1. Extensions and Tests of the Classical Model of Trade
Chapter 4
Extensions and Tests of the Classical Model of Trade
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Learning Objectives
Demonstrate how wages, productivity, and exchange rates affect trade patterns.
Examine the implications of extending the basic model of comparative advantage.
Show that real-world trade patterns are consistent with underlying comparative advantage.

3. Adding Money to the Classical Model
Suppose a money economy instead of a barter economy.
A wage rate for each country, stated in that country’s currency (e.g., in U.S. $2 per hr., in the U.K., £1 per hr.).
An exchange rate that relates the countries’ currencies (e.g., $1 = £1).

4. An Example
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5. An Example
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6. Adding Money to the Classical Model: An Example
The U.S. will export wheat, since it can produce wheat for a lower price ($4, as compared with $6).
The U.K. will export cloth, since it can produce cloth for a lower price ($4, as compared with $6).

7. The Export Condition
Country 1 should export good j when: a1j*W1*e < a2j*W2, where
a1j and a2j are the labor requirements/hr to produce good j in countries 1 and 2
W1 and W2 are the wage rates/hr in countries 1 and 2
e is country 1’s exchange rate (# of country 2’s currency units per 1 of country 1’s).
Note: RA and RB are inverses of each other, and only equal if RA = RB = 1. If US is country A and $1 = 5 pesos, then RA = 5. RB is Mexico’s exchange rate: RB = 0.2.

8. The Export Condition
Country 1 should export good j when: a1j*W1*e < a2j*W2.
That is, when country 1’s good j price is lower than 2’s, stated in a common currency.
Therefore, the pattern of trade is determined by
relative labor efficiency,
relative wage rates, and
the exchange rate.

9. The Export Condition
Country A should export good j when: a1j*W1*e < a2j*W2.
Let’s re-write this as follows:
Country A should export good j when:
a1j/a2j < W2/(W1*e).

10. Wage Rate Limits
As Country 1’s wage rate goes up relative to Country 2’s, Country 1 finds it harder to sell its exports to Country 2.
As Country 1’s wage rate goes down relative to Country 2’s, Country 1 is less interested in importing from Country 2.

11. Wage Rate Limits: An Example
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12. Wage Rate Limits: An Example
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13. Wage Rate Limits: An Example
Should the U.S. (Country 1) export wheat?
It should if a1j/a2j < W2/(W1*e).
Since 2/6 < 1/(3*0.5), the U.S. should export wheat [or: the U.S. wheat price is $6; the U.K. wheat price is £6 = $12].
It’s easy to show that the U.K. should export cloth.

14. Wage Rate Limits: An Example
What if the U.S. wage rate rose to $6?

15. Wage Rate Limits: An Example
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16. Wage Rate Limits: An Example
Now the U.S. wheat price is the same as the U.K.’s, if we state them in a common currency.

17. Wage Rate Limits: An Example
Now the U.S. wheat price is the same as the U.K.’s, if we state them in a common currency.
Therefore, if the wage rate in the U.S. should rise above $6, the U.K. will no longer buy U.S. wheat (trade will cease).

18. Wage Rate Limits: An Example
What if instead the U.S. wage rate fell to $2.67?

19. Wage Rate Limits: An Example
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20. Wage Rate Limits: An Example
What if the U.S. wage rate fell to $2.67?
Now the U.S. cloth price is the same as the U.K.’s, if we state them in a common currency ($8).
Therefore, if the wage rate in the U.S. should fall below $2.67, the U.S. will no longer buy U.K. cloth (trade will cease).

21. Calculating Wage Rate Limits Using the Export Condition
Solve the export condition for W1, for good X.
Solve the export condition for W1, for good Y.
These will give you Country A’s wage rate limits.

22. Calculating Wage Rate Limits Using the Export Condition
a1j/a2j < W2/(W1*e)
For wheat:
2/6 = 1/(W1*0.5) → W1= 6
For cloth:
3/4 = 1/(W1*0.5) → W1= 2.67

23. Country 2’s Wage Rate Limits
Changes in Country 2’s wage rates also can affect the pattern of trade.
If 2’s wage rises too much, they will not be able to export any more.
If 2’s wage falls too much, 2 will no longer wish to import.
Solve the export condition for W2 for each good.

24. Exchange Rate Limits
If Country 1’s currency appreciates, imports will seem cheaper and exports more expensive.
If 1’s currency appreciates enough, A will no longer be able to export.
If 1’s currency depreciates enough, A will no longer wish to import.
Solve export condition for e.

25. More Than Two Goods
Having more than two goods has no effect on the basic Classical model.

26. More Than Two Goods: An Example
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27. More Than Two Goods The export condition can still be used.
Perhaps it is better to put all of the products in ascending order:

28. More Than Two Goods: An Example
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29. More Than Two Goods: An Example
Suppose the exchange rate is still $1 = £0.5 (that is, e = 0.5).
Then W2/(W1*e) = 1/(3*0.5) = 0.67
Use this as a “pointer”: Country 1 should export everything to the left of the pointer.

30. More Than Two Goods: An Example
W2/(W1*e) = 0.67
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31. More Than Two Goods: An Example
If the U.S. wage rate were to fall, the pointer would move to the right, and the U.S. would start exporting goods it presently imports.
If the U.S. wage were to rise, the pointer would move left.
Changes in the U.K.’s wage, or the exchange rate, would also move the pointer and thus affect the pattern of trade.

32. Adding Transportation Costs
Assume:
all transportation costs are paid by the importer.
transportation costs are measured in terms of their labor content.
Country 1’s export condition:
(a1j+trj)/a2j < W2/(W1*e)
Suppose in previous example t-costs are 1 labor hour.

33. Transportation Costs: An Example
W2/(W1*e) = 0.67
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34. Transportation Costs: An Example
Notice that although the U.K. has a comparative advantage in cloth, it will no longer export this product, since
(a1j+trj)/a2j = 0.6 < W2/(W1*e) = 0.67.
In the real world, some products with high t-costs (e.g., bulky ones) are not traded.

35. More Than Two Countries
Having more than two countries also has no effect on the basic Classical model.

36. More Than Two Countries: An Example

37. More Than Two Countries: An Example
U.K. has the CA in cloth, since its autarky cloth price is the lowest.
U.S. has the CA in wheat, since its autarky wheat price is the lowest.

38. More Than Two Countries: An Example
If the terms of trade are 1C = 1.8W (or: 1W = .55C), then the U.S. will export wheat (because the international wheat price is greater than the U.S. domestic price).
France and the U.K. will export cloth (because the international cloth price is greater than their domestic prices).

39. More Than Two Countries: An Example
ToT: 1C = 1.8W (or: 1W = .55C)

40. More Than Two Countries: An Example
If the terms of trade are 1C = 1.6W (or: 1W = .625C), then
the U.S. and France will export wheat (because the international wheat price is greater than their domestic prices).
The U.K. will export cloth.

41. More Than Two Countries: An Example
ToT: 1C = 1.6W (or: 1W = .625C)

42. Evaluating the Classical Model
Empirical studies generally show that the classical model is consistent with observed trading patterns.
However, the complexity of today’s world means the Classical model cannot supply a complete understanding of international trade.