Sunday, 19 March 2017

The utility value of a towel

Sooner or later, students of operational research encounter the economic concept of utility.  It can lead to an interactive lecture, when one offers a volunteer from the class a fair bet of either £0 or £10, and then offers to exchange that bet for a certain amount £X.  What value of X do you select?  (I found it helped to actually have a £10 note in my hand when I did this.)  With suitable repetitions it is possible to select a few points on that volunteer's utility for money curve, and then sketch the general shape of it.  Most students are risk-averse and this is the typical concave-downwards curve, so X will be less than 5.
 In general, a risk-averse person offered a fair bet between £S1 and £S2 will exchange that bet for an assured amount < 0.5(S1+S2)
This discussion - when I taught it - following the example of the text books - leads on to assessing the utility of non-monetary outcomes, as a way of looking at the results of management decisions.  There was a story, often quoted, of the student who assessed the choice between his status quo for the next academic year and a free ticket to every campus event for the next twelve months.  He preferred the status quo, on the basis that he would not have the numerous temptations of missing classes and essays.
One morning earlier this year, Tina and I arrived at the city swimming pool to find two damp towels in the rubbish bin, and two damp swimming costumes, and a receipt from a (low cost) city centre shop for these four items, dated the previous day.  We recovered the items, put them in the next domestic washing machine load, and gave them to a charity shop later on.
We tried to reconstruct the back story for this purchase and disposal.  One credible account for it was:
Two people were visiting the city and staying in a hotel; they wanted a swim, so made the purchase, and then had the damp towels and costumes to cope with.  Because they were visiting, they had no way of drying them, or wish to take them away, so they chose to dump them.  
Now consider the choice these two had made.
Either:
(Plan A) Don't swim - cost zero
Or
(Plan B) Swim: cost of a towel, costume and one pool entry each - about £15 each
Not everyone would consider the utility of Plan B to exceed that of Plan A; would you?
Meanwhile, Tina and I had the choice:
Either
(Plan Y) Leave these wet items where they were
Or
(Plan Z) Carry them home and spend a little time dealing with them
... and you can work out which had the greater utility for us.


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