Consider a bank with a sudden decline in the value of assets, such that it has following balance sheet. Required reserves are $8\%.$

$\backslash$table$[[$Assets$,$Liabilities$],[,,,],[$Required reserves,$10\mathrm{.}4,$Deposits,$$130$ million$],[$Excess reserves,$28\mathrm{.}6,$Capital,$-$$$16$ million$],[$Loans$,75,,]]$

a$.$ To avoid insolvency, regulators decide to provide the bank with $$25$ million in capital. What does the bank's balance sheet look like? $[$The $$25$ million in capital initially shows up on the asset side of the balance sheet as cash reserves$].$

b$.$ What is the bank's total level of reserves after the capital injection? How much of these reserves are required? How much are excess?

c$.$ The bad news about the bank is featured in a local newspaper, causing a bank run. As a result, $$30$ million in deposits is withdrawn.

i$.$ What is the level of total reserves after the bank run?

ii$.$ Show the effect on the bank's balance sheet.

$6.$ Bank panics

a$.$ What role does asymmetric information play in causing a bank panic?

b$.$ How do liquidity and solvency problems interact during a banking crisis? $($Address both how liquidity problems create solvency problems, and why insolvency fears cause widespread liquidity problems$).$