Sunday, October 24, 2010

value of time

One thing I always disagree with in cost-benefit analysis that economists like to provide to justify every day-to-day decision they make is the value of time calculation. They say something like "I make $100,000 a year for my full-time job so the value of an hour of my time is about $50". Therefore, I'd rather hire someone to install a new sink in my bathroom than do it myself, and I'd rather give away a box of old stuff to goodwill than take the time to sell it for only a few dollars."

BS. Pretty blatant BS, in fact, that is nonetheless such a convenient justification for taking the easy way out that it has caught on like wildfire among the general populace that otherwise usually fails spectacularly at economic reasoning. (I firmly believe that if the law of supply and demand were really taught well to every schoolchild, many of the biggest political problems we fight like cats and dogs about would vanish into thin air...)

Here are a few people that it is valid for: very successful rich people who are constantly bombarded by small speaking and writing requests that they can never possibly accept all of. Here are a few people that it isn't valid for: everyone else.

I make a fixed salary per year, no matter how much I work (beyond some minimal acceptable level of course...) I can take on extra jobs and make more, but those are at minimum several-month commitments for several thousand dollars. I absolutely can not say "I'm going to pay a mechanic to change my oil and go work for an extra hour at a higher wage rate to make up for it." My choice set in income level is very coarsely discrete.

Having chosen my work commitments at approximately the level I want to cover the expenses I need and desire, the opportunity cost of any extra time I have is only the enjoyment I would derive from another activity. And frankly, if I didn't spend the summer repainting my car, I would've spent most of that time reading books or papers or blogging or twiddling my thumbs. The time sink was much more enjoyable in the long run.

For another example, it's kind of a pain to sell books on You have to print the shipping information, wrap them, stand in long post office lines, mail them, confirm shipment online, and then amazon takes a big cut of the revenue. I probably make around $5 or $8 an hour doing it. But that's a few bucks an hour that I wouldn't otherwise have, earned with time I would have otherwise used making no extra income.

You say I could skip all of these little money-saving tasks that each take an hour but add up to a month of work over a year, and take on another month-long research assistant position? Yeah, maybe so. But after having done that, the marginal benefit of each little task is still greater than the marginal cost. And, I don't want another job. If I did, I would have approximated my work/income bliss point at a higher level to start with.

A closely related phenomenon is the laziness about very minor things that save very minor amounts of money. In this case, people aren't choosing not to do things because "their time is more valuable", but are choosing not to do some nitpicky thing simply because the annoyance of doing it outweighs the benefit. I do things like go to the city intentionally during rush hour to avoid the bridge toll, carry around my free refill containers if I'm going to be back at the same place later, go out of my way to be at that same place later, always always always take home leftovers (other people's too if they let me...), cook my own rice instead of getting a side with the take-out, etc. My boyfriend always says "Is it really worth it? You can buy another drink later for a dollar. The rice is only 85 cents extra. French fries are gross when they're old. Wouldn't you pay that tiny amount to avoid all this trouble?" Well, no, those tiny insignificant expenses are exactly what add up to a shocking part of your paycheck. Same as buying coffee at a coffee shop every day instead of investing in a French press, or picking up a paper to read on the commute instead of carrying around a book, or buying a piece of pie just to use the free wifi somewhere instead of going to the library. Instead of thinking, would I pay $3 to avoid going to the library? Ask "Would I pay $1000 per year to always work at this coffee shop instead of the library?"*

Ok, that's my frugality rant of the week and my anti-idealistic-economics-logic rant of the year.

*Nitpicky point for the economists: I'm not saying that MB=MC isn't the equation you should be using, I'm saying to make sure you're accurately estimating that equation.


Anonymous said...

The optimization problem you face at the per-year level can be reasonably approximated by: how to allocate your time between three activities.

1. Normal job.
2. Pure leisure.
3. Leisure with some money-saving inconveniences that save v dollars per hour relative to pure leisure.

Call these activities x, y, and z. Normalizing the value of money to 1 and calling your wage from (1) w, we can write

u(x, y, z) = U(x,y,z) + w x + v z
subject to the usual constraints

Here U measures the pure consumption value of the various activities, aside from the income they generate.

(I've assumed a silly additive separability across time and goods, which isn't crucial for this problem.)

You would probably agree that we can reasonably approximate these choices on some long-enough time scale as continuous choices.

You are just arguing that under reasonable assumptions, at the optimum you set z positive.

