The Roommate Problem or Part One Of A Review Of The Darwin Economy

It’s taken awhile, but I’ve finally finished reading it and suffice it to say that reading The Darwin Economy has been an enlightening experience.  It took so much time because it was a challenging book that required quite a bit of counter-intuitive(that is to say counter to normal human intuition)reasoning.  Much like other books I’ve read about the severe disconnect between the everyday human experience and an actual rational human existence, it required me to step outside of myself and try to consider things more objectively than normal.  Consider the Roommate Problem.

Robert Frank presents the problem very clearly and his conclusions appear true, but it took me some deep thought to actual resolve the problem in a way that I could understand it.  That is to say that my personal resolution of the Roommate Problem didn’t require advanced degrees in Economics, it just needed me to formulate a simple statement of the conclusion of the problem itself.  That would be this:

People who enjoy a benefit should pay a premium.  People who have to suffer a penalty should pay a discount.


I don’t mean it to be a Truth or anything, but it’s a good start and a quick guide to understanding when and why we should pay more or less for something.  And now on to the line of reasoning that leads to the above.

Consider two people A and B.  They may each live separately and pay $2000 a month in rent or they may live together and pay $3000 in total.  Obviously the only rational choice would be that they should live together.  Together they share a savings of $1000; this savings they can spend any way they please on dragons, werewolves, or any other thing they fancy.

If you want to stop now and consider other possible variables.  Please feel free, variables like personal compatibility and such should definitely be considered, however if such considerations do not exceed the maximum value of $1000 together or $500 for A and B apart then they are irrelevant both A and B will still get more value living together than apart.  That said...consider the next iteration of the same problem.

Consider two people A and B.  They may each live separately and pay $2000 a month in rent or they may live together and pay $3000 in total.  The house they find isn’t perfect.  It has two bedrooms but one bedroom is substantially larger than the other.  Most people would agree that the person who gets the bigger bedroom should pay a bigger share of the rent; I might even suggest that person should pay a bigger share of the rent that is proportional to the relative sizes of the two bedrooms.  But that’s just me I’m sure other people can divide the total rent in a myriad of ways that are both fair and reasonable.  Regardless of how the division is made the person who gets the big bedroom pays a premium, and if that is true then the person in the smaller bedroom pays a discounted rate.  It shouldn’t strike any as unfair that this is true.  I’m sure most people recognize that the person in the smaller bedroom is suffering a penalty and that penalty demands a discounted rate.

Up to this point most people can agree.  In the third iteration of the problem--it’s the same problem as described in Frank’s book The Darwin Economy--people can get bogged down.  I certainly did.  Before you start going on about how I’m trying to promote some sort of smoker’s conspiracy or that maybe smoker’s shouldn’t have to pay taxes...blah blah blah, I urge you to take a moment to consider and think what the distinction or difference is between the person in the bigger bedroom and non-smoker B.  They both enjoy a benefit: one gets a bigger bedroom and the other gets a smoke-free space.  Shouldn’t both pay a premium for those benefits?  If that’s too difficult then consider the possibility that it’s not smoking we’re discussing it’s some other vague benefit entirely.  It shouldn’t matter what the benefit is; whoever enjoys a benefit should pay a premium for it.

Consider two people A and B.  They may each live separately and pay $2000 a month in rent or they may live together and pay $3000 in total.  Person A isn’t perfect.  He enjoys smoking tobacco.  Person B is allergic to tobacco.  In the world we live in these two people probably shouldn’t live together, but examining the problem in a little depth should reveal some interesting things.  This isn’t quite like the problem with the big/small bedroom; it’s not so easy to quantify people’s preferences when it comes to things like this.  Person A has to calculate a dollar amount that reflects the value he would receive if he were allowed to smoke in their shared space.  Person B has to do the same except he needs to determine how much it is worth to him to live in a smoke-free space.  Frank sets those values for us.  Person A’s value--what it’s worth to him to smoke in the space--is $800.  Person B’s value--what it’s worth to him to live in a smoke-free space--is $1600.  
At this point the author goes on a tangent about income disparities.  Maybe Person B earns more and so can leverage his higher income to influence the outcome of the problem by setting a higher value on a smoke-free space than Person A can afford.  “It’s not fair that rich people get more influence,” some might remark.  It’s true it’s not fair but does it make sense to subvert all logic for that reason?  I’m not sure either way, the only thing I might add to that tangent is that if that were the case both Person A and B should try to find someone to share a space with that earns a similar income to themselves.
Given these values it makes the most sense for Person A to not smoke in the space.  Don’t think that it’s about some weird anti-smoking issue.  This is a simple comparison of values.  $800 is less than $1600.  Therefore it is more efficient that Person A doesn’t smoke in the space.  Some might just leave it at that.  Person A and Person B should just split the shared rent like in the first iteration and call it a day.  However such a quick conclusion neglects the results of the second iteration.  Why should Person B get their way and not pay for it?  If this were the second iteration you could just compare the size of the bedrooms and calculate a fair premium, but this isn’t as quantifiable as that.  Luckily we do have a quantity to work with, $800.  It’s a given--that is to say it doesn’t have any basis in facts--but we can still use it to work out a fair division of rent.  Person A suffers an $800 loss or penalty because he isn’t allowed to smoke in the house.  Should Person B pay that premium completely?  Of course not, if Person B did then his rent would be $2300 and would be better off living alone for $2000.  Besides Person A would be enjoying the cash equivalent of his loss without paying a premium for it.  The only rational way to divide the rent is taking the $800 value and splitting it in two.  Person A will pay a $400 discount $1100, and Person B will pay a $400 premium $1900.  In this both Person A and Person B still enjoy some benefit out of living together.  Person A has an extra $400 dollars to spend to offset his penalty of not smoking in the space and the $500 benefit of living together.  Person B has an extra $100 that he wouldn’t have had if he lived alone, not to mention the benefit of a smoke free space.  And everyone lives happily ever after?

Of course not.  One of the human foibles that we all share will make everyone who reads this think it’s unfair somehow.  Some will insist that Person B’s extra $100 isn’t worth it and that Person B should just live alone.  It’s inside all of us to despise this sort of unfairness.  I direct you to take a look at some studies of the Ultimatum game.  The results of those studies suggest that when it comes to situations like the Roommate Problem, we don’t act rationally.  Despite how you feel about the conclusion, I'm still sure you can sense the rightness of it.  It may not be "fair" but it's not too far off from it.

With that out of the way, I encourage everyone to pick up The Darwin Economy.  It’s simply fascinating.  Don’t you want to read something that picks up where Coase and Mills left off then applies it in a relevant and meaningful way to our society?  Haven’t you ever wanted to read something about Economics that didn’t revere and adulate Adam Smith?  Okay, Frank does give Smith the credit he deserves, but he does something more interesting when he suggests that Charles Darwin may be the more appropriate saint of Economics.  I might write about that in Part Two or I might just write some few words about the Hockey Helmet problem.