Allocating fruit among household members

This story is loosely based on real-life events. In the summer, members of my wife’s family all come together to stay with the “grandparents” in one large household. There are typically around 12 of us and we have many small problems. One of these is the allocation of fruit (and other snack items – but I will concentrate on the fruit problem as it is the easiest to describe) among household members. Mind you, this is not a problem that we talk about (much) in the household. Many of us perhaps do not even recognize it as a problem, but it is a problem and one that we solve inefficiently.

Consider peaches. Almost all household members like peaches, but we all vary in our exact preferences. Some of us would happily eat many peaches at various points in time, some would rather eat just one at a specific time of day. Some prefer peaches when they are still quite hard, some prefer them when they are essentially mush. [Some even like them slightly moldy, at least that’s what I infer from fruit choice observations that I made.]  So, we all have different bliss points as to the optimal stage in the ripening process when a peach should be eaten. I could probably show you a graph with peach ripening stage on the x-axis and derived pleasure from eating a peach on the y-axis and you would see a nice concave (for the mathematical economist) initially upward curve that reaches a peak at some point, the bliss point, and then bends down again. Each family member would have a somewhat different curve with different bliss points and different up- and downward curves before and after the bliss point, respectively.

Having drawn such a picture, one could go on to mark the level of derived pleasure from eating a peach, at which you would rather eat a different fruit, an apple, say, or even just nothing (rather than a moldy peach, for instance). Again, all this is different for all household members and would also depend on the ever-varying quality of apples (and that bit about the quality of apples that matters to whichever household member we are talking about). To make the fruit allocation problem even more complicated, we all seem to have variable preferences. Some days, when the weather is bad for instance, just don’t seem to be peach days, at least for some of us. Or you may have eaten or drunk something else today that does not go well with peaches. On top of that, peach quality seems to vary from batch to batch and so our preferences change accordingly as well.

Why am I talking so much about preferences? There are two reasons. One, we all want to be kind and let someone else eat a peach instead of us if they also want it. Second, if we think of the problem from the social (household) planner’s point of view, that person would like to allocate peaches to individuals in some sort of efficient way, give more peaches to people who like them more, perhaps also keep fairness in mind, etc. The problem now is that none of us perfectly know other household members’ personal peach preferences on any given day. This is both a problem for the social planner as well as for each of us when we consider eating a peach. [There is also the additional problem sometimes that the number of available peaches is not even always clear. Sometimes extra peaches are “hidden” in the larder, so there are more than you think. Sometimes some peaches are actually reserved to be made into a cake – and this fact may not be known to everyone – although sometimes the social planner labels peaches accordingly.]

So how do we solve this allocation problem, why is it inefficient, and what would other mechanisms look like? For us, it all begins with the purchasing decision (with nowadays online delivery – this also impacts peach batch quality, by the way) made once or twice a week by the head of household, in her capacity as household chief procurement officer (or CPO). The CPO makes these decisions, considering an amazing number of factors based on an incredibly high degree of empathy towards all household members. Yet, even the CPO is not fully aware of all aspects of the daily changing peach preference profile in the household. At the end of the day the CPO settles on some quantity of peaches and this is where our problem now begins.

There are many mechanisms that we could use to tackle our fruit allocation problem. Let me first unashamedly tell you that we do not use a market mechanism. What would a market mechanism look like? Well, we would all be given a share of all fruit and snack items that were purchased. We would all have something called “money” that we all accept in exchange for the various fruit and snack items. We would meet regularly in a “market”, the kitchen for instance, where we all set up shop and trade among us. Market prices would, we would hope, adapt on a daily and perhaps even hourly basis so that supply meets demand, so that no peach is left uneaten and no additional peach would be wanted to be eaten at these prices.  As we can assume that there are no worrying externalities when it comes to fruit and snack choices (except perhaps that parents sometimes worry about the kids’ sweet choices) such a market mechanism is expected to deliver a, so-called, Pareto optimal allocation, an allocation of fruit and snack items that is such that if we wanted to improve the material (fruit and snack) well-being of one individual by adjusting the allocation, we would have to reduce the material well-being of another. We could also aim for a reasonable degree of fairness by adjusting the initial allocation (before trade happens) of fruits and snacks.

But, surprisingly, this is not what we do. Our system instead is as follows. All the peaches (with some of the qualifications pointed out above) are simply displayed in the kitchen and anyone is free to take one at any time. I am pretty sure that this leads to an inefficient (not Pareto-efficient) allocation, at least in our case. Not for the reason you might think of at first. True, in a world full of people who are interested only in their immediate material (fruit and snack) well-being, like a world of small children perhaps, we might find that all the peaches are eaten by the first person who spots them. You might say that, while this may not be fair, this is ok from an efficiency point of view. But not necessarily. Imagine one person eating all the peaches, because he or she spotted them first, and another eating all the chocolates, because he or she spotted them first. They might have both been better off had they traded some of their peaches against chocolates and vice versa. But, in any case, this is not the problem we have. Our problem is that people are too altruistic, I believe, and too careful not to eat a peach that somebody else might also like, perhaps at a later stage in the ripening process. The sad result is that many peaches simply remain un-eaten (and thrown away) at the end of the day. Well, sometimes, to be fair, they are rescued and baked into a cake (at a point where I am happy not to know how advanced those peaches already were in their ripening process). But even in this latter case, some of us, perhaps all of us, might have preferred a peak peach over a post-peak peach cake.

You might say that communication should solve the problem. Maybe. However, we have many other problems (and not only problems) to discuss and the peach problem does not seem high up there on the list of problems. Also, even if we did, most of us would probably find it hard to articulate our exact peach preferences (we often don’t seem to have a good prediction of our future preferences ourselves). Also, we only come together for about a month in the summer every year, and for such a short time, it may be inefficient to spend hours solving the inefficiency in our peach allocation. So, as much as it pains me, as a trained economist, to accept inefficiencies, I guess I will just have to accept it.

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