For me the key Keynesian insights are:
The economy can be in equilibrium at a high level of unemployment.
People can choose more goods and less money, or more money and less goods. If they choose the in a sufficiently dramatic and surprising way, then you can end up with a general glut.
Of course both these arguments predate Keynes and Keynesian economics but nevertheless.
Microeconomics has its own ways of explaining persistent unemployment beyond the "natural rate" without invoking irrationality. These explanations have to do with a lack of information. They aren't particularly new, either. Armen Alchian pioneered these models half a century ago.
Here's an example of how things could go.
Aggregate demand drops, and so the employer, whose demand has also gone down, tries to lower the wages of his employees, who do not know that aggregate demand has dropped. They only see that their employer's demand has dropped. They can rationally decide that it is worth quitting their job rather than taking they pay cut and looking for a job that will pay them what they think they are worth elsewhere. If this is happening in businesses all over the country, unemployment could get large quickly for entirely rational reasons.
Now, workers might realize their mistake and try to ask for lower wages. But this won't get them hired either, because stepping out of the crowd to ask for a lower wage just sends a signal that you're not worth very much and also that you're unusual in some way. Employers won't be interested in hiring a high-risk low-productivity worker. And furthermore, the workers know that employers will react in this way, so no individual will even bother trying.
Employers will see that people aren't willing to work at the wage necessary to make it profitable to hire them and that they're not budging on this. So they'll start restructuring their business, substituting capital for the labor that has gone. Now you have a skills mismatch where the workers can't do the sorts of things people are willing to pay them to do because the jobs they were trained for are now done by machines. And that can give you pretty persistent unemployment just with rational imperfect information microeconomics.
Now, workers might realize their mistake and try to ask for lower wages. But this won't get them hired either, because stepping out of the crowd to ask for a lower wage just sends a signal that you're not worth very much and also that you're unusual in some way.
The fellow could be unusual in accurately assessing likely wage rates faster than his fellows. You're making huge assumptions about the priors of the attitudes of employers.
I've always found that learning new areas always goes a lot better if you start with a key insight of what the field is about. Often this is not presented or explained at the beginning of the course, and you have to deduce it later on.
For instance, I would have better grasped the epsilon-delta definition of a limit if the instructor had started with something like:
Similarly, I would have made more rapid progress with Gödel's theorems if, before giving the formal definition of Gödel numbering and of the provability symbol □, someone had clarified that direct and indirect self-reference was a problem. If a formal system of a certain complexity can talk about its own structure, even without "realising" that it's doing so, problems will arise. Some of my other key insights in the field can be found in my post here.
So when I do stumble upon a key insight, I want to share it. I've found some recently in Keynesian economics, giving me a much better grasp of what makes that economic theory tick, and which would be my point of entry should I ever study the subject in detail. The two key insights are:
Of course, Keynesianism makes great use of irrationality or partial rationality of the agents (such as the stickiness of wages or the irrationality of bubbles), but it was a revelation that rational models, full of Homo Economicus, could still produce excess unemployment.
This seemed intuitively very odd. After all, if there is unemployment, wages should fall, making it more attractive to hire workers. Therefore the equilibrium should be that everyone who wanted to work at the wages available should work. And this is not only an equilibrium, but an attractor: free-floating wages should move the economy towards the equilibrium.
But this lecture presented the rest of the argument. In a closed economy, investment (by firms) plus consumption (by individuals) must be equal to the total production of the economy - you can't sell stuff to thin air. Similarly, the amounts sold by firms translate into income for firms, shareholders and workers - you can't generate income without selling to someone. Over the short term, things can move out of equilibrium (people can increase or cash in their savings), but over the long term it has to balance.
That equilibrium is also an attractor. So we have two equilibrium processes - the wage changes, and the consumptions plus investment equality. Notice, though, that they interact! As wages rise and fall, people's incomes rise and fall, and hence their consumption, which feeds through to the incomes of firms and hence to their own levels of investment and salaries...
The question then, is whether there exists a joint equilibrium for both processes at once (more properly, since consumption consists of many markets, a general equilibrium for the whole economy). We'd want an equilibrium that was also an attractor, since we'd want to move to that state. In some circumstances, such attracting joint equilibriums exist - but in others, they don't.
So, at least in the model, excess unemployment can persist in the presence of fully rational agents.