1. Differences in technology
Lezione 2 bis
Differences in technology
Giuseppe Celi
IEG 2007

2. The causes of international trade
Now we start to consider the causes of international trade. We will investigate the economic characteristics underlying the pattern of comparative advantage.
A convenient method to investigate the cause of international trade is to imagine a world in which there is no trade. In terms of our simple model this circumstance occurs when all autarky price ratios are identical and there are no scale economies
Giuseppe Celi
IEG 2007

3. The causes of international trade
In particular, five conditions guarantee the no-trade situation:
1) identical production functions among coutries
2) the same relative endowments in all countries
3) constant returns to scale
4) identical and homogeneous tastes in all countries
5) the absence of distortions (taxes, subsidies, imperfect competition)
If any one of these five conditions is relaxed, then international trade will occur. Therefore, in a reverse way, the five conditions underlying the no-trade situation can be thought of as the principal determinants of international trade.
From a methodological point of view, it is useful to analyse each determinant in isolation through specific models. Now we will focus on differences in technology between countries (differences in production functions)
Giuseppe Celi
IEG 2007

4. A simple model of production function differences
We consider the Ricardian model, a one-factor model in which differences in technology are expressed in terms of differences in labour productivity across countries: the amount of output that can be obtained from one unit of labour differs across countries.
Constant return to scale are assumed. Given that this is a one-factor model, this hypothesis implies a linear production possibility frontier.
The other implication associated with the hyphotesis of a single factor is that the second condition of the five illustrated previously is not relaxed (the same relative endowments in all countries)
We also impose the remaining conditions: no distortions and tastes are identical
Giuseppe Celi
IEG 2007

5. Absolute and comparative advantage
In the model, labour is the only constraint on the production. If the economy produces good X and good Y, we can write the production functions and the labour constraint as:
Under the hypothesis of constant returns to scale, we can express production functions as:
Giuseppe Celi
IEG 2007

6. Absolute and comparative advantage
where and are positive constants and represent the marginal products of labour in industries X and Y respectively
The Ricardian approach based on the concept of comparative advantage is illustrated in the following tables.
In table 1, country H has an absolute advantage in the production of Y: Country F an absolute advantage in the production of X:
Table 2 shows the possibility of increasing world production of both commodities through specialization
Giuseppe Celi
IEG 2007

7. 3. Marginal products of labor
2. Changes in outputs due to
reallocation of one worker from X
to Y in Country H and one worker
from Y to X in Country F
Marginal products of labor
Home
Foreign
Home
Foreign
Total X X
–20
+30
+10 Y Y
+20
–10
+10
4. Changes in outputs due to
reallocation of four workers from X
to Y in Country H and one worker
from Y to X in Country F
3. Marginal products of labor
Home
Foreign
Home
Foreign
Total X X
–20
+30
+10 Y Y
+20
–10
+10
Giuseppe Celi
IEG 2007

8. Absolute and comparative advantage
Table 3 shows a different situation. Now Country F is more efficient in the production of both goods. Is trade still possible in this new situation?
Yes, because H has a comparative advantage in the production of good Y: (or, equivalently, we can say that H has a relative lower opportunity cost of Y in terms of X)
Table 4 illustrates the existence of gains from specialization and trade also in the case in which a country (in this case, Country F) has an absolute advantage in both productions
Giuseppe Celi
IEG 2007

9. The production possibility frontier
The following figure illustrates the production frontier for country H and F based on the pattern of comparative advantage as reported in the previous table 1
we denote and the labour endowments in the two countries H and F, respectively. The production frontier for Country H (HH’) has a maximum X output of and a maximum Y output of The production frontier for Country F (FF’) has a maximum X output of and a maximum Y output of
The slope of a country’s production frontier is:
Giuseppe Celi
IEG 2007

10. Production frontier and autarky equilibriumH Ah F ● Af ● X H’ F’
Production frontier and autarky equilibrium
Giuseppe Celi
IEG 2007

11. The production possibility frontier
The country’s autharky price ratio is given by the slope of its production frontier. But the slope reflects comparative advantage. Therefore autarky prices reflect comparative advantage
The following diagram shows what happens when countries open to international trade. If for country H is indifferent to producing at any point along the production frontier.
At any price ratio p* that differs from the slope of the production frontier, a country will specialize completely.
If H will specialize in X at point H’. The reason is that
Giuseppe Celi
IEG 2007

