clothes
Steel S3 S2 S1 S0 C3 C2 C1 C0
Country I: Labor-abundant country KI LI

17. Constant vs. Increasing Opportunity Cost on the PPF
Good Y
Good X
PPF (or contract curve)
with constant opportunity cost
Constant increase
Increasing Opportunity Cost
PPF (or contract curve)
Decreasing increase

18. General equilibrium: domestic demand = domestic supply
Production at point A0 is satisfied and
consumed by consumers demand within
a country with constant opportunity cost.
(Classical case)
Good Y
Good X
PPF & budget curve
CI0 A0
(Px/Py)
CI1
CI2

19. Classical Autarky Equilibrium
CI0
CI1
CI2 B A PX PY E
(autarky price)
X -Cloth
Y-Steel
PPF
Marginal rate
of transformation
(MRT)
Of substitution
(MRS)

20. General equilibrium: domestic demand = domestic supply
Production at point A0 is satisfied and
consumed by consumers demand within
a country with increasing opportunity
cost. (Neo-classical case)
Good Y
Good X
PPF
CI0 A0
(Px/Py)
CI1
CI2
Budget curve

21. Community Indifferent curves
Autarky Equilibrium
CI0
CI1
CI2
Community Indifferent curves
X -Cloth
Y-Steel
PPF B A PX PY E
(autarky price)
Marginal rate
of transformation
(MRT)
Of substitution
(MRS)

22. x ay ax a L Y - = - ax ay y a x L + = the slope is = - Px Py
Given labor endowment is fixed with L y a x L + = LA aX
Good X
Good Y ay PX PY
Country A
Solving for x ay ax a L Y y - =
the slope is
- ax ay =
- Px Py

23. Unit cost in producing X is ax or (w x ax) |w –wage in money term
Total cost in producing X is axx
Then x X a P MC =
=>
In perfect competition:
Similarly:
Thus:

24. Trade Triangle Concept From the export country view of point:
exports 10 units
imports
10 units
PT = 1 = terms of trade or relative price
exports 10 units
imports
5 units
PT =1/2 =Terms of trade becomes worse

25. Trade Triangle Concept
exports 10 units
imports
15 units
PT = 3/2 = Terms of trade better off for
export country