We saw in the previous section why the two countries H and F would want to trade - if together they own all of the goods X and Y in the economy, trade is the only way for them to both increase their level of satisfaction.
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Now, given that H would like to move to a point above IH, and F would
like to move to a point below IF, the resulting position following an
exchange of goods will be in the area indicated by the arrow.
So, what point will they move to? Let's imagine for a moment that F is happy to remain at IF but is willing to trade with H in order for H to improve. What point gives H the greatest level of satisfaction? |
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Consider the graph to the right. The indifference curve I'H intersects
IF at two points, that is, there are two points where F maintains
the current level of satisfaction but H attains the level of satisfaction given by
I'H. As we increase the level of satisfaction of H, the two points
converge, until finally we arrive at a utility level given by I''H
that meets IF just once. At that point, the tangents of both
curves are identical. This point can be achieved by trade: H gives the amount of X indicated
in the graph to F, and receives an amount of Y in return.
If we tried to increase H's utility level further, F's utility level would have to decrease in order for the two curves to still meet. |
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| The same argument can be applied to F to show what would happen if H was happy to remain at IH. In practice, of course, both H and F would like to improve their positions -- the two shown are merely the extremes, where one is willing to forego improvement. So where will they end up (i.e. where is the equilibrium after trade)? That depends on their relative bargaining power. | |
| For every utility curve IH', there is a corresponding curve IF' that only intersects it at one point. If we look at this point of intersection for all possible utility curves, we see they form a line. At any point on that line, each party has maximised their own satisfaction given the other party's level of satisfaction. The image to the left shows some example utility curves and their points of intersection. Any point on that line is reachable by trade, and by reaching some point on that line, no-one's utility gets hurt -- any point on that line is superior to the initial endowment point. |
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Price Ratio | |
| Consider H and F have traded goods X and Y until they have reached a final position in the Edgeworth Box. Let us compare that final position with the starting position. | |
| Observe that to reach the position indicated in the graph, H had to give up x' units of X, and in return was given y' units of Y. The quantity y'/x' gives us the exchange rate of the goods X and Y in this economy and is equal to Px/Py, known as the price ratio of those two goods, or the "Terms of Trade" for H. (F's Terms of Trade is therefore Py/Px.) The tangent of both curves, known as the Marginal Rate of Substitution, is also equal to Px/Py: |
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