How Trade Possible under constant opportunity cost under the law of comparative advantage
As the first step in this direction, we learn behind the labor theory of value. There is a way to abandon the labor theory of value and yet retain the theory of comparative advantage as a principle of international trade.
If we assume that a nation’s production possibilities are limited to two types of goods. We can derive a so-called transformation function.
Under any transformation function, the economy must give up some quantity of one good in order to increase the output of the other.
When production shifts are small, the rate at which they occur is defined by the marginal rate of transformation. Graphically, the marginal rate of transformation is shown by the slope of the transformation function at each point along the curve.
The transformation function that we have described here is linear. This means that the marginal rate of transformation is constant throughout their respective lengths.
The transformation function here is linear, meaning that constant opportunity costs prevail.
In figure illustrates one of the highly simplified straight-line transformation functions.
United States can produce either 50 units of B or 30 units of A or any combination of the two along transformation curve WX. By the same token, the United Kingdom can produce either 15 units of B or 30 units of A. or any combination theory along transformation curve YZ.
To produce one additional unit of B in the United States, the economy must always sacrifice 0.6 units of A to do so. This is true no matter whether a great deal of B and little A is produced or vice versa.
Constant opportunity costs also prevail in the United Kingdom, except that there, the addition to the output of one unit of B always calls for the reduction in A output by 2 units. In short, the marginal rate of transformation of B into A is 1:0.6 in the United States and 1:2 in the United Kingdom.
The marginal rate of transformation of goods B and A. in the US one unit of B “costs” 0.6 that of A, and in the UK the same that of B “costs” 2 units of A.
It would appear that good B is in a real sense cheaper in the former country. Whereas good A is cheaper in the latter.
The US has a comparative advantage in the production of good B, whereas the UK has a comparative advantage in the production of good A.
According to the theory of comparative advantage, the two nations would do well to trade, with this US exporting good B to the UK in return for good A.
Both should be able to hence their economic well-being by so doing. In order to show this, let us simply place both the US and the UK transformation curves on the same diagram.
By this diagram so that they touch at point X (or Z). Note that the British B:A exchange ratio of 1:2 the slope of the line, has not been changed in the process.