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Capla comments on The "best" mathematically-informed topics? - Less Wrong Discussion
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Economics optimization problems
Microeconomics contains several useful tools for thinking about the world, but those tools are only somewhat driven by math. For example, let's consider "supply and demand."
In a basic econ course, you'd focus on the math (which is basically just algebra). You'd have a increasing linear function for 'supply,' and a decreasing linear function for 'demand.' (Both represent the quantity supplied or demanded at a particular price.) You would then find the intersection of those two lines, and this is the "market price." You would then consider increasing or decreasing the supply or demand curve, and notice how this changes the intersection.
In a basic econ philosophy book, you'd focus on the feedback mechanism that generates the lines discussed above. "Suppose there are more people who want to buy the good than there are sellers of the good at a particular price," the armchair philosopher would say, "and one of the buyers will craftily offer to pay more than the listed price in order to secure a spot in line." This would give you a sense of why the supply line is increasing and the demand line is decreasing.
The idea of what an equilibrium means, and the math underpinning their study, seems useful. But for the math you're potentially better off looking at control theory / controls engineering / feedback systems / signal processing / there might be more names I'm forgetting.
I don't think macroeconomic tools are personally relevant to you, but you can learn about the models in any standard undergraduate text, and it probably won't even require calculus.
Numerical optimization is only kind of in economics. This is the class of problems where you have an exact statement of what you want ('this is my objective function, these are my constraints') and it just takes a lot of pushing numbers around to figure out what the best option is. Once you know linear algebra, you can figure out the basic approaches here, but I don't think this is particularly useful unless you're employed in a context where you need to solve these sorts of logistical problems.
I have what I think are very strong economic intuitions: it just makes sense to me and always has. I frequently think in terms of supply and demand. Do you think I would gain a great deal of value from the explicit mathematical formulations?
Are your "very strong economic intuitions" correct and how do you know whether they are or not?
They are informed by and consistent with the books I've read.
I should note that I don't know much about macroeconomics. Keynesian economics (like Marxism) baffles me. I need a Keynesian to explain to me why there should be "leakages" in the banking system.
Are they consistent with reality?
I believe so, but I don't know how to check.
Well, on which basis do you believe so?
What I am getting at is that you were informed by some books and, unsurprisingly, found your knowledge consistent with these books. But that's no guarantee of correctness. There are a lot of books which teach and advocate views that range from not quite true to quite not true. The arbiter of correctness is reality.
You said that you have correct economic intuitions. So let me ask again -- why do you believe they are correct, is that only because a book told you so?
Let me be clarify:
When I was very young, my dad t aught me the basis of economic concepts . They made sense to me. Latter, when I took economics classes, the instruction seemed obvious. I found myself having a feeling for the principles, in contrast with others that I spoke to. For instance, my peers were astonished to learn about the huge mark-up on "fancy" water. A high school friend commented that the water is obviously not worth that much. I knew that "value" is subjective, rather than being an intrinsic property of an object, and that the price, rather than reflecting that supposed real-value, was the result of the interaction of supply and demand. The water was "worth" exactly as much as it cost, by the simple fact that people would pay for it at that price.
I read other economists. They sometimes expressed ideas from new perspectives, but the fundamental ideas were the same. I took college level classes.
My confidence in my economic understanding parallels my confidence in evolution: the ideas make sense to me, and they are, to my knowledge, endorsed by the professionals who work in the field, yet I don't know of a way of verifying those concepts for myself, without relying on the testimony of those experts. I discount my economic knowledge somewhat, since economics in general seems more contentious than biology, and especially the foundation of biology.
Does that clarify? What should I be asking?
Well, it's pretty easy -- try to make some real-life forecasts. There is a lot of economic activity happening all around the world and enough of it is visible and documented.
Take something you have an interest in, look at the current situation, explicitly apply the economic concepts you have, create a forecast (which you will be able to verify). Then see if your forecast worked out. Make a bunch of forecasts to get some diversification.