THE STOLPER-SAMUELSON THEOREM
topic 4.4
The factor that is used intensively in the product whose price has risen gains from this price rise, while the other factor loses.
Consider figure 4.4.
There are two isoquants that overlap when the level of output is set the same for both goods, at $1 for T and $1 for S.
We are looking at country B here, the country which is abundant in labor. We know that B exports,T, and so when trade is opened it must be the price of T that increases.
If the value of Pt should increase while we keep Ps the same, the new isoquant for T is closer to the axis since it requires a lower quantity of T to constitute $1 of value.
So the new isocost line is obtained by rotating an isocost line clockwise. The new isocost line is tangent to the original S isoquant and the new T isoquant.
Looking at the intercepts, W must have increased while R must have decreased.
Looking at the intercepts and then comparing to the change in prices:
For capital units, their 'reward' R has decreased while the price of T has increased and the price of S is the same. So capital is definitely worse off.
For labor it is less clear why labor gains. W has increased to be sure, but then the price of good T has increased. We need to know whether the percentage increase in W is enough to offset the price increase.
It is. We need to look at the geometry of the diagram. Comparing the proportional shift inward of the T isoquant (which gives us the percentage price increase) and the proportional movement along the W axis, we see that W must increase proportionally more than Pt increases. So it is true that labor gains.
This illustrates the theorem.
Why is it that 'in the context of the H-O model this theorem translates into the simple statement that the abundant factor gains from trade while the scarce factor loses'?
According to HO the labor abundant country will export the labor intensive good, which is the good which must experience a price rise when trade is opened up (otherwise there is no incentive to export). The SS theorem says that if opening up to trade increases the price of T, then it will increase W becasue L is the factor used intensively in producing it.
So opening to trade benefits the abundant factor. Notice that to make this statement we have to link up both the HO and SS theorems. So it is not really a 'simple statement' after all!
A footnote about country A and B. If we start out with one country producing the same value of both goods (like in the case above) it cannot be the case that the other country is doing the same thing. In our model one country (A) is always more capital abundant than the other. Using the price definition of abundance, this means that the isocost lines in the two countries do not have the same slope. The labor abundant country, for example, has flatter slopes for the isocost lines, by the definition of labor abundance. If you look at the diagram, if one country is starting out with overlapping isocost lines, forcing the other country's isocost lines to have a different slope means that they cannot be overlapping. The bottom line is that it is impossible for A and B to be both simultaneously starting at a point with overlapping isocost lines.
Wednesday, October 22, 2008
Wednesday, October 15, 2008
topic 4.3
THE RYBCZYNSKI THEOREM
topic 4.3
The theorem is:
If a country experiences an increase in its endowment of any one factor holding all other things constant (including prices of products and factors) then the output of the good that uses the factor intensively will rise and the output of the other good will fall.
Consider figure 4.3 (p. 115).
To orient ourselves consider two isoquants: S output valued at $1 and T output valued at $1. (This is an arbitrary starting point -the theorem does not depend on it.)
The relative goods price is Ps/Pt = 1.
Ps/Pt = 1 implies that both S and T isoquants 'use' the same isocost line. So in the figure the isocost line is really two overlapping isocost lines.
Cost equals price of production so the isocost line represents an expenditure on hiring factors of production of $1 total.
For the isocost line the intercepts are 1/R (all the value of output goes to capital) or 1/W (all the value of output goes to labor).
The Rybczynski theorem keeps Ps/Pt constant by definition so wherever production occurs the isocost slope is the same which means that:
All the labor and capital has to be absorbed into production. That can only occur at E if GE is the ray for T production and EH is the ray for S production.
Now suppose we increase the labor endowment so E' is the new combination of L and K that must be absorbed.
Then (keeping Ps/Pt and K constant) we can only move from E to E' if the new rays are G'E' and H'E'.
So production of T increases and S decreases.
This proves the theorem.
The intuition is: to absorb all the factors (no unemployment), if we increase the total labor available we have to increase production of the labor intensive good relative to the other good.
