Krugman has a model of the contagion episode of the financial crises here. My reactions:
But we’ve known for some time that trade flows aren’t the only source of international interdependence. The Asian financial crisis of 1997-1998 was notoriously marked by “contagion,” the spread of crisis to economies with seemingly weak links to the original victims. In particular, the most severely affected nations were small economies that were not each others’ major trading partners, yet they experienced a dramatically coordinated slump...This is entirely true, and was obvious to anyone actually working in the field at the time (which I was). The role of financial intermediaries has grown since then, but no regulatory framework was put in place based on what was learned (or not) in 1998. His model has two lenders: the general public, and highly levered institutions (HLIs). HLIs use leverage, and are their demand for the risk asset is driven by the equity on the balance sheet. Therefore, they have an upward sloping demand curve. Sadly, Krugman does not take this upward sloping curve to its logical conclusions:
The proposed channel that seems most relevant, however, seems to have been originally proposed by Calvo (1998): contagion through the balance sheets of financial intermediaries. Loosely, when hedge funds lost a lot of money in Russia, they were forced to contract their balance sheets – and that meant cutting off credit to Brazil.
As drawn, the supply curve from the general public is flatter than the demand from HLIs; this is the case in which equilibrium is locally stable, because a rise (fall) in q will lead to an excess supply (demand), pushing the price back to its original level. It’s clearly possible in this model for the equilibrium to be unstable instead; in that case we’ll have the possibility of vicious circles that drive the asset market to a low-level equilibrium, virtuous circles that drive it to a high-level equilibrium. My reading of developments so far does not seem to require multiple equilibria – notably, house prices are still above the levels that you can justify in terms of traditional fundamentals. In any case, for current purposes I’ll focus on the case in which pure self-fulfilling crises are not the problem.So, in the middle of the largest bank run ever, Krugman decides to ignore the fact that there are two equilibria in a world of term transformation. Given these assumptions, it's trivial that the model recommends equity injections in HLIs.