The text worked a simple problem to illustrate that
with a winnertakeall markets, there was a tendency
for too many people to compete for the prize and that
as a result, there was an inefficiency. Here is
another simple story that tries to illustrate the
logic why winnertakeall markets tend to attract more
people than is economically efficient. See if you can
work out the answers.
Suppose that on Potter Island everyone makes pots
and that by some freak of nature all of the
inhabitants fall into two groups. One hundred of them
can make ten pots per day and one hundred of them can
make twelve pots per day. Pots sell for $10 each.

a) How much per day will the less productive members on the island make per day?
$


b) How much per day will the more productive
members on the island make per day?
$


c) What will total income per day be on the island?
(Multiply the amount made per day by the number who
make that amount, and add the two amounts together.)
$


d) Is this a winnertakeall market?



Now suppose that a tourist industry arrives and that the islanders have a chance to be underwater performers in a special tourist show that will highlight the native culture. All potential performers will have to train so they cannot make pots. At the end of each day the five who can hold their breath the longest are chosen to perform, and each one chosen will make $1000
for the day. Although they do not realize it, if all
the islanders trained, the ability of the best of
islander would be only 20% more than the ability of
the worst islander. There is no way to tell at the
beginning of any day which one will end up the winner
for the day. Assume that they are risk neutral, and
they will decide whether to enter the competition
based on the expected value of entering the competition.

e) If only five enter, what will each expect to
earn each day? $


f) Given this earning, would another islander find
it worthwhile to enter the competition?


g) Suppose that 25 abandon pottery making and enter
the competition. What is the expected value that they
would get? (Hint: it is $5000 divided by 25.)
$
Would more islanders find it worthwhile to enter the
competition?


i) It will become a bad decision to enter when
there are
already in the competition.


j) What will the total income per day be on the
island when it is no longer worthwhile for anyone else
to enter the competition?
$


k) What is the largest total income that the island
could have?


l) Has the distribution of income on a daybyday
basis gotten more equal or less equal?


Note that a similar logic is used in examining the
problem of the
commons and also rent
seeking. In all these cases, people respond to average rather than marginal costs or benefits.