12. Specialization at alternative world price ratiosY H C2 ● C1 ● ● Ah X H’
Specialization at alternative world price ratios
Giuseppe Celi
IEG 2007

13. The production possibility frontier
Equilibrium with is given by
, Y=O
Giuseppe Celi
IEG 2007

14. Excess demand and international equilibrium
Results previously illustrated are transferred to an excess demand diagram.
The “flat” section of Country H’s excess demand curve at its autarky price ratio reflects the result discussed in the previous diagram: H will consume at Ah but will be indifferent to producing at any point on its production frontier
At world price ratios greater than autarky price ratio H will wish to export X. At world price ratios less than autarky price ratio H will wish to import X
Giuseppe Celi
IEG 2007

15. Country H‘s excess demand curve International equilibriump
p = px / py ● ● ● ● C1 Eh C2 Ef Eh
-(Xc –Xp) H’ H
(Xc –Xp)
-(Xc –Xp) Ef
(Xc –Xp)
Country H‘s excess demand curve
International equilibrium
Giuseppe Celi
IEG 2007

16. Excess demand and international equilibrium
The right side diagram in the previous figure shows the excess demand curve for both countries based on their production frontiers
International equilibrium occurs at price ratio p* at which the import demand of H matches the export supply of F.
The equilibrium world price ratio falls between the autarky price ratios of the two countries. In the case in which this circumstance does not occur, both countries would wish to export the same good
We know that when free trade price ratio is different from autarky price ratio for both countries, they attain mutual gains from trade. In the present model both countries must gain from trade although the distribution of the gains from trade could be uneven (the country with a larger distance between free trade price ratio and autarky price ratio gains more)
Giuseppe Celi
IEG 2007

17. The role of wages
Until now, we have seen that in the Ricardian model comparative advantage is determined simply by differences in technology across countries. What is the role of wages in Ricardian model?
International differences induce adjustment of wages in order to reflect underlying real productivity differences. More productive economies will have higher real wages in equilibrium. However all workers gain real income in moving from autarky to free trade
The discussion about the role of wages in the model can start from the initial equilibrium in autarky. Because of perfect competition, we have:
Giuseppe Celi
IEG 2007

18. The role of wages
From the previous profit maximization condition, it follows that the relative price in autarky is independent of the wage rate:
Given that the ratio between the marginal products in the two industries is equivalent to the ratio between input coefficients in the two industries, the previous expression reflects the Ricardian Labour Theory of Value
However, the wage rate is relevant for determining real wages of workers:
These “real wages” can be interpreted graphically as the end points on the budget line of an individual worker who owns 1 unit of labour
Giuseppe Celi
IEG 2007

19. Budget line of an individual worker in Country H
Slope p* ● ● Uf Ua ● ● X
Budget line of an individual worker in Country H
Giuseppe Celi
IEG 2007

20. The role of wages
Now we consider the move from autarky to free trade. This movement induces an adjustment of nominal wages in both countries.
To determine the impact on real wages, note that H Country exports Y and F Country exports X. Therefore, in H country the real wage for a home worker is constant in terms of good Y because the competitive condition of production in industry Y requires that
Of course, the previous condition does not involve the good X because this good is not produced at home. This means that the real wage in terms of X changes because of the new price ratio determined by trade.
Giuseppe Celi
IEG 2007

21. The role of wages
If H Country exports good Y, the international price ratio will be lower than the autarky price ratio and now the home worker can buy X at a lower price:
Given that the price ratio p* is the vertical intercept ( ) over the horizontal intercept, this last one has to be
So the new real wage in terms of good X (the new horizontal intercept) increases in the presence of free trade:
Giuseppe Celi
IEG 2007

22. The role of wages
So trade does not change the domestic real wage in terms of the good exported but alters the domestic real wage in terms of the good imported. Note in the previous figure that with the new budget line the utility of the domestic individual worker increases (same argument applies to the worker of the foreign Country, whose income is constant in terms of the good X but increases in terms of the good Y).
A final important point about the role of wages. It is probable that in free trade real wages are higher in one country in comparison with the other. Suppose that the home country has an absolute advantage in both industries. In such situation, for the good X we have and therefore:
(same dimonstration applies to good Y).
Giuseppe Celi
IEG 2007

