In order to understand the precise predictions of the Leverage Cycle theory, in this last class we explicitly solve two mathematical examples of leverage cycles. We show how supply and demand determine leverage as well as the interest rate, and how impatience and volatility play crucial roles in setting the interest rate and the leverage. Mathematically, the model helps us identify the three key elements of a crisis. First, scary bad news increases uncertainty. Second, leverage collapses. Lastly, the most optimistic people get crushed, so the new marginal buyers are far less sanguine about the economy. The result is that the drop in asset prices is amplified far beyond what any market participant would expect from the news alone. If we want to mitigate the fallout from a crisis, the place to begin is in controlling those three elements. If we want to prevent leverage cycle crashes, we must monitor leverage and regulate it, the same way we monitor and adjust interest rates.