Bank run and deposit insurance
A solvent bank can still fail if depositors expect others to run, and deposit insurance removes the reason to run first.
The bank holds A$100 of deposits: a slice as liquid reserves, the rest lent out as illiquid loans worth full value at maturity but only a fraction if dumped early. Depositors are served in order. Move the sliders and watch the till.
Withdrawal queue (served in order →)14 of 24 try to withdraw now
Paid in fullPart-paid (marginal)Gets nothing in the run
RUN SURVIVED. Reserves plus recoverable loans (A$60.40) cover the A$58.33 the run demands. The bank is solvent and stays liquid, so no one loses.
Solvency (held to maturity): SOLVENTLiquidity (today's run): LIQUID
Deposits (claims) DA$100.00
Reserves R (liquid)A$12.00
Loans L (illiquid)A$88.00
Run demand (now)A$58.33
Cash the bank can raiseA$60.40
Liquidity shortfallA$0.00
First mover (runs)A$4.17
Late mover (waits)A$4.17
Each of 24 depositors claims A$4.17. The bank pays from reserves first, then fire-sells loans at the recovery rate. It honours the run only when reserves + recoverable loans ≥ run demand.
Deposit insurance
In the US, insurance guarantees up to A$250,000-equivalent per depositor per insured bank. When it is on, insured depositors have no reason to run.
Reserve ratio12%
Fire-sale recovery on early loans (ρ)55%
Depositors who panic (π)60%
Try this:
Discuss. The bank in this model is always fundamentally solvent, yet it can still collapse. Why does the chance to withdraw first turn a liquidity mismatch into a self-fulfilling run, and how does a credible deposit guarantee break that belief loop without the bank ever having to sell a single loan?