OK, apparently I have more frustration from yesterday bottled up than I thought.
In the last post I discussed that it's important to keep in mind that textbooks and intellectual histories are two very different things.
Here I want to stress that models of the world and understandings of the world are also two very different things and you're going to get tripped up if you forget that.
I may have a model where I have a nice social welfare function generated from perhaps unreasonably smooth utility functions, maybe just incorporating risk - maybe not even incorporating risk! - where I assume that all the agents are excellent at calculus.
I don't think through this model because it necessarily matches my vision of the real world in all it's particulars. Instead, I think through this model because it offers me a way to work through the most important ideas while pushing the less important ideas (for this application at least - they may be very important elsewhere) into the background. We all do this all the time. The benefit of doing it with math is at least I'm being upfront about what I'm assuming!
So it would be a waste of your time to try to tell me, for example, that not everyone knows calculus (or even has all the data to apply calculus to). I know that. If you get worked up about this, you are confusing:
1. Making an assumption in the model, and
2. Making an assumption about the real world
If you think I'm doing #2 then you are misunderstanding the whole exercise and how economic science is done.
Even if you understand I am doing #1, we might still have a fruitful debate over whether I should do #1. Maybe the departure from reality is sufficiently great that only nonsense comes out of the model - no insights worth working with. We can argue about that. I might say that although people don't actually do calculus when making decisions, we can probably agree they're trying to figure out the best option for them, and they are probably saying something in their head like "I'm going to keep doing this until the cost to me of doing it again is higher than the benefit of doing it again". That's not a very big assumption on my part, after all. And that's a pretty fair account of all that I'm importing into the model by using calculus.
So I'd maintain it's still a nice little model to help me think about the world and keep all the forces I'm juggling in some semblance of order so that my puny little brain that evolved on the savannah can get some take-away insight from the exercise.
A final note - this is not Friedman's methodology. I am not saying that any assumptions are OK as long as they produce an outcome that matches reality. What I am saying is that imperfect representations of reality (calculus optimization vs. humans seeking out the best option), by making the problem easier to work with, can generate more insights than the imperfection costs.