6.1 Mutual Gains from Trade
In the last lecture we established that some allocations in the Edgeworth Box are not Pareto efficient: there are other allocations which could make at least one agent better off, without making any agent worse off. In particular, this occurs when agents’ marginal rates of substitution at an allocation are different: that is, when the relative values they place on goods differ.
It follows that at such a point, there are potential mutual gains from trade: that is, the two agents can find another bundle which represents a Pareto improvement, and trade to it. The graph below shows Alison and Bob’s initial allocation $E$, both from the perspective of the Edgeworth Box and from their individual perspectives. Bundle $X$ represents a potential trade. If you drag bundle X around the box, you can see that some allocaitons (i.e. the ones in the “lens” of Pareto improvements) make both Alison and Bob better off. Others make only one of them better off, or even neither better off:
[ See interactive graph online at https://www.econgraphs.org/graphs/exchange/edgeworth_box/gains_from_trade ]
Such a bilateral trade is the most basic economic transaction, and can be used to analyze many situations involving the applications we’ve looked at in this part of the textbook:
- If both “goods” are goods, then it’s just describing trading one good for another
- If good 1 is some good and good 2 is money, then it’s trading money for goods
- If good 1 is present consumption and good 2 is future consumption, then it’s one agent lending the other some money
- If the goods are money in different states of the world, then it can represent a contract like a bet, in which one agent pays the other in one state of the world, and vice versa
For each type of trade, there are various ways at which we can arrive at a new allocation:
- One agent proposes a “take it or leave it” trade to the other, who accepts or rejects the offer
- One agent sets a price ratio at which they are willing to trade; the other chooses how much to trade at that price
- The “market” sets a price at which all agents may trade; agents then choose how much to trade at that price
While all of these are interesting, we’re going to focus (for now) on the last one: one in which there is a market price that all agents take as given, and each agent chooses how much to trade at that price. This is called a competitive equilibrium.