) Assume that there exists limited liability and deposit insurance in an economy and that the net deposit rate in an

economy is rd = 0.1 + 0.01N , where N is the number of banks that exist in the economy.

Banks can invest in an asset that requires a unit investment and has the following gross return structure

2.5+ 2p with probability 1 - p

0 with probability p

The bank can choose the unobservable probability of failure p. Banks have no equity and are funded by depositors.

c) Imagine that capital requirements are imposed. They establish that banks have to have at least 8% of equity to

fund their project. The expected net required return of equity is 0.5. Show

i) What would be the probability of bank failure of a bank if N=10? Do capital requirements reduce the probability

of bank failure in this setup? (hint, compare to the setup with no capital regulation)

ii) Will banks hold more than 8% capital? Does this depend on the number of banks competing?