How many elk are too many elk?

It's an important question that you've probably never put much thought towards: how many elk are too many elk? As Oregon Public Broadcasting reported last month, it's a question that the town of Warrenton, Oregon, has had to consider:

Over the last 30 years, the elk population along Oregon’s northern coast has ballooned. An elk sighting used to be an unexpected thrill, but now the animals, which can weigh 1,000 pounds, are trampling pets to death, ramming cars and even attacking people.

The population has boomed for several reasons. There is less willingness to shoot elk than back in the day. City limits have expanded into elk habitat. And elk have gained a taste for the plants humans like to cultivate, such as rhododendrons and grass.

Elk [*] are cool, and their babies are so cute:

Look at that little guy. Is it really possible that a town could have too many elk, and be thinking about culling the elk population, like the town of Warrenton is? Marginal analysis, which I covered in my ECONS102 class this week, says that the answer is probably yes. Despite the extreme cuteness of baby elk, it is possible for there to be too many of them.

To see how, consider the diagram below. Marginal benefit (MB) is the additional benefit to a town of one more elk. The marginal benefit of elk is downward sloping - it is very cool for your town to have its very own elk. I wish my town had an elk. The marginal benefit of the first elk is surely very high. But once your town has an elk, each additional elk adds some more benefit, but not as much additional benefit as the previous elk (because your town already have some). By the time that you get to an elk herd where every household can have their own elk, the marginal benefit of adding more elk is likely to be very low. Economists note that this process of diminishing marginal benefit happens due to satiation (which, literally, means getting full as you eat more - even if we aren't eating the elk). Marginal cost (MC) is the additional cost to a town of one more elk. The marginal cost of elk is upward sloping - the more elk a town has, the higher the opportunity costs of adding more elk. Consider it this way: as a town adds more and more to the elk population, they have to give up more valuable resources to support that elk population. Initially, they can probably keep the elk in reserves and parks, but eventually the number of elk are going to grow to such an extent that household gardens and lawns are covered in elk. The 'optimal quantity' of elk occurs where MB meets MC, at Q* elk.

Now, consider a town that has more than Q* elk, such as Q2. For every elk beyond Q*, the extra benefit (MB) of each elk is less than the extra cost (MC) of each elk, making the town worse off. So, it is clear that it is possible to have too many elk. If a town has more than Q* elk, then it has too many.

It is also possible for a town to have not enough elk. That would be the case for a town that has fewer than Q* elk, such as Q1. For every elk below Q*, the extra benefit (MB) of each elk is more than the extra cost (MC) of each elk, so the town would be better off with one more elk.

Finally, exactly how many elk is Q*? Our model doesn't answer that question directly. It will depend on exactly how large the marginal benefit of elk is, and how quickly a particular town gets satiated by elk (in other words, how steep the marginal benefit curve is). It will also depend on exactly how large the marginal cost of elk is, and how quickly marginal cost increases with more elk (in other words, how steep the marginal cost curve is). Nevertheless, we can be pretty sure that there is an optimal quantity of elk for each town, and that it is possible for a town to have too many of them. Regardless of how cute baby elk are.

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[*] Weird as it may be, the plural of elk is also elk. Just in case you were wondering.