An Economic Theory of Dirty Dishes

The dishes really piled up last week. I attribute it to an era of frugality inspired batch of late night bulk cooking, which generated a bunch of large dirty pots which we would clean in the morning. It never happened, and it wasn't until this weekend that we finally got a handle on it. I was reminded of my theory of dirty dishes however.

The theory basically says that the marginal cost of cleaning a single dish is essentially constant, but that the marginal utility of cleaning a single dish decays as a function of the total number of dirty dishes. (This is because, when are there are many dirty dishes, there is little sense of progress on each one.) Therefore, if a spike in the number of dirty dishes occurs, the equilibrium supply of dirty dishes becomes trapped away from zero. The only way out is to wait for the marginal cost of cleaning a dish to fall, i.e., for the weekend to show up so that you are feeling less lazy.

But hey, a picture is worth a thousand words right? Let's assume you have 10 dishes, and a sink that holds 6 dishes, and can hold 2 without the dishes being visible from afar. Then a model of the utility of a particular state of the kitchen is given by the silly picture. (Not captured: once all dishes are dirty, there is some utility to have a clean dish when you need to eat something.) This implicitly represents the demand for clean dishes: points where the slope of this curve are high correspond to states of the kitchen where you would pay the most to have a dish cleaned.

Of course by paying I mean actually cleaning something. I model the cost of cleaning one dish as roughly independent of the number of dirty dishes; instead it varies over time based upon psychological factors such as exhaustion and alternate uses of time at the current moment. There are economies of scale, however: the cost of cleaning subsequent dishes falls rapidly since one is "in the zone". For simplicity, I'll model the cost of cleaning subsequent dishes as zero. Therefore, the decision to do all the dishes hinges upon whether the marginal utility of doing one dish is sufficiently great. Since our unit of utility is arbitrary, I'll just say the units are "cleaning 1 dish". In this case, we only need the one silly graph I've already produced above, with the understanding that it will scale greatly for different people, or even for the same person at different times of the week.

So the theory admits several outcomes merely by scaling the above graph, including equilibrium at all dishes dirty (aka college), all dishes clean, and some dishes clean. Importantly there is a range where you normally manage to keep all the dishes clean, but if you experience a black swan in the number of dirty dishes you can get permanently behind. Since this dynamic happens for more than dirty dishes, this argues for having an infrequent housekeeper visit, e.g. biweekly, to prevent undesirable absorbing states.

It also makes one interesting testable prediction: you can get your spouse to clean more dishes by hiding most of the dirty dishes, and producing them only when they start to clean them. I'll be trying that one out on Nicholle.