Okay, so on the blog Marginal Revolution, there is
this post today that asks a reasonable question. Why do public charity events have a per-unit donation? For example, a donation for each time a kid jumps rope or a donation per mile in a charity walk. Tyler Cowen answers that this is done for publicity reasons and that the participants are generally exercisers anyway (or in the case of middle school kids, jumping rope is a required gym activity).
I don't necessarily disagree with this, but I was interested by a few of the comments left in response. A couple people decided to focus on the inefficiency of this system. (What happens if a 5k walk has a real fat guy like me participating? Wouldn't it be easier for people to just make a lump-sum donation so that if need be, I can stop without shame?) A couple people mentioned the opportunity cost involved, but I don't think they fully fleshed out the idea.
See, let me give you an example, something I think is pretty reasonable. Say you have a small law firm, 5 lawyers, where the standard per hour fee charged is a tiny $100 per hour. (Just go with me to make the math easier.) Say the race takes all day, 8 hours, simply because there is the race and all the extra stuff that charities have.
So, how many billable hours were donated to the charity? Well, 5 lawyers for 8 hours at $100 per hour. That would be $4000 donated from the law firm to the charity. Except, wait! The charity doesn't get that money. Instead, it gets money from the donations to the people doing the walking. Now, one argument is that lawyers have rich friends and could pull in high donations. But remember, in our scenario, the opportunity cost per lawyer (walker) is $800. Remember, the opportunity cost is what could have been made had the person not taken the day off to participate.
Why do I mention this opportunity cost? Well, suppose this walker is able to only get donations (both flat-sum and per-kilometer) of a nice $600. Okay, so the opportunity cost was $800 compared with the $600 that the charity received. (Just as an aside, remember also that to put on the event had some cost to the charity, though for a single-walker, maybe it wasn't that much. In this analysis, assume that the charity charges each walker a fee for dinner and a shirt and what-not that will offset any marginal costs related to that walker.)
Now that I have two different costs, we can do analysis. Well, think about it. What is the end goal of a charity drive? To raise funds right? Well, taking Prof. Cowen's remarks, maybe they are also hoping for publicity. So is this the optimal method to accomplish those two goals? Well, no, it isn't. Instead, imagine this scenario. The lawyer hires his next door neighbor's kid to walk for him, working for minimum wage (assume $5 an hour). Now, because the charity wants to raise the most money, the lawyer decides to work for clients and donate the billable hours. So, instead of taking time off and raising $600, the lawyer can donate $800, less the time paid to the kid to walk (at most 8 hours, the kid cost $40). So, in this case, the charity actually raises $760, unless of course the lawyer pays for the kid directly and gives the full $800 to the charity.
Well, there is another slight issue to point out. What if the lawyer can't walk 5k? Maybe they need to train to survive it. (This is easy to imagine if you think of the stereotypical fat lawyers who can barely make it through a round of golf using a golf cart.) If the lawyer has to spend any time training or gaining experience to complete the walk, say if it is a 10 or 20k instead, that will add to the opportunity cost and also affect the analysis.
Of course, there are a few other concerns to point out. Part of the joy for the lawyer is the socializing. In that case, the lawyer needs to figure out how many hours will be spent walking vs. socializing. The optimal solution also depends on how successful the lawyer is in getting donations. Let me give a more complicated example. Suppose the lawyer wants to spend 3 hours socializing, maybe for a dinner afterwards. (To add flair, the charity also has an after-dinner auction, not all that crazy of an assumption.) So, suppose the lawyer will only donate 5 hours, or $500 of time. Well, what happens if the lawyer is a workaholic and doesn't have people who will donate. (For instance, suppose the lawyer's friends are all the other lawyers in the office, each of whom is also walking from my original example.) Now, taking out the 5 hours of time for the kid, $25, the charity gets $475. As long as the lawyer can't raise that much, it is better for the charity to do this arrangement rather than have the lawyer spend all day walking.
Now, let's go back to my original example of looking at the whole law firm. Why have 5 lawyers each take off a whole day to walk? Take that $4000 and just donate it and have a firm party.
