International Trade Theory (1/2008)
Chulalongkorn University
Lecture 3: The Endowment Model
Kornkarun Cheewatrakoolpong, Ph.D.
So far the Ricardian/DFS model only concerns about the production side. Now
we begin with the simple general equilibrium model with pure exchange economy
case where there is no production. We will consider the case that each country
endows with the fixed amount of goods. Later, we will continue the 2x2 production
economy in the Heckscher-Ohlin Model.
The tricky thing in the general equilibrium model is not production but
“income effect”. Suppose that the price of one good decreases, then normally this
means that we are richer. However, in the endowment model, when the price of one
good decreases, the total amount of wealth in the country decreases as well. So we
need to decompose the income effect into ordinary income effect and endowment
income effect. There are two ways to deal with the endowment model:
1. Import demand/ export supply
2. Offer curves
Both yield the same result. For this course, I will go by the import demand
export supply curve.
The basic model
- Two goods: Chips and Fish
- Two countries: Canada and Japan
- Homogenous consumers with a representative agent.
- Fixed amount of endowment : ω c , ω F , ω *c , ω *F
Autarky equilibrium
In the autarky equilibrium, Canada must consume at the endowment level.
fish
ωF
chips
ω
c
The import demand curve
Import
M = Dc = ω c
Pc/Pf
M(P, ω )
M
Why downward sloping M(P, ω )?
1. Substitution effect
When the price of chips decreases, the demand for chips and import of chips
increase.
2. Ordinary income effect
Assume that the money income is fixed and chips are normal goods, when price of
chips decrease, the demand for chips and import of chips increase because the real
income increases.
3. Endowment income effect
When price of chips decreases, the value of endowment decreases.
Comparing the effect of 2 and 3, we can see that the income effect depends on the
whole consumption of chips while the endowment income effect has an impact on the
level of endowment only. Therefore the effect of 2 is bigger than of 3. Hence, we
always have the inverse relationship between M(P, ω ) and P.
The export supply curve
Pc/Pf
X*(P, ω *)
X*
Why upward sloping X*(P, ω *)?
1. Substitution effect
When the price of chips decreases, the demand for chips and export of chips
increase.
2. Ordinary income effect
Assume that the money income is fixed and chips are normal goods, when price of
chips decrease, the demand for chips and export of chips increase because the real
income increases.
3. Endowment income effect
When price of chips decreases, the value of endowment decreases.
Since chips are the exported goods of Japan, the endowment income effect is
bigger. Now the rest is to compare the income effect with the substitution effect. If the
income effect is bigger, then the export supply curve is upward sloping. Once the
income effect is smaller than the substitution effect, the export supply curve is
downward sloping.
Equilibrium
In the equilibrium, we have the trade-balance condition in which :
M(P, ω ) = X*(P, ω *)
the equilibrium world price lies between the autarky price of both countries.
Pc/Pf
X*(P, ω *)
M(P, ω )
X*
Multiple Equilibrium
For any equilibrium there might be multiple equilibria.
Consider the picture in the previous page for a comparative static that shifts
the export supply function outward. Suppose that right now the economy is at point A,
there is a change in technology in Foreign so that the export supply change to X *' .?
There are 4 candidates for the new equilibrium, A’, B’, C’, D’. However, the only
candidate that makes sense is A’. At the original relative world price, there is excess
supply of chips in the world market; therefore, it makes more sense that in the new
equilibrium, we have higher level of chips imported.
Therefore, we must have the mechanism that restricts our attention to only
equilibrium that makes sense. In the equilibrium, we know that:
M ( P, ω ) = X * ( P, ω * )
(1)
Total differentiate (1)
∂X *
∂X *
∂M
dP =
dP +
dδ
∂P
∂P
∂δ
∂X * / ∂δ
∂P
=
(2)
∂δ ∂M ∂X *
−
∂P
∂P
*
∂X *
∂M ∂X
Suppose that
> 0 , then we must have
< 0 . How to have this?
−
∂δ
∂P
∂P
From balance of trade:
PX * = M *
(3)
Differentiate (3) with respect to P, we get:
∂X * ∂M * 1 X *
−
(4)
=
∂P P P
∂P
We want:
*
∂M ∂X
<0
(5)
−
∂P
∂P
Substitute (4) into (5) to have:
*
*
∂M ∂M 1 X
+
<0
(6)
−
∂P P P
∂P
Rearrange (6) in the elasticity term and multiply both sides by P/M :
*
P ∂M ∂M 1
+1 < 0
−
∂P M
M ∂P
M*
*
, we have
From M = X =
P
*
P ∂M ∂M P
−
+1 < 0
(7)
M ∂P
∂P M *
∂M P
∂P M
∂M * P *
*
ε =− *
∂P M *
ε =−
Elasticity of Canada import demand
Elasticity of Japan import demand
Then (7) becomes: ε + ε * − 1 > 0 , this is “Marshall Lerner Stability
Condition”.