Friday, October 16, 2009

Marginality, Reconsidered

Back in my undergraduate economics class, I was introduced to the idea of "marginal cost". The idea was that economic decisions occur at the margin: I will consume any good until the marginal utility of one more unit of the good falls below the marginal cost of that unit, and at that point consumption ceases. This was one of those blindingly obvious insights that made me wonder why I didn't think of it myself, and get my name in the textbook. But recently, as I reflected on my recent experience, I began to wonder if the psychology really works that way.

My employer puts great store in the physical fitness of its employees. (I think it's a deal they worked out with our health insurance company.) To this end, they have provided free gym memberships to all employees and our families as part of our compensation. But up until this year, the membership has not included swimming. Because I like to swim as part of a well-balanced exercise program, I had to shell out about $100 for a nine-month pass to our community indoor pool, and about $200 for a summer family pass.

Spending this money had an interesting psychological effect. As I blogged before, my forties have not been kind to my motivation to exercise. I used to work out six days a week without fail. Now? Well, some weeks are good, others are not so good. It's just frickin' hard getting old, and its hard summoning my former enthusiasm to get going (though once I get going, I usually do okay). However, as I contemplated the pass, I reasoned thusly: if I swim twice a week, then the average cost of a visit comes to about $1.50. Which is a reasonable cost. But if I don't swim twice a week, I drive up that average cost, potentially a lot. And since I didn't want to pay a high average cost, I darn well made it to the pool two times a week, and sometimes three!

But this year, the company added free pool access to the fitness plan. Some details here may be important. The pool they got us access to was on the other side of my morning commute instead of being on the way. And it's only open three days a week. Neither of these factors present much of a burden, but I should mention them anyway to help you evaluate what happened.

Now, keep in mind that the marginal cost of a pool visit in both cases is essentially zero. According to economic theory, the $100 pool pass constitutes a "sunk cost" that should have no effect on my decision to go swimming on any given day. But yet, it did have an effect. It made me think that I was "wasting money" if I didn't go. Yes, the waste was only retroactive, but it still impacted my behavior. And now that a pool visit is "free", I don't have any discretionary income invested in whether or not I swim. And the frequency of my swimming took a substantial dive; I may have only averaged one swim day a week this fall.

I'm actually contemplating buying another pass just to keep me motivated. Mrs. Φ likes a high thrust-to-weight ratio, so the exercise has got to get done.


Anonymous said...

Don't be so quick to discount the free pool's inconvenient location and hours as a reason for your lack of attendance. One general rule that marketing studies have shown is that on average people are willing to drive only a surprisingly small distance to use fitness facilities. If I have more time later today I'll try to look for cites, but from what I recall people usually won't go more than about ten miles (obviously that'll vary depending on traffic conditions). No doubt the "inconvenience factor" also is significant with respect to facility hours, though that's less likely to be an issue in practice because most such facilities have long opening hours.


Burke said...

The pool is a few miles away from where I work, maybe a ten minute drive. So maybe a twenty minute driving overhead per day.

The MWF schedule has had perhaps the greater impact.

The summer pools were of equal convenience both by location and hours. Yet when I didn't have to pay $200 for it, I went a lot less.

Anonymous said...

Given how you motivated yourself previously, I think you may be missing a point.

Find out what the ususal membership cost is for the "new" facility; this is your marginal cost.

The benefit is offset by that same amount of money - money you are not receiving in additional pay or as an alternate benefit. (you may even be getting taxed on this benefit.)

If you break this down the same way as you did when you were paying it out of your pocket directly, you will get your per unit cost.


Burke said...

Steve: I understand what you're saying, but in this case I have no option to receiving the benefit, only in utilizing it. I don't know whether or not the company is taxed on it, but I am not taxed on it directly.

But I suppose that by working for this particular employer, I am theoretically forgoing a different compensation structure at a different company. But that's further removed from my decision process.