School Fairs and showing-you-care equilibra

The curse of inefficient "showing you care" equilibria. I'd hit on the economics of charity races a few times; Mike Reddell went after school fairs this past weekend.

From his excellent rant:

We don’t usually get very involved in the fair. But I’d donated perhaps $25 of ingredients a while ago for people making preserves, sweets etc. And yesterday I made them a plate of chocolate marshmallow slice – a slightly fiddly recipe and, between ingredients and time, that probably cost at least $15. My nine year old is on the School Council and was “coerced” into manning a stall. She spent two and half hours doing that. I’m not sure how to value her time, but it isn’t zero.

And because she was on the stall and they needed parent volunteers as well, we weakened and put in half an hour or so each (getting to and fro etc made that perhaps 45 minutes each in total). How to value our time? Well, the marginal cost has to be above the average cost, and one needs to think in after-tax terms. $50 per hour seems very much towards the low end, but if we run with that, it was a donation of $75 between the two of us.

After running the numbers, he reckoned that it cost them rather a lot to provide a bit to the school:

That adds up to a contribution of $125 from our family – costed at the low end of a possible range of estimates. Had we just written a cheque for $110 to the school as an additional donation, we’d have been able to claim back a tax refund (as it would be a charitable donation) for a third of the amount. So we spent $125 to provide the school $110, even though we could have provided the same benefit to the school for perhaps $73. This can’t be an uncommon story. I might have costed our time a bit higher than the average parents would have, but this is a decile 10 school. Parental time is scarce and valuable.

And then there's all the time put in by the organisers, and the time wasted by the kids in prepping for the thing.

Were there any offsetting gains to compensate for the wasted $52? Well, it was nice to see the nine year old responsibly helping run the activity (but she has other involvements outside the home). Perhaps some people get a warm fuzzy feeling from “doing something together for the community”. But this is a school. We don’t apply this funding model to the local GP or, say, the supermarket We write a cheque. As a pro-defence conservative, the old liberal line about holding cake stalls to fund the air force once annoyed me a little, but…….they make a fair point. Cake stalls to fund our education system?

Now I know that high decile schools are somewhat caught. They are funded much less well than lower decile schools, and they are not allowed to charge fees. They can ask for “donations”, and most parents pay them, but even at lower-end decile 10 areas (which is how I’d characterise Island Bay), the resistance will start to rise if the requested donation is raised too far. But the economics of the current model just don’t seem to add up. And while there are deadweight losses from taxes, from the less inefficient taxes they are not as large as the waste implied by my cost calculations above.

I suspect that, from the school's view, there are benefits from parent engagement beyond the cheque. And I also suspect that muggles just don't view these things as harshly as economists do. We see the inefficiency and it causes huge disutility. Others view the participation as a benefit, not a cost, and so put value on their time measured against other fun things they could be doing instead.

Heck, some people even show up for graduations.

Mike's reckoned I'd be able to point to fun academic papers looking at the topic. I can't think of any off the top, but reader pointers appreciated.

Update: I left this as comment over at Croaking Cassandra. I still wonder about a general theory here:

Can’t point to any lit off the top, but a general theory on this needs to explain also why we wind up with ‘charity race’ equilibria rather than ‘work overtime and donate to the cause followed by a parade for the donors’ thing. And it might also have to explain why university graduation ceremonies are as tedious as they are for each and every person involved. And it’ll be related to the rise of the higher-cost religious denominations in the US relative to the ones that don’t ask as much of adherents.
There’s something weird going on in ‘showing you care’ equilibria where our normal intuitions break. Costs become benefits.