Whether this is true comes down to the shape of U. If (3:inconvenienced leisure) is just like (1:job), then clearly you should set z equal to 0 and put all that time into (1) as long as v < w, which it is for almost everyone. The sloppy argument you criticize is flawed not in most of the ways you discuss, but in the glib assumption that (3) is just like (1).

If the marginal value of (3) is very much like that of pure leisure for you, then you can get a little money almost for free.

I think your U is shaped a little differently from that of many.

But, in brief, I agree that assuming that (3) is just like (1) is silly.

Vera said...

nope, I think it's not a continuous problem at all. maybe if I had a really long lifespan and actually chose smooth consumption/labor/leisure/etc over that whole time period at once, you could say it was approximately continuous. (still only very approximately. especially because we dont have infinite job mobility etc). but no one does that. i'm not taking out loans now in anticipation of higher income in five years. you can argue that you /should/ but I don't think so, beyond some much closer time horizon. Not only is the future very uncertain, I don't want to commit to a lifetime of choices now and by acting them out I am, in effect, doing that, in order to make the lifetime budget constraint hold. common sense shows the way to the right answer on that one, and so we thankfully don't have thousands of people on welfare after counting their chickens before they hatched.

Anonymous said...

I guess one could try to rescue the standard argument as follows:

Let's assume (essentially via a normalization) that (1:job) yields no consumption value, and that (3:inconvenienced leisure) is some minutes per hour of (1) [or something less pleasant] and the remaining minutes per hour of (2:pure leisure). In that case, you SHOULD replace those minutes of job in (3) by the higher-paying (1), which you can certainly do at the year level.

So it seems the only real rescue for your argument is to argue that (3) is not really separable in this way, which I think is probably pretty reasonable.

What's NOT reasonable is this paragraph:

You say I could skip all of these little money-saving tasks that each take an hour but add up to a month of work over a year, and take on another month-long research assistant position? Yeah, maybe so. But after having done that, the marginal benefit of each little task is still greater than the marginal cost. And, I don't want another job. If I did, I would have approximated my work/income bliss point at a higher level to start with.

Almost everything in it is wrong -- but most importantly, the last sentence. In the separable model (everything is either pure job or pure leisure), once you've chosen your hours of work correctly, adding an extra minute of any kind of work is not worth it. That's the definition of the optimum. And if you're doing the wrong kind of work with some of those minutes of work (Amazon mailings), you should switch and do the higher-paying kind of work (research, tutoring, whatever).

Vera said...

well, we do actually. but not some high percentage =p

Anonymous said...

On your reply: for the coarseness of your problem at the year-level to be a serious issue here, you'd need to believe that the total amount of time you spend on the small tasks adds up to less than a "unit" of time at your "high wage", so that you can't swap one for the other. But especially with the relative flexibility of RA hours, that's probably not true...

Vera said...

"In the separable model (everything is either pure job or pure leisure)"

....yes of course that is crucial. I have a very discrete choice set over my primary job. I can only get CLOSE to optimum. And optimum also depends on how much I like doing my job for how long, so it's perfectly reasonable to prefer a 40 hr/week job at $30/hour and a diverse set of other tasks at $10/hour for another 20 hours a week. everything is NOT pure job or pure leisure, and there are many kinds of both.

Vera said...

and, if you want to nitpick, you're correct that I should have phrased one sentence there differently. Change to "But after having done that, the margina opportunity cost of a little task is less than my hourly wage rate, and so many of those tasks are worth doing if I don't find them too distasteful even if I can pay to have them done for me less than my hourly wage rate".

Anonymous said...

Yes, so the nonseparability I basically buy.

Vera said...

that's really what I meant by "I don't want another job." The enjoyability of work after 40 hrs/week affects my utility wage-rate so that choose another unit of a real job is /not/ optimal even if I spend more time than that on other jobs. Apparently more "real" economists read this than the layperson I had in mind as an audience, where intuition and common sense gets across those points with only a few words =)

Bruce said...

You have a great blog here!

I checked out by clicking "next Blog" at Mankiw's blog.

Do you realize an externality from your "neighbor"?? Though I sure if your blog is next in some static sequence, or did just random chance take me here.

Vera said...

thanks Bruce =) huh I always thought that "next blog" was completely random but from playing with it a bit it seems that now it's random only within some set of "related" blogs. Maybe google changed the protocol when they took over blogger. Pretty cool!