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Partial and General Equilibrium in Toilet Flushing

Posted Feb 18 2009 12:09pm

I have been traveling a lot lately doing flyouts for job interviews.  I was at an airport recently and forgot to flush the toilet.  Usually this is not a problem, since most urinals at airports are automatic flush toilets.  However, in this case the toilet was not an automatic flush toilet.  This got me thinking about the economics of automatic toilet flushers.

On average, individuals will flush the toilet with some probability, p.  If a toilet has an automatic flush mechanism, then the toilet will flush with probability 1.  Of course, not all toilets are automatic flush toilets.  Thus, if f percent of toilets are automatic flush, the increase in the probability of flushing a toilet is f*(1-p).

Chart

In a partial equilibrium setting, marginal effect of adding an automatic flush toilet increases flushing rates by 1-p. 

  • ∂[f+p(1-f)]/∂f = 1-p

So automatic flush toilets are a good thing right?  Probably, but maybe not as much as expected.  People may get used to having automatic flush toilets (as I did).  As the proportion of automatic flush toilets increases, this may decrease the probability that anyone flushes the toilet in the non-automatic setting since have become so  accustomed to having an toilet that flushes itself.

The probability of flushing a non-automatic toilet may depend on the proportion of toilets that are automatic flush.  In the general equilibrum, we can replace p, with p(f) where ∂p(f)/∂f<0). Now the impact of installing an automatic flush toilet is not as large. 

  • ∂[f+p(f)(1-f)]/∂f = (1-p)+(1-f)p’ 

What this equation says is that installing an automatic flush toilet increases the chance that a specific toilet flushes, but decreases the probability an individual flushes a toilet in a non-automatic setting.

Who would have thought that airport toilets could be so interesting!

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