Exploring producer and consumer with math

Exploring Why Winner-Take-All Markets Are Inefficient

The text worked a simple problem to illustrate that with a winner-take-all 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 winner-take-all 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 winner-take-all market?

Do not enter the dollar sign with your answers.

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 day-by-day basis gotten more equal or less equal?

Do not enter the dollar sign with your answers.
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.

The text worked a simple problem to illustrate that with a winner-take-all 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 winner-take-all 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 winner-take-all market?
Do not enter the dollar sign with your answers.
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 day-by-day basis gotten more equal or less equal?
Do not enter the dollar sign with your answers. 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.