23. The distribution of gains from trade: big versus small countries
One of the most important determinant of the distribution of the gains from trade among countries is the size of economies, measured in terms of either their factor endowments or their productivity levels
Suppose to make Country F bigger by shifting its production frontier farther out in a parallel way. This can be achieved either by increasing factor endowment or by increasing and
The following figure shows the expansion of production frontier from to
Giuseppe Celi
IEG 2007

24. Y C1 C0 X
Growth in Country F
Giuseppe Celi
IEG 2007

25. The distribution of gains from trade: big versus small countries
The expansion of the production frontier will lead Country F to wish to trade more at any international price ratio.
In the next figure, we can observe the effect of the growth of the Country F in terms of the excess demand curve. The horizontal segment (equivalent to the distance ) expands indicating that the Country F now wishes to trade more at any price ratio.
But the equilibrium price ratio also changes and can no longer be an equilibrium price ratio: there is an excess supply of X, so the world price ratio must fall
Giuseppe Celi
IEG 2007

26. Expansion in Country F’s excess demand● ● ● ● ● ● ● ● ● ● ●
-(Xc –Xp)
(Xc –Xp)
Expansion in Country F’s excess demand
Giuseppe Celi
IEG 2007

27. The distribution of gains from trade: big versus small countries
The change of international price ratio has important implications in terms of the distribution of the gain from trade.
Country F gains less by growth than in the case of equilibrium at the initial world price ratio In particular, F’s terms of trade have deteriorated, while H’s terms of trade have improved
The positive impact of F’s growth on H’s welfare due to a decline of international price ratio from to is shown in the following figure.
Giuseppe Celi
IEG 2007

28. Effect of growth in country F on country H● C0 ● X H’
Effect of growth in country F on country H
Giuseppe Celi
IEG 2007

29. The distribution of gains from trade: big versus small countries
The following figure shows an extreme case of uneven distribution of the gains from trade. Now Country F is so large in comparison with Country H that the equilibrium is reached at the autarky price ratio of Country F. In this case, all gains from trade are captured by Country H and Country F is indifferent to trade.
The discussion on the trade effects associated with the growth of country size leads to observe that smaller economies are the more probable gainer from free trade
Another point to remark is that the productivity growth of a country may be beneficial for the other (in the cases illustrated previously, H benefits from productivity growth of F in terms of a lower price of its import good)
Giuseppe Celi
IEG 2007

30. Equilibrium world price equal to Country F’s autarky price● ● ● ● ● Ef Eh
-(Xc –Xp)
(Xc –Xp)
Equilibrium world price equal to Country F’s autarky price
Giuseppe Celi
IEG 2007

31. Concluding remarks: key points
The slope of of a country’s production frontier reflects its relative abilities to produce X and Y. When the slope of production frontier differs between two countries a pattern of comparative advantage emerges. Actually, differences in the slope of PPF imply differences in the autarky price ratio and this creates the potential for gains from trade also in the case a country has an absolute advantage in both industries
Even if potential for gains from trade exists, it is not sure that these gains are captured in free trade. Another condition is required: the equilibrium free trade price ratio must lie between the autarky price ratios for the two countries. If this condition is satisfied, each country specializes according to its comparative advantage and gains from trade
Giuseppe Celi
IEG 2007

32. Concluding remarks: key points
Individual workers in each country gains from trade in terms of an improvement of their living standards relative to autarky However, real wages can be different in the two countries and the country with an absolute advantage necessarily has the higher real wages. So absolute advantage (in terms of productivity) is an important element of evaluation in international real wage comparison but is not relevant in terms of the direction of trade
The economic size is an important factor affecting the distribution of gains from trade. The economic size can be measured as the distance of PPF from the origin. When a country becomes bigger, its terms of trade tend to deteriorate and the equilibrium world price ratio tend to converge to the country’s autarky price ratio. This implies a transfer of gains from trade to the other country (because the distance between the word price ratio and the autarky price ratio of this country becomes maximum)
Giuseppe Celi
IEG 2007

33. Concluding remarks: key points
Therefore small country are likely to be the major gainers from free trade. That countries benefit from productivity growth in trading partners through the decline in prices of import goods
Giuseppe Celi
IEG 2007