The Advantage of Trading

by
Jason Kantz
Dec 2007

Homer and Apu are going spend an hour picking apples and catching fish.

They determine that in one hour, dividing their time equally between the two activities they could each produce the following amounts for themselves:

          Homer     Apu

apples    50        100

fish      50        200

Apu would love to have 12 more apples but still have 200 fish. He offers to make a deal with Homer: Apu will give homer 50 fish in exchange for 37 apples. Homer asks Lisa to work out how much he could get if he spent more time picking apples and Apu spent more time catching fish:

1.        Homer       Apu

apples    50 + 37     100 - 25

fish      50 - 37     200 + 50 

2.        Homer       Apu

apples    50 + 37     75
fish      13          200 + 50

Then they would make their trade:

3.        Homer       Apu

apples    50          75 + 37

fish      13 + 50     200

4.        Homer       Apu

apples    50          112

fish      63          200

So Homer figures that by trading, they can both have more, and he accepts the deal. However, Mayor Quimby has some public initiatives that can only be funded by a 26% percent tax on all trades. Homer has Lisa recalculate the deal:

1.        Homer              Apu              Mayor Quimby

apples    50                 75 + 37 -.26*37    + .26*37

fish      13 + 50 - .26*50   200                + .26*50

2.        Homer              Apu              Mayor Quimby

apples    50                 75 + 37 - 10       + 10

fish      13 + 50 - 13       200                + 13      

3.        Homer              Apu              Mayor Quimby

apples    50                 102                + 10

fish      50                 200                + 13

Homer realizes he won't come out ahead, and cancels the deal.

By imposing a tax, Mayor Quimby gave Homer an incentive to work alone. So Mayor Quimby needs to find the sweet spot where the benefits of the public initiatives exceed the amount of wealth and cooperation everyone could have enjoyed.

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