Stephen Williamson has a good post on micro foundations. I only want pick one nit, and that’s because it suits a longer term agenda.
Optimization is pretty weak. It’s just some notion that the people living in the fictional world we have constructed are doing the best they can under the circumstances. The circumstances could be pretty bad, in that these people may not know a lot about what is going on. They may not know things about the people they are supposed to be trading with, and/or they may not be able to observe some aggregate variables, for example. There are many equilibrium concepts – standard competitive equilibrium, Nash equilibrium, pricing using bargaining solutions, competitive search, etc. All that we require from the equilibrium concept is that it coherently yields consistency among the decisions made by individuals.
I don’t think optimization is weak, though I don’t know exactly what Williamson means by this term.
However, what I would say is that optimization is the mathematical frame for attacking problems of choice.
Optimization sounds like it means doing the best or something like that. However, that’s projecting too much human emotion on to the mathematical process.
Optimization is dividing into parts. Things like this, not like that.
It short, optimization and choice are two different words for the same thing. If there is a choice then there is some optimization problem which represents it.
This is part of why I argue that utility is not happiness or satisfaction or anything like that. It is simply that thing which turns human choice into an optimization problem. Utility maximization could make you miserable. There is nothing inconsistent or even odd about that.