We get this strong result because we are not allowing 'prices' (W/R) to change. All the adjustment to the 'shock' (endogenous increase in L) has to occur on the quantity side.
topic 4.3
The theorem is:
If a country experiences an increase in its endowment of any one factor holding all other things constant (including prices of products and factors) then the output of the good that uses the factor intensively will rise and the output of the other good will fall.
Consider figure 4.3 (p. 115).
To orient ourselves consider two isoquants: S output valued at $1 and T output valued at $1. (This is an arbitrary starting point -the theorem does not depend on it.)
The relative goods price is Ps/Pt = 1.
Ps/Pt = 1 implies that both S and T isoquants 'use' the same isocost line. So in the figure the isocost line is really two overlapping isocost lines.
Cost equals price of production so the isocost line represents an expenditure on hiring factors of production of $1 total.
For the isocost line the intercepts are 1/R (all the value of output goes to capital) or 1/W (all the value of output goes to labor).
The Rybczynski theorem keeps Ps/Pt constant by definition so wherever production occurs the isocost slope is the same which means that:
- S production will occur along the Ks/Ls ray.
- T production will occur along the Kt/Lt ray.
All the labor and capital has to be absorbed into production. That can only occur at E if GE is the ray for T production and EH is the ray for S production.
Now suppose we increase the labor endowment so E' is the new combination of L and K that must be absorbed.
Then (keeping Ps/Pt and K constant) we can only move from E to E' if the new rays are G'E' and H'E'.
So production of T increases and S decreases.
This proves the theorem.
The intuition is: to absorb all the factors (no unemployment), if we increase the total labor available we have to increase production of the labor intensive good relative to the other good.
We get this strong result because we are not allowing 'prices' (W/R) to change. All the adjustment to the 'shock' (endogenous increase in L) has to occur on the quantity side.
Monday, October 6, 2008
topic 4.2
PROOF OF THE H-O THEOREM
topic 4.2
Assume:
Industry S is capital intensive, both countries have the same set of isoquants that expand along the same rays and look the same in every way. So figure 4.2 works for both countries. But because factor endowments are different each country will choose to produce on a different specific pair of (unit) isoquants, the isocost curve will be different and (at least in autarky) the slope -W/R will be different.
If capital and labor are perfectly mobile with a country then in equilibrium the wage rate and rental will be the same in both industries (why would labor accept a lower wage in one industry when they can move to the other industry?)
To summarize figure 4.2. Both countries have the same set of isoquants. S is relatively capital intensive and so the S isoquants expand along a ray to the left of the ray for industry T. Now let's discuss choosing actual production levels.
First we have to make a change in our definition of relative factor abundence. We shall adopt the 'price definition' of relative factor abundance:
A country is relatively capital abundant if the wage/rental payment in its country is higher than the wage rental in the other country.
This definition uses the measure of the relative price of the factor inputs instaed of quantities. This definition may not always match what we would get with the 'quantity' definition.
Restating the H-O theorem using the price definition of factor abundance:
When the autarky wage/rental ratio is higher in A than B (A is capital intensive)the autarky relative price of S is lower in A than in B (A will export S).
If the autarky price of S is lower in A than B we know that when trade is opened up A will export S and import T. So what this defintion is saying is that the capital abundant country will export the capital intensive good.
PROOF
We will prove H-O by using figure 4.2.
However, we will do it differently from the text. The text starts with country A and then does a comparison with country B. We will do the opposite, going from B to A.
Suppose that the two isoquants shown are the isoquants for producing one unit of each good.
Then by comparing isocost lines which would apply to producing one unit of each good we know which good has the higher cost per unit.
Because these countries have perfectly competitive markets:
price (per unit) = marginal cost = average cost
So, knowing about relative costs of production tells us something about the relative prices of goods.
To begin, suppose we ask what is the relative cost of producing one unit of S and one unit of T in country B.
Suppose Wb/Rb are as shown in figure 4.2 and so production (of one unit each) will occur at X and Y. Since the isocost line for producing one unit of S goes through X, and the isocost line for producing one unit of T goes through Y, we can see that the cost of producing (one unit of)S is greater than the cost of producing (one unit of) T [the S isocost line is further out]. This means that Ps>Pt.
