Due to the most frequent comment on this blog being something akin to "I have no idea what you are talking about" I thought I'd take some advice from Paul Krugman and write something less abstruse.
I would say that the big idea in the last couple of posts (see links linked here), from an economics perspective, is a two-way Lucas critique. Lucas asked if macro observations were consistent with microeconomics. I'm asking what microeconomics are consistent with macro observations (and vice versa). In particular, I found long run neutrality of money (and other observations that fall under the "homogeneity postulate") and the efficient markets hypothesis (prices are maximally uninformative) lead to the same equation. This is interesting because not only is the former is a macro observation while the latter is a micro observation, but the equation itself leads to supply and demand diagrams. This could explain why supply and demand reasoning works well for a market for a single good as well as for macroeconomics (AD-AS, IS-LM). It is actually pretty magical that these diagrams can be used for individual markets and entire economies! It didn't have to turn out that way (it's a bit like a biologist using Newton's laws to describe an ecosystem and finding it works out).
This has import in the microfoundations debate: there are no assumptions about the motivations of economic agents being made at all. No rational expectations. No utility functions. This is not to say microfoundations aren't correct or useful, only that the EMH and long run neutrality give us enough information to write down e.g. the IS-LM model without specifying the behavior economic agents.