Consider an OLG economy with an infinite horizon. Individuals live for two periods and only care about consumption when old. Young individuals are endowed withyunits of the consumption good and the old are endowed with nothing. There are two spatially separated islands and in each period there areNpeople born on each island. Capital has a one-period returnx >1. Each individual has probability >0 that they will be relocated. If an individual is relocated they can take their money with them but cannot take their capital. Suppose that there is a bank that takes deposits and is able to pay different returns to movers and non-movers. At the start of the period, before they find out if they must move or not, individuals choose to how much of their endowment to deposit, how much money to acquire, and how much capital to create.

(a) (10 marks) Consider the case whereis known by all agents in the model. Explain how the bank is able to solve the liquidity mismatch problem faced by individuals. Be sure to make specific reference to:

(i) the returns on money and capital,

(ii) the return on deposits the bank promises to movers and non-movers,

(iii) the bank's choice of reserves, and

(iv) the consumption of movers and non-movers with and without the bank.

(b) (10 marks) Consider the case whereis unknown to all agents in the model. That is, suppose

thatcan take on two values:Hwith probabilityandL< Hwith probability 1.

Further suppose that the probability of theHevent is small (i.e.is small), but thatHisL

very large compared to. In this case there is both individual and aggregate risk.

Propose a strategy for the bank that can help it remain liquid if theHevent occurs. Be sure to clearly state:

(i) the returns promised to movers and non-movers,

(ii) the fraction of deposits the bank will hold as reserves, and

(iii) explain why this strategy may achieve the desired result.