Then again, to really make things easier, just have the walk on a weekend, which actually, is something most charities have gone with to avoid the issues raised. However, even then, it might be easier for the lawyer to donate time working rather than raising donations and walking personally.
Now, let's take a slightly different charity and really see why opportunity costs is important. One charity in particular is famous for building houses. Well, because there is an actual output, I am going to introduce something that I purposely skipped in the prior example of the 5k walk, different relevant skills. Let's take an accounting firm with 20 employees with billable hours of $100 again to make things easier. Now, 20 people can build a house in pretty good time so let us assume that the house will take a total of 10 hours to complete. (Once again, just to make the numbers easier to work with.) Now, what is the opportunity cost of building this house for the accounting firm? Well, 20 people working 10 hours at $100 per hour, or $20,000. (Boy! Didn't think it would be that much, did ya?) So, for that 20 grand, what exactly does the charity get? A bunch of accountants trying to hammer nails and put up walls. What skills are involved in driving nails? Eh, one would be the correct answer. Honestly, the only skill a person needs is the knowledge of WHERE to drive the nail. Remember, building a house is the goal, not working without tools. Instead of having 5 people with hammers, have one person with a power nail gun. No point being Amish if we don't have to be.
So, here's my question to you. You are a home-builder, volunteering your time as a contractor to run this home construction. Which would you rather have, a bunch of accountants pale from being in the office all day OR hired laborers used to building things and working with their hands? Ding Ding Ding! Tell 'em what they won! Of course the hired laborers would be better! So, let's figure out how the charity could best benefit using hired laborers instead of accountants.
Well, assume for sake of argument that a hired laborer works for a $20 an hour wage. Well, that means each accountant actually costs the charity 5 laborers. So, first off, which is better when building a house, 1 (totally unprepared) person OR 5 (reasonably expert) people? Sorry, no prize this time. So, now we know that it is cheaper to hire people. So, now we face the next bit of savings. If it takes 10 hours for 20 people to build a house this way and we switch laborers for accountants, we now have 100 skilled people working on the house. Do we need that many? Remember, we said 20 unskilled people took 10 hours. What if we said 20 skilled people took 5 hours or that to build a house in 10 hours, it took 10 skilled workers? How would that change the charity's decision?
Well, essentially, that means by switching to skilled workers, we can build 2 houses instead, be it all 20 workers building 1 house in half the time times 2 or splitting the workers into 2 teams each building a house. But wait! I only accounted for 20 skilled workers. Remember, I showed early that 20 accountants equals 100 skilled workers. What this means is that the capacity is there to be 10 houses with the skilled labor.
So, you are a charity, which would you like, an office of accountants building one house OR an office of accountants spending a day filling out tax forms, donating the money to the charity, and the charity hiring skilled laborers to build 10 houses? Hmmm...that's a tough one, eh?
Now, someone might say, "Wait! Why would the accounting firm donate all that money to the charity? Maybe it is the group experience the firm wants." Well, that is a good point. However, the way I set up my assumptions, the obvious answer would be from the charity, "See, you guys can help us build one house with your building it or you can give us the money you would have made with that time and help us build 10 houses. Is the physical labor REALLY going to help your employee morale or bring the company together? Wouldn't it be easier just to make that donation day a special day? Maybe put up a banner saying, 'Doing taxes to build a house' and getting clients to help donate too?" (Mind you, I must put one caveat in. If an accounting firm decided that physical labor from building a house as a team or office bonding thing, the most likely outcome would be the accountants bonding to say hell no to anymore building projects. Remember, the complaints from taking people from a comfortable environment and putting them in a strenuous one are also one drawback for the accounting firm.) I would imagine that a charity that laid out the case as I have done, with all the relevant numbers calculated, would be better prepared to increase donations.
Ultimately, it comes down to this fact. What is the point of the charity? If in the first case it is to raise money and awareness, what would be the best way to accomplish that feat? If it is the second example to build houses, what is the point of having unskilled people, some of whom are probably not totally committed to building a house, out there trying to accomplish a task that would be more optimally performed by skilled laborers? Just something to think about. Just because it is obvious to see that a whole firm can take a day off and build a house doesn't mean that the charity would be helped the most through that action.