II - Differences in Technology: The Ricardian Model n General purpose: to generalize the example of North-South trade given in the Introduction
n Trade based on differences in technology, not factors: polar opposite to the HO model of chapter III
1
1. The Closed Economy 1.1 Production 2 goods: X and Y 1 input: labor
L
total labor endowment:
Production functions: constant returns to scale
⎧ X = F X (L X ) = αL X ⎨ ⎩Y = FY (LY ) = βLY
α, β: positive constants 2
Perfect competition in product and labor markets Important assumption: perfect mobility of labor between sectors ⇒ same wage in both sectors:
w
X
=w Y =w
Production possibility set and frontier given here by the full-employment constraint:
X Y L X + LY ≤ L ⇔ + ≤ L α β
3
Y
βL
αL
X
4
1.2 Demands Assumption: identical consumers, same preferences ⇒ we can consider a representative consumer whose income is the country total income: w L
5
Assumption: imperfectly substitutable goods iso-utility curves:
Y
X
6
1.3 Equilibrium under Autarky Perfect competition implies zero profits. Profits equal:
X ⎛ w ⎞ πX = p X X − w = ⎜ p X − ⎟ X α ⎝ α ⎠ w , x =0 If p X < α w , x =∞ If p X > w α pX = ⇒ only possible equilibrium price: α w Similarly: p Y = β 7
Remark 1: ⇒
pX β p = = pY α ∂FY
= MRT =
∂F X
= - PPF slope
∂LY ∂L X
= marginal rate of transformation 8
Remark 2: Here, production frontier = budget constraint budget constraint: p X X d + p Y Y d = w X LX + w Y LY because no income from profits that are zero using equilibrium prices: w d w
X + Y α β
=w L d
=w L
using the good market equilibrium: d s and d s
X
=X
⇔
s
Y
s
=Y
i.e. the production possibility frontier (PPF)
X Y + =L α β
9
n Equilibrium under autarky
Y
βL
y
•
x
A
αL
X
10
2. Differences Between the Closed and the Open (Trading) Economy n Assumption: when frontiers are open, perfect competition still applies, firms and consumers are still price and wage takers
n Important assumption: No international labor mobility n No trade costs: world relative price of X equal to n
p*
p* =
is in general different from the autarky price
p
* pX p Y*
11
Quantities firms: constrained by the same production frontier labor endowment unchanged, no migrations
s
s
X Y + =L α β consumers: can buy goods on the world market only constraint : budget constraint
12
using the zero profit and market-clearing conditions in both sectors:
p *X X d + p Y* Y d = w X LX + w Y LY = p *X X s + p Y* Y s ⇔
* pX
X
s
(X
s
d
−X s d Y −Y
−X
d
)+ (Y * pY
s
−Y
d
)= 0
: net exports of good X : net exports of good Y
ü At world prices, export value = import value. ü The zero profit condition is equivalent to balanced trade. 13
The trade balance equilibrium : * pX
(X
s
−X
d
)+ (Y * pY
s
−Y
d
)= 0
implies that a country must be a net importer of one good and a net exporter of the other good In this framework it is impossible to export (or import) both goods.
14
Conclusion: differences in equilibrium characterization in autarky, for any country i
! a,i i p = MRS (consumer optimality) ## " p a,i = MRT i (firm optimality) # i,d i,s i,d i,s X = X and Y = Y (market equilibrium) #$ under free trade
⎧ p * = MRS i , for any country i ⎪⎪ i ⎨ p * = MRT , for any country i ⎪ ∑ X i ,d = ∑ X i ,s and ∑Y i ,d = ∑Y ⎪⎩ i i i i
i ,s
⇒ differences in price levels and market clearing conditions
15
We can rearrange conditions under free trade to make the trade balance condition appear. i
⎧ p * = MRS , ∀ i ⎪ i ⎪ p * = MRT , ∀ i ⎨ p * (X i ,s − X i ,d ) + p * (Y Y ⎪ X i ,d i ,s ⎪ ∑ X = ∑ X ⎩ i i
i ,s
−Y
i ,d
) = 0, ∀ i
16
Price and quantities variations case 1:
ü
p* < p
p * < MRT
a
⇒ reallocation of production towards
good Y ü the reason is that the marginal productivity of labor in sector Y is
relatively higher than in sector X in this country
∂FY
* p ∂LY a * ∂F X * ∂FY X p* < p ⇒ * < ⇒ pX < pY ∂L X ∂LY p Y ∂F X ∂L X 17
⇒ complete specialization in good Y
Y = Y = βL
p * ≠ MRT
ü We reach a corner solution because only one input is used and production frontiers are straight lines. (See in chapter III the HO model with 2 inputs for an interior solution.) ü Consumers’budget constraint:
* X
d
* Y
p X +p Y ⇔
d
* Y
* Y
= p Y = p βL
Y d = βL − p * X d 18
n Figure: Open Economy Equilibrium with
p* < p
a
Y
E X P O R T S
Q βL • a
y y*
•A
x
a IMPORTS
•E * x αL
X
19
p* > p
case 2:
a
⇒ same analysis but with complete specialization in the production of good X ü consumers budget constraint: * X
d
* Y
p X +p Y
d
* Y
= p αL
1 d X = αL − Y p* d
⇔
20
n Figure: Open Economy Equilibrium with
p* > p
a
Y
βL * y I M P O R T S
y
a
•E •A Q •
x a x*
αL EXPORTS
X
21
case 3:
p* = p
a
ü it is optimal for firms to produce any bundle on the PPF ü equilibrium consumption is the same as in autarky
⇒ production depends on foreign demand ü there are no gains from trade
22
Useful tool: excess demand function: ü difference between the local demand and the local production as a function of the world price ⇒
(X d
− X s )( p * ) = E ( p * )
ü usually, the inverse excess demand function is plotted
23
Determination of the excess demand function: We go through all three possible cases
if
⇒
p* = p
a
then
X d = X d ,a
and
X s ∈ [0 , αL ]
X d − X s ∈ #$ X d,a − α L, X d,a %&
24
If
p* < p a
ü
Xd
⇒
If
Y = βL
p* d s X − X (p * )
(
s
X =0 p*
ü complete specialization in Y, then s and irrespective of
decreases with
)
p* > p
is a decreasing function
a
ü complete specialization in Y, then X s = αL s and irrespective of p * ü
Xd
⇒
Y =0
decreases with
p*
(X d − X s )( p * )
is a decreasing function
25
Figure: Excess demand function
p*
Specialisation in Y β p = α a
Specialisation in X
X d , a − αL
X d ,a
d
X −X
26
s
3. Equilibrium in the Open Economy 3.1 Technology Trade liberalization between 2 countries (1 and 2) with the same labor endowment but different technologies.
