@Keith: just to avoid misunderstanding, the "free disposal" that is a common assumption in economics is the assumption that "commodities" (or byproducts) can be destroyed (i.e., put out of the model's view) at will; there is no common assumptions that liabilities (i.e., things someone is legally liable for) can be freely disposed of. On the contrary, unless one is explicitly modeling bankruptcy constraints, it is generally assumed that debts will be repaid in full.
A couple more comments:
1) standard (a.k.a. "neoclassical", even though I dislike the term) economics is really not into "ignoring" things, be it permanently or, worse, temporarily. Model outputs are typically Nash equilibria of games with perfect recall. There are some theoretical models with imperfect recall, but I cannot recall seeing them in applied work.
2) there are plenty of non-linearities in economic models, so I would not worry much about destroying linearity (of course, there are also a lot of linear models and linear approximations of non-linear models, but that is not just in economics). Perhaps the only linearity that is really hard for standard economics to give up is the one embedded in Expected Utility Theory, i.e., the fact that (under the standard assumptions) agents (can be taken to) evaluate "lotteries" using functions that are linear in the probabilities of the various possible outcomes (though typically non-linear in the evaluation of the certain outcomes). Much of behavioral economics was born out of attempts to relax these assumptions and use more general evaluation functions.