The Advantage of Trading

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, Mr. Burns steps into the story and
threatens to impose a 26% percent tax on all trades.  Homer has Lisa
recalculate the deal:

1.        Homer              Apu              Mr. Burns

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

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

2.        Homer              Apu              Mr. Burns

apples    50                 75 + 37 - 10       + 10

fish      13 + 50 - 13       200                + 13      

3.        Homer              Apu              Mr. Burns

apples    50                 102                + 10

fish      50                 200                + 13      


Homer realizes he won't come out ahead, and cancels the deal.  By
threatening a tax, Mr. Burns gave Homer an incentive to work alone,
reducing the amount of wealth and cooperation everyone could have
enjoyed.