This is my second post on Pokemon Go this week (earlier I wrote about 'How much are you willing to pay to catch them all?'). This time though, I wonder: is it even best to catch them all? It didn't take long for someone to become the first Pokemon Go Master (by catching them all). But should everyone have this as their goal? In ECON110, we use marginal analysis to identify the optimal quantity of something - the quantity where net benefit of that thing (whatever it is) is optimal. So, I'm going to do the same here.
Finding the optimal quantity of Pokemon to collect requires us to consider the marginal benefits and marginal costs of catching Pokemon. The marginal cost (the additional cost of catching one additional Pokemon) is likely to be upward sloping. This implies that each additional Pokemon caught costs more than the previous Pokemon. It is easy to see why this should be the case. Consider the costs of catching Pokemon. The most obvious cost is time - you get your first Pokemon for free just by starting the game (marginal cost close to zero), and it is pretty easy to find the first few Pokemon just by walking around. However, it then becomes progressively harder to find new Pokemon (i.e. Pokemon that you haven't already caught at least once before). So the amount of additional time (the marginal cost) required for finding one more Pokemon (that you haven't already caught) increases.
The marginal benefit is a little trickier to conceptualise. The benefit of catching Pokemon is the satisfaction the player gains by building their collection, especially with rarer Pokemon. With most activities, the marginal benefit declines as you do more of the activity, due to satiation. Think about an obvious example - eating pizza when you're hungry. The first slice of pizza will provide you with some amount of satisfaction (marginal benefit), but the second slice will provide less additional satisfaction (because you aren't as hungry anymore), and the third slice will provide even less additional satisfaction. So marginal benefit (the additional benefit of eating an additional slice of pizza) declines as you eat more pizza. However, with Pokemon this diminishing marginal benefit might not necessarily be the case. The first Pokemon provide relatively high marginal benefit, but subsequent Pokemon you catch may not necessarily provide lower marginal benefit because they are likely to be rarer Pokemon (and more valuable as a result). So, there are two effects here which work in opposite directions - satiation (reducing marginal benefit for additional Pokemon), and rarity (increasing marginal benefit for additional Pokemon, since those additional Pokemon are likely to be rarer). For simplicity, let's assume that these two effects exactly offset, and so marginal benefit of catching additional Pokemon (that you haven't already caught) is constant. [*]
So, as shown in the diagram below, marginal cost (MC) is upward sloping, and marginal benefit (MB) is constant. For small numbers of Pokemon (less than Q*), the marginal benefit (the additional benefit from catching one more new Pokemon) is greater than the marginal cost (the additional cost of catching that Pokemon). So catching one more Pokemon makes you better off (increasing net benefit). However, once you get to Q* Pokemon and beyond, each additional Pokemon beyond that quantity has a marginal cost that is greater than the marginal benefit - catching additional Pokemon beyond Q* will make you worse off (decreasing net benefit), because the extra benefit (satisfaction) you get from them is less than the extra cost (in terms of time, effort, etc.).
Should you catch all of the Pokemon? Only if Q* is some number greater than all of the around 140 Pokemon available (noting that Q* will be different for each person, because the intrinsic benefit or satisfaction from catching Pokemon will be different for different people). So, for at least some people, it might be best not to catch them all.
[*] One additional point to make here is that, for the very last Pokemon required to complete the entire set and become a Pokemon Go Master, the marginal benefit of that final Pokemon is likely to be very high.