## How gains from trade arise

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In a simple two-consumer economy, there is a possibility that both consumers can end up better off through trade with each other. If we model an economy with only two goods, and a given initial quantity of each of these goods, then we can represent the utility of the two consumers on the same diagram by using the Edgeworth Box model.

If we call the consumers Abe and Boris, and a fixed initial quantity of two goods, say 100 bananas and 50 coconuts, and we assume that all the goods are distributed to just Boris and Abe, then we can represent this as follows:

This diagram with one of the consumers axes inverted is an Edgeworth Box model. If we are at point X, then we can see that Abe has 20 bananas and 20 coconuts. As all the goods have been distributed, this means that Boris must have 80 bananas and 30 coconuts, and if we read from his axes we can see that this is indeed the case. They could also be at point Y, a different allocation of the goods, or indeed at any other point in the box.

Abe and Boris will both have indifference curves, and at any point in the box they will both be on an indifference curve of their own. Now we can see how gains can arise from trade. A person is better off if they can move to a higher indifference curve. If we assume that Abe and Boris are at point D, and draw their respective indifference curves, we can see that there is a region between the two curves.

If they were to move to any point inside this region, at least one consumer would be better off, as they would have moved to a higher indifference curve. Say that through negotiations, Abe and Boris agreed to trade goods and as a result moved to point E.

At this point E, both Abe and Boris have moved to a higher indifference curve, so both would consider themselves better off than before. Point E is Pareto Preferred to point D. However, we can see that there is still a region between the curves where one or the other or both can be better off. Eventually, through repeated trade and negotiations, they will come to a point where their indifference curves are tangential, point F.

There is no longer a possibility of a trade that will leave one consumer better off without the second consumer being worse off than before. This point is called Pareto Optimal. Both Abe and Boris have maximised the possible gains from trade between each other.

Intuitively, it makes sense that the Pareto Optimal point should be at the point where the indifference curves are tangential. This is because the slope of the tangent represents how much of one good they would be willing to trade for one unit of the other good. If their tangents are the same, then they will both be willing to trade one good for the other at exactly the same rate. This means that trade cannot take place between them as there is no benefit for either. Therefore, once trade ceases, we will be at the Pareto Optimal point.

However, there is more than one Pareto Optimal point. In fact, there will be an infinite number of these points; anywhere there is tangency between an indifference curve of Abe’s and indifference curve of Bill’s. Joining up all of these Pareto Optimal points we obtain the Contract Curve.

Where we are on the contract curve depends on both the initial utility allocation, and the negotiation skills of Boris and Abe. If we start at G, as discussed above, voluntary trade will eventually move them onto the contract curve. However, we will only ever end up at a point between H and J, as below H Abe will be worse off, and similarly for Boris above J. If we start at point K, we will end up on the contract curve between L and M.

If we are at point G, where we end up on the contract curve between H and J is determined by the respective negotiating ability of Abe and Boris. If Abe is a bit of a charmer he may be able to end up at J, as Boris will be no worse off than when he started. However, if Boris has true Russian blood in him he won’t back down so readily, and a likely outcome is somewhere in the middle of H and J.

From the contract curve we can see that just because a point is Pareto Optimal, it does not necessarily mean that the position is good for both of them. If we are a point where Abe has just two bananas and one coconut, and Boris has the remaining ninety-two bananas and forty-nine coconuts, their indifference curves may be tangential, but Abe is likely to starve. In real-life situations with this ratio of allocation of goods, it may be both desirable and necessary for the government to intervene on behalf of the demographic represented by Abe.

Another time that the government may wish to intervene in the system is when the trade affects people other than those trading. For instance, say the good being traded is tobacco. If we still consider a two-person economy, we can use the Edgeworth box model with one axis representing cigarettes, and the other representing everything else. The two consumers can improve their own bundles by buying and selling cigarettes until the pareto optimal point is reached. However, when the cigarettes are smoked, not only is the health of the two consumers harmed, but others around them are also harmed through passive smoking. Tobacco leads to a huge number of diseases, in particular lung cancer, and these illnesses must be treated.

In the UK with the National Health Service, the bill for treatment is footed by the taxpayer. In this case, the trade now affects others not involved in it. Therefore, it makes sense for the government to intervene in this trade in such a way that prevents people outside the trade from being affected. The normal way of achieving this is to tax the good in question. Now every time cigarettes are bought, the consumers pay more on top of the true value of the goods, and this extra money goes to the government. If the tax is at the right level, then ideally this extra money should pay for any treatments or other problems caused as a result of smoking. Of course, putting an accurate figure on the total damage caused is very hard.

In conclusion, gains from trade will continue, until the pareto optimal point is reached. Where the two consumers are on the contract curve is determined both by the initial allocation of resources, and their respective negotiating ability. However, just because they are on the contract curve does not imply that they are both well off, and in some cases the government should intervene. Other cases where the government may need to intervene are ones where the goods being traded adversely affect others not involved in the trade.

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