Now move over to country A. By the definition of factor abundance Wa/Ra > Wb/Rb. If we rotate the two isocosts lines to make Wa/Wb higher the distance between the two isocost curves decreases. In fact, there comes a point where the two isocost lines will merge into one (this is shown on figure 4.2). At this point Ps + Pt. So Ps has fallen below its value in B.
[There is nothing really special about the case where Ps = Pt. This happens to be the case where the dollar price of both goods is the same. It is only used because it makes the fall in the price of S as we increase W/R especially clear.]
Since autarky Ps/Pt is lower in the country which is more capital abundant we have proved the H-O theorem. Capital abundant S will export the capital intensive good.
topic 4.2
Assume:
- isoquants manifest constant returns to scale
- both countries have identical isoquants (same technology)
- both countries have identical consumption preferences
- A is capital abundant
- S is capital intensive
- both countries start on the two unit isoquants
- the price of the two goods is equal in A (this is arbitrary and only to make the demonstration easier)
- there is perfect competitionm and so prices exactly equal the cost of production
Industry S is capital intensive, both countries have the same set of isoquants that expand along the same rays and look the same in every way. So figure 4.2 works for both countries. But because factor endowments are different each country will choose to produce on a different specific pair of (unit) isoquants, the isocost curve will be different and (at least in autarky) the slope -W/R will be different.
If capital and labor are perfectly mobile with a country then in equilibrium the wage rate and rental will be the same in both industries (why would labor accept a lower wage in one industry when they can move to the other industry?)
To summarize figure 4.2. Both countries have the same set of isoquants. S is relatively capital intensive and so the S isoquants expand along a ray to the left of the ray for industry T. Now let's discuss choosing actual production levels.
First we have to make a change in our definition of relative factor abundence. We shall adopt the 'price definition' of relative factor abundance:
A country is relatively capital abundant if the wage/rental payment in its country is higher than the wage rental in the other country.
This definition uses the measure of the relative price of the factor inputs instaed of quantities. This definition may not always match what we would get with the 'quantity' definition.
Restating the H-O theorem using the price definition of factor abundance:
When the autarky wage/rental ratio is higher in A than B (A is capital intensive)the autarky relative price of S is lower in A than in B (A will export S).
If the autarky price of S is lower in A than B we know that when trade is opened up A will export S and import T. So what this defintion is saying is that the capital abundant country will export the capital intensive good.
PROOF
We will prove H-O by using figure 4.2.
However, we will do it differently from the text. The text starts with country A and then does a comparison with country B. We will do the opposite, going from B to A.
Suppose that the two isoquants shown are the isoquants for producing one unit of each good.
Then by comparing isocost lines which would apply to producing one unit of each good we know which good has the higher cost per unit.
Because these countries have perfectly competitive markets:
price (per unit) = marginal cost = average cost
So, knowing about relative costs of production tells us something about the relative prices of goods.
To begin, suppose we ask what is the relative cost of producing one unit of S and one unit of T in country B.
Suppose Wb/Rb are as shown in figure 4.2 and so production (of one unit each) will occur at X and Y. Since the isocost line for producing one unit of S goes through X, and the isocost line for producing one unit of T goes through Y, we can see that the cost of producing (one unit of)S is greater than the cost of producing (one unit of) T [the S isocost line is further out]. This means that Ps>Pt.
Now move over to country A. By the definition of factor abundance Wa/Ra > Wb/Rb. If we rotate the two isocosts lines to make Wa/Wb higher the distance between the two isocost curves decreases. In fact, there comes a point where the two isocost lines will merge into one (this is shown on figure 4.2). At this point Ps + Pt. So Ps has fallen below its value in B.
[There is nothing really special about the case where Ps = Pt. This happens to be the case where the dollar price of both goods is the same. It is only used because it makes the fall in the price of S as we increase W/R especially clear.]
