The Flat Tire as Discontinuity

From the current draft of my macro book:

The gas pedal is a metaphor for continuity. The flat tire is a metaphor for discontinuity. If the economy is characterized by continuity, then in the absence of a large shock, it cannot suddenly “jump” from one state to a very different state. Typically, macroeconomic models embody continuity, so that they do not allow for sudden jumps. To do so, a model must incorporate multiple equilibria, or what I would prefer to call discontinuity.

…With respect to perception and reality (or liquidity and solvency), a firm might be in one of three states:

1) insolvent under all circumstances. Investors with funds at risk with the firm are going to experience losses, whether they realize it or not.

2) solvent under all circumstances. Even if investors were to lose confidence in the firm, it would be able to meet its obligations to them.

3) solvency contingent on investor perceptions. If investors maintain confidence, so that the cost of short-term funding is low, the firm’s net worth is positive. However, if investors lose confidence and the cost of short-term funding rises, the firm’s net worth would become negative.

It may be the norm for financial institutions to be in state (3), meaning contingent solvency. They are solvent if their investors remain confident, but they are insolvent otherwise.

…If banks are normally in a state of contingent solvency, then there arises the possibility of discontinuity in the financial sector. A relatively modest adverse shift in perceptions, by causing a run, can lead to a large decline in both liquidity and solvency among affected banks. This can cause a sudden drop in financial intermediation.