GLOBAL POLITICAL ECONOMY: Comparative Advantage Example

 

In what follows I lay out the logic and provide an example of comparative advantage in trade. 

 

1) First, we have some Assumptions:

·                          each country has the same amount of resources available. 

·                          all goods are produced entirely in one country or the other and then traded, i.e. producers cannot relocate their capital and capacity to other countries at this point.

·                          no externalities or other “uncaptured” costs, such as transportation included yet.

 

2) Production Possibility Frontier: Now, suppose Britain and the U.S. can produce a maximum of EITHER the quantities of wheat or iron shown below, or some combination of the two.  It would good practice to draw the Production Possibility Frontiers for each country.

 

Wheat    Iron     Ratio    Ratio                   OppCost of Wheat         Opp Cost of Iron

Wt:Ir     Ir:Wt

Britain                300  or   400     3:4         4:3                        1 1/3(1.33)  units of     .75 units iron to wheat

iron per unit/wheat        [ratio Ir:Wh now 4:3]

Unites States     100  or   200     1:2         2:1                        2 units of iron                .50 iron to wheat,  

per unit wheat. [ratio Ir:Wh now 4:3]

Totals:                400  or   600     4:6         6:4

 

 

In our example, Britain has an absolute advantage in both goods, i.e., it can produce more for the same resource input.  More output per unit input means Britain is a more efficient producer of each good.

 

3) Opportunity Cost Before Trade.  Each country must give up some of one good in order to increase its output of the other good. The amount forgone to create another unit of an output is the opportunity cost. It measures the cost as the resources and their output that have to be dedicated to the newly created good.

 

·                          Britain can trade each unit of wheat for iron before trade at a rate of 3:4, and thus must give up 1_ units of iron for additional each unit of wheat it wants. [Divide the ratio 3:4 through by 3 to get a ratio of 1: 1.3.]

 

·                          The U.S. must trade two units of iron per unit wheat, because its INTERNAL ratio of exchange is 1:2.

 

 

4) Determining the Comparative Advantage for Each Country:  

 

Each country must now specialize in the good that they can produce at lowest opportunity cost. Because the ratios of exchange are not the same in the two countries, there will be beneficial trading possibilities.

a) Now, you can see from the above that Britain can produce wheat relatively or COMPARATIVELY more cheaply than the U.S..  That is, Britain has a lower opportunity cost for wheat measured in sacrificed units of iron, 1.33 (vs.  2). Britain therefore has a comparative advantage in WHEAT.

 

b) Conversely, you could look at the opportunity costs for iron in each country and see that the U.S. is the low opportunity cost producer of iron. The U. S must only sacrifice ˝ (vs 3/4 for Britain) of a unit of wheat per additional unit of iron and thus has a comparative advantage in iron production.

 

c) Another way to look at it, is to see that Britain has a 3:1 advantage in Wheat and only a 2:1 advantage in Iron and should specialize in the good in which its advantage is greatest. The U.S. a should specialize in the good in which its disadvantage is smallest.

 

5) International Rate of Exchange between Wheat and Iron:  Now, if Britain and the U.S. are to trade internationally, they will need to agree on a “price”, that is a rate of exchange of wheat for textiles that will be in their mutual interest.   In particular, Britain must be able to exchange wheat for more than the 1.33 units of iron that British wheat producers can get at home. Likewise, U.S. iron producers must be able to get more than the .5 units wheat they can get at home for a unit of iron.

 

If we imagine that the two economies were now taken as a single, global economy, than the total amounts of wheat OR iron that could be produced are the totals of both countries, 400 wheat and 600 iron. Now that the countries are specializing, its as if there is a more global production possibility frontier that includes the possible output from both countries.  The rate at which wheat can be exchange for iron in this global economy is 4:6 or 2:3 or 1: 1 ˝.   This is the new international rate of exchange between wheat and iron.  Notice, the international rate of exchange will always be mathematically between the two country’s separate rates. .

 

 

6) Computing the New Opportunity Costs and Production Possibility Frontiers after Specialization and Trade:

 

Once we know the rate of exchange between wheat and iron, we can deduce the amounts of each that define the countries new maximums given trade. Britain specializes in wheat and can still only produce a maximum of 300 units. But now, it can get textiles for wheat, on the international market, at a rate of 1:1.5, rather then the rate of 3:4 from before.  So, now we have a simple equation to solve.  How much iron can Britain get in the open market if it produces 300 units of wheat and then trades wheat at a rate of 2 wheat per 3 textile?

 

We also want to know how much wheat the U.S. can get if it specializes in iron and then can trade up to its 200 units iron at the same international rate of 1:1.5.  Thus, the U.S. can get up to two thirds the number of textile units in the form of wheat through trade, rather than the one half it could get before.

Before trade we could have represented the amount of iron produced in Britain using the following formula:

 

Britain:

1.)  1: 1_ = 300:x     This is a way of saying that if we know the rate of exchange (1:1_) and the amount of wheat (300), we can figure out how much iron Britain must be capable of producing. We could also represent this expression like this: 1/1.33 = 300/x .

 

This expression, by cross multiplying, is: x = 300 X 1.33  

 

Thus, x =  400.      Or,   1:1.33 = 300/400.

 

 

2.)  NOW, after trade, we know that the rate of exchange is 1:1.5 and thus we can deduce the new maximum level of iron that Britain could obtain through trade with wheat.

 

1/1.5 = 300/x,   or x = 300 X 1.5  

 

Thus x = 450.   Britain can expand its possible combinations of wheat and iron because it can get more iron for its wheat than without trade.

 

We now know that Britains production possibility frontier, based on trade is defined by 300 units of wheat and 450 units of iron.

 

U.S.

1.)  The U.S. used to trade iron for wheat at a rate of 2:1. Now, after trade it only has to trade 1.5 units of iron for each unit of wheat.  We can find the new maximum amount of iron that the U.S. can get in trade as follows:

 

1:1.5 = x/200 , or

 

1.5x = 200, or

 

x = 200/1.5, or

 

x = 133.3.          Therefore, after trade, the U.S. can produce 200 units of iron and trade that for up to 133 units of wheat, which is more than the 100 unit prior to trade.

 

[Notice that we could have calculated the maximum U.S. wheat level in trade by starting with the opportunity cost of iron, as follows:

 

.75:1 = x/200   and then we have;  x = 200 X .75,  which gives us the same result, x = 1.33.]

That is, China can get 133.33 units of wheat, rather than the 100 it could get before.

 

 

The Gains from Trade:  Production Possibilities After Trade: Below are the new possible combinations of wheat and iron with trade.

 

Wheat                  Iron                      International ratio:

Britain                300                       450                       3:2

U.S.                      133                       200                       3:2

 

Totals                  433                       650                       3:2

 

It appears, as if by magic, more is possible in the world economy and thus each country can have more of each good. [Draw the new PPF for each country and show this result for each.]

 

Where does the gain come from?

 

We move from having two separate economies with internal rates of exchange based on their production possibility frontiers, to having a single economy in which the totals capable of being produced rises. It does not rise because there are any more resources in this expanded, two country economy, than there were in the two separate economies.  But prior to specialization, each country was having to sink some of its resources into the production of a good that the other country could make for fewer resources (measured in opportunity cost, that is, how much has to be given up to make something).  After specialization, each country can devote a larger share of its resources to producing a good that it can then convert or exchange into the other at a better rate.  This gain springs from the specialization within each country that allows each to switch resources into the comparative advantage good that trades for fewer resources when produced abroad than if they had been produced at home. In short, specialization and improved efficiency in the deployment of resources leads to the gain.