Since autarky Ps/Pt is lower in the country which is more capital abundant we have proved the H-O theorem. Capital abundant S will export the capital intensive good.
Friday, October 3, 2008
topic 4.1
THE HECHSHER-OHLIN MODEL
Topic 4.1
The H-O model differs from the classical model because the explanation for international differences in PPFs is different.
In the classical model there is effectively only one factor of production - labor. The different PPFs reflect different production technologies (using labor) for each country.
In the H-O model technology is the same for all countries but factor endowments are different. This causes the PPFs to be different between countries.
Differing factor endowments are attractive as an explanation for trade because (at least some) factors of production are immobile between countries whereas technology is a public good which flows freely across borders. If there is a superior technology for making a product a country can always license it from abroad.
Assumptions:
Let's consider the capital intensity assumption a little futher. What this means is that no matter what the W/R ratio is, industry S always uses a higher K/L than industry T. And this is true for both countries whether they are in autarky or trading with each other.
There are different types of production structure that can insure ('ensure' in British english) that this is true. The simplest is to set K/L at a fixed ratio for every level of production in each industry. This 'fixed coefficients' technology generates right-angle isoquants that expand al0ng a ray from the origin. Whatever the W/R ratio the same K/L will be chosen. Diagrammatically the isocost lines are always tangent at the corner points of the isoquants.
This diagram shows right-angled isoquants (there are actually an infinite number of them) with the K/L ratio fixed for every level of production. Whatever the value for W or R the isocost line will always touch an isoquant at a corner. So production will always use K/L in a fixed ratio.
Capital intensity of A (in this fixed coefficients case) means that the ray for industry S is to the left of the ray for industry T.
Topic 4.1
The H-O model differs from the classical model because the explanation for international differences in PPFs is different.
In the classical model there is effectively only one factor of production - labor. The different PPFs reflect different production technologies (using labor) for each country.
In the H-O model technology is the same for all countries but factor endowments are different. This causes the PPFs to be different between countries.
Differing factor endowments are attractive as an explanation for trade because (at least some) factors of production are immobile between countries whereas technology is a public good which flows freely across borders. If there is a superior technology for making a product a country can always license it from abroad.
Assumptions:
- There are two factors of production: labor (L) and capital (K) which are paid wages (W) and rental (R).
- Countries have identical production technology.
- In both countries the S industry is more capital intensive than the T industry (notice we use the word 'intensive' when speaking of indutries).
- Countries differ in their endowments of factors of production. Country A is relatively capital abundant (we use 'abundant' with reference to countries).
Let's consider the capital intensity assumption a little futher. What this means is that no matter what the W/R ratio is, industry S always uses a higher K/L than industry T. And this is true for both countries whether they are in autarky or trading with each other.
There are different types of production structure that can insure ('ensure' in British english) that this is true. The simplest is to set K/L at a fixed ratio for every level of production in each industry. This 'fixed coefficients' technology generates right-angle isoquants that expand al0ng a ray from the origin. Whatever the W/R ratio the same K/L will be chosen. Diagrammatically the isocost lines are always tangent at the corner points of the isoquants.
This diagram shows right-angled isoquants (there are actually an infinite number of them) with the K/L ratio fixed for every level of production. Whatever the value for W or R the isocost line will always touch an isoquant at a corner. So production will always use K/L in a fixed ratio.
Capital intensity of A (in this fixed coefficients case) means that the ray for industry S is to the left of the ray for industry T.
Friday, September 26, 2008
appendix 3.2
OFFER CURVES AND THE TERMS OF TRADE
Appendix 3.2
Offer curves are an alternative way to represent the reciprocal demand that determines the terms of trade.
Figure A 3.2 shows A's desired trade for three different values of the terms of trade. As the TOT line gets steeper we see A's desired imports rise from T0 to T3, while desired exports rise from S0 to S3. As the TOT rises A is able to achieve a higher standard of living.
This change in the TOT is 'favorable' to A because it favors the good that A exports.
Figure 3.3 plots A's desired exports against A's desired imports.