Autarky prices must be different. By convention we assume that country 1 has comparative advantage in the production of Y, with relative productivities
β1 β2 > α1 α2
⇔
β1 β2 a p = > = p2 α1 α2 a 1
27
n Figure: Examples of production frontiers
Comparative advantage Absolute advantage of Absolute advantage country 1 in both of country 1 in both of country 1 in Y. productions. productions. β1 L Y Y But comparative Y But comparative β1 L β1 L advantage in X. advantage in Y. β2 L β2 L β2 L
X α1 L
α2 L X
α 2 L α1 L
X α2 L
α1 L 28
3.2 World Price Good X world market equilibrium ⇒ world Price ⇔ ⇒ ⇒
d 1 d 1
d 2 s 1
s 1 d 2
s 2 s 2
X +X =X +X X −X +X −X =0 E1 + E2 = 0
Plot of good X excess demand function in both countries and determination of the free trade equilibrium price
29
Remark: we assume identical preferences in both countries country 1 has comparative advantage in Y ⇒ a 1
p >p
a 2
bth assumptions imply
X but
d ,a 1
α 1 = 1 ,a * = pX p* pX 2 ,* 2 ,a w w = α 2 = 2 , a ⇒ unchanged Country 2: * pX pX w 2 ,* w 2 ,a * = α2 p * > β2 = pY p Y2 , a ⇒ increases ⇒ real labor income increases 39
Final remarks the real wage ratio between countries equals the ratio of nominal wages (since prices are the same) and depends on absolute advantage, as under autarky for instance:
w w
1 ,a
p 2 ,a
1 ,a X
p X2 , a
α1 = α2
w
1 ,*
and
w
2 ,*
* pX
p *X
β1 α1 = > α2 p * α2
⇒ welfare increases in both countries, but inequalities between countries may either increase or decrease role of labor mobility assumption
40
5. Country Size and Growth Suppose now that the production set of country 2 grows, while that of country 1 is the same. This may come from: labor endowment growth productivity growth in all sectors
Country 2 will now want to export and import more at the same world relative price.
The relative price of country 2’s export good falls. ⇒ the small country gains more than the large country
Intuition: the world price is closer to the autarkic price of the larger country
41
n Figure: Graphic determination of world price
p*
p1
A
p* p* p2
E2
A
β1 = α1
β2 = α2
E1
42
In the case of very large country size differences, the world price may be equal to the large country price under autarky ⇒ the large country is indifferent between the closed and the open economy in this case ⇒ the small country still gains from free trade
43
Impact of country 2’s growth the price of the good country 2 exports decreases intuitions: country 2 fully specializes in the production of X, thus an increase in its labor force increases the quantity of good X produced, and thus decreases the good X price define the terms of trade as the ratio of the price of exports over the price of imports ⇒ terms of trade have deteriorated in country 2 while they have improved in country 1
44
n Figure: Country 2 situation after country 2 growth
Y
Growth
B
C
A
Growth
X
45
n Figure: Country 2 situation after country 2 growth if the world price had not changed
D Y
Growth
B
C
A
Growth
X
46
terms of trade effect: the slope of the budget constraint
under free trade and growth (going through C) lies between the autarky and the free trade/no growth slopes.
in country 2, the impact of growth on welfare is lower than if the world price had remained constant
but country 2 still prefers free trade to autarky
47
‘Immiserizing growth’ if demand is very elastic, the situation in country 2 can be worse after growth than with no growth: C below B ⇒ this is referred to as "immiserizing growth“ still, the country will be better off than under autarky Applicable to commodities with large supply shocks like cocoa, coffee?
48
n Figure: Immiserizing growth
B
Y
Growth
C
A
Growth
X
49
4. References Markusen, J., J. Melvin, W. Kaempfer, and K. Maskus, 1995. International Trade - Theory and Evidence, Mc Graw-Hill. Chapter 7.
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