>Let's take electrical engineering as an example.

I'd usually say you're shifting the goal posts, perhaps muse about how dehumanising and simplistic it is to think of humans as components in an electrical circuit, and move on. Then I thought that it'd be more illuminating to address your analogy, because your reasoning suffers from the same problem that I've been talking about.

>If you model an electrical circuit, you assume that there simply is a voltage source where electricity comes from. That assumption is of course complete nonsense: In reality, electrical energy is not just there, it has to be generated somewhere, for example in a power plant. The electricity also flows through a grid that is shared with many other consumers.

I think it might help to read Musgrave's paper[0] (the abstract will do if you can't get the paper itself) on the three kinds of unrealistic assumptions, in which he attacked Friedman's twist. The assumption you pointed out is the most benign type: a negligibility assumption. It's like assuming that a object falling through air experiences no friction: complete nonsense, but air friction exerts only a negligible effect on most falling objects, unless the object is, say, a feather.

In the case of your example, taking into account the power plant adds nothing to the analysis, because the electrical circuit you're concerned with usually doesn't output electricity. Usually. But in the 21st century, that can change...

>So, according to your requirement to always use the more realistic model, electrical engineers should always model a whole power plant and an entire power grid in each circuit, because otherwise their model would be bullshit.

Firstly, I did not say the more realistic model should "always" be used. The situation in economics is more like the more realistic model is ignored in favour of the incorrect unrealistic model, even when the more realistic model is appropriate. The analogy with Newtonian/Einsteinian mechanics is quite shaky here, since as I've said, Newtonian mechanics is vastly more accurate than neoclassical microeconomics.

To take another example from engineering and continue the theme of relativity, error corrections required for GPS depend on an understanding of relativity.[1] If, as you've previously suggested, the simpler and more easily understandable model should be preferred, then we would not have GPS and allied technologies today.

Secondly, in the 21st century when we have renewable energy, electrical engineers are now required to take into account a power grid, because consumers are now also power plants if they have solar power, for example, and want to feed the excess power generated into the power grid.

The point is this: if the circuit you're modelling is a passive one that doesn't generate electricity, sure, make use of the unrealistic assumption that there's an unknown voltage source. However, if your circuit is also a voltage source, that assumption is then false, and you need to update your model.

The same should apply in economics. Unfortunately, it turns out that markets and economies are far more complex systems than power grids: as soon as you have more than one agent (e.g. humans, corporate entities, HFT algorithms, etc.), the simplistic analysis derived from marginal utility theory fails. So, outside of the laboratory perhaps, the models used in neoclassical microeconomics are probably almost never appropriate for the problems they're treating.

>> Yes, it does.[2]

>Do you know of any empirical studies that show that the models currently used in macroeconomics actually cause problems with real data?

This is a really garbled question. Firstly, nowhere did I assert that economic models "cause problems with real data". I really don't understand this assertion and would welcome any clarifications.

Secondly, I think you misunderstand the point of my argument about the SMD theorem. The point is that, as soon as you have more than one agent/consumer (human, firm, algorithm, what-have-you), they will interact in a non-linear way, giving rise to a nonlinear market demand function that gives a "weird" market demand curve.

This has nothing to do with any effect that the belief in a certain economic model would have on the economic behaviour of an agent. That is an entirely separate question altogether.

Back to your question about whether "weird market demand curves are possible" only "in a few exceptional situations". The SMD theorem basically says no: in all but the most exceptional cases, multiple market equilibrium points can exist.

The implication is that the aggregation problem[3] is not solved by the neoclassical assertion that the market demand curve for a well-defined commodity has the same pleasant mathematical properties -- in particular, that it is monotonically decreasing ("downward-sloping"), i.e. obeys the "law" of demand -- as the demand curve for that commodity of a rational agent.

And the reason why the aggregation problem isn't solved is because, as soon as you have more than one agent or commodity (like in most IRL markets), you get a complex system. And when you have a complex system, you can't draw line diagrams like you do in the textbooks. You need to do modelling and numerical analysis. There's a field called complexity economics[4] that's only beginning to do that, some 40 years after the SMD theorem appeared. Better late than never, but it's still a lot later than the other less "dismal" sciences, which have come to realised that they're dealing with complex systems and have updated their thinking accordingly.

[0] https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-6435....

[1] https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_...

[2] https://en.wikipedia.org/wiki/Sonnenschein%E2%80%93Mantel%E2...

[3] https://en.wikipedia.org/wiki/Aggregation_problem

[4] https://en.wikipedia.org/wiki/Complexity_economics