If we think of the TOT as a price then as it rises A 'offers' a specific exchange of S for T.
The offer curve combines supply and demand behavior in one curve. It takes money prices out of the picture. Instead of offering to pay a certain number of dollars for a good, countries are going straight to making a barter offer.
In this approach money is a distraction and models that dispense with it get to the 'real' economics of trade.
Country B also has an offer curve.
Figure 3.4 puts the two offer curves on the same diagram.
There is only one TOT where the desired exports and imports all match. This is the equilibrium TOT.
At this equilibrium the two country's CICs must be tangent to each other.
Production choices, consumption choices, the terms of trade, goods prices and the exchange rate are all consistent with each other in general equilibrium. Unless there is some shock to the system the world will remain in this equilibrium state.
Appendix 3.2
Offer curves are an alternative way to represent the reciprocal demand that determines the terms of trade.
Figure A 3.2 shows A's desired trade for three different values of the terms of trade. As the TOT line gets steeper we see A's desired imports rise from T0 to T3, while desired exports rise from S0 to S3. As the TOT rises A is able to achieve a higher standard of living.
This change in the TOT is 'favorable' to A because it favors the good that A exports.
Figure 3.3 plots A's desired exports against A's desired imports.
If we think of the TOT as a price then as it rises A 'offers' a specific exchange of S for T.
The offer curve combines supply and demand behavior in one curve. It takes money prices out of the picture. Instead of offering to pay a certain number of dollars for a good, countries are going straight to making a barter offer.
In this approach money is a distraction and models that dispense with it get to the 'real' economics of trade.
Country B also has an offer curve.
Figure 3.4 puts the two offer curves on the same diagram.
There is only one TOT where the desired exports and imports all match. This is the equilibrium TOT.
At this equilibrium the two country's CICs must be tangent to each other.
Production choices, consumption choices, the terms of trade, goods prices and the exchange rate are all consistent with each other in general equilibrium. Unless there is some shock to the system the world will remain in this equilibrium state.
appendix 3.1
THE CLASSICAL MODEL WITH MANY GOODS
Appendix 3.1
Suppose:
In Table 3.1 are the labor/output ratios.
Country A's comparative advantage is in good Y.
We guess that B will export T and A will export Y, but what about the other 3 goods?
We know that goods T and Y determine the range for relative wages.
1/3 < Wa/(E.Wb) < 1
Table 3.2 ranks the value of (labor hours per unit B produced/labor hours per unit A produced) for each good.
B's greatest comparative advantage good (its most competitive export) is on the left. To produce one unit of T, country B only requires one-third as much labor as country A does.
This ordering is called 'the chain of comparative advantage'.
Suppose the relative wage rate was 2/3. Then B would produce all the goods except Y.
Where do the wages rates actually get detemined? In theory the wage rates in each country should adjust so that trade is balanced. If the wage rate in one country is 'too high' then the price of its least competitive export will be too high to compete in the market. So the country will tend to do some combination of lowering the wage rate and cutting back production of its least advantageous good until trade is balanced.
Appendix 3.1
Suppose:
- there are 5 goods
- all other classical assumptions hold especially fixed labor/output ratios
In Table 3.1 are the labor/output ratios.
Country A's comparative advantage is in good Y.
We guess that B will export T and A will export Y, but what about the other 3 goods?
We know that goods T and Y determine the range for relative wages.
1/3 < Wa/(E.Wb) < 1
Table 3.2 ranks the value of (labor hours per unit B produced/labor hours per unit A produced) for each good.
B's greatest comparative advantage good (its most competitive export) is on the left. To produce one unit of T, country B only requires one-third as much labor as country A does.
This ordering is called 'the chain of comparative advantage'.
Suppose the relative wage rate was 2/3. Then B would produce all the goods except Y.
Where do the wages rates actually get detemined? In theory the wage rates in each country should adjust so that trade is balanced. If the wage rate in one country is 'too high' then the price of its least competitive export will be too high to compete in the market. So the country will tend to do some combination of lowering the wage rate and cutting back production of its least advantageous good until trade is balanced.
Monday, September 22, 2008
topic 3.4
THE CLASSICAL MODEL OF INTERNATIONAL TRADE
Topic 3.4
Trade and wages
If labor is the only factor of production then in pretrade equilibrium the price of a good is simply the number of hours to produce it.
Psa = Wa x 3
Pta = Wa x 6
Psb = Wb x 12
Ptb = Wb x 8
Suppose both countries use the same currency.
Then for trade to occur the pretrade price of S must be lower in country A than in country B. And the opposite must be true for T.
Psa < E x Psb
Pta > E x Ptb
Where the exchange rate E converts country B currency into country A currency.
Then
Wa/(E x Wb) < 4
Wa/(E x Wb) > 4/3
that is 4/3 < Wa/(E x Wb) < 4
The middle term is the relative wage ratio.
Workers in A must earn more than in country B as measured in country A currency.
Differences in labor productivity explain the wage differences. Labor in A is 4/3 times as productive as labor in B (in textiles) and 4 times as productive in S production. These numbers set the limits for wage differences.
If the wage rate for labor in country A is more than four times the wage rate in country B then that would erase the advantage of buying goods from A. The extra high wage in A would erase any price advantage for S goods imported from A.
For good T, if wages in country B are more than ¾ the wages in A, it wipes out the productivity advantage of country B in the production of T.
To summarize, the wage rate in a country cannot be so high that it wipes out the natural comparative advantage that country has in its export good.
Another way of thinking about it: we know that productivity determines the standard of living in a country. It makes sense that relative productivity determines the relative wage rate between two countries. So the relative advantage A has in its export good sets the upper bound on its wage premium.
But, and this is truly surprising – it is not absolute advantage that sets the (limits for) the wage premium. It is comparative advantage. Being the lowest cost producer of a good in terms of labor costs does not raise your relative wage. It is the structure of comparative advantage (lowest opportunity cost) that matters.
Another remarkable result: it is the trade sector that drives relative wages. Because trade in this model drives both countries to specialize completely (by assumption), the whole production pattern of an economy is determined by comparative advantage.
Topic 3.4
Trade and wages
If labor is the only factor of production then in pretrade equilibrium the price of a good is simply the number of hours to produce it.
Psa = Wa x 3
Pta = Wa x 6
Psb = Wb x 12
Ptb = Wb x 8
Suppose both countries use the same currency.
Then for trade to occur the pretrade price of S must be lower in country A than in country B. And the opposite must be true for T.
Psa < E x Psb
Pta > E x Ptb
Where the exchange rate E converts country B currency into country A currency.
Then
Wa/(E x Wb) < 4
Wa/(E x Wb) > 4/3
that is 4/3 < Wa/(E x Wb) < 4
The middle term is the relative wage ratio.
Workers in A must earn more than in country B as measured in country A currency.
Differences in labor productivity explain the wage differences. Labor in A is 4/3 times as productive as labor in B (in textiles) and 4 times as productive in S production. These numbers set the limits for wage differences.
If the wage rate for labor in country A is more than four times the wage rate in country B then that would erase the advantage of buying goods from A. The extra high wage in A would erase any price advantage for S goods imported from A.
For good T, if wages in country B are more than ¾ the wages in A, it wipes out the productivity advantage of country B in the production of T.
To summarize, the wage rate in a country cannot be so high that it wipes out the natural comparative advantage that country has in its export good.
Another way of thinking about it: we know that productivity determines the standard of living in a country. It makes sense that relative productivity determines the relative wage rate between two countries. So the relative advantage A has in its export good sets the upper bound on its wage premium.
But, and this is truly surprising – it is not absolute advantage that sets the (limits for) the wage premium. It is comparative advantage. Being the lowest cost producer of a good in terms of labor costs does not raise your relative wage. It is the structure of comparative advantage (lowest opportunity cost) that matters.
Another remarkable result: it is the trade sector that drives relative wages. Because trade in this model drives both countries to specialize completely (by assumption), the whole production pattern of an economy is determined by comparative advantage.
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