3. (Loan allocations with structural monetary policy). Consider the bank's liquidity manage- ment problem in a three-period model. At period 0, the bank's liabilities and equity consist of deposits D and paid-in capital E. The bank has made the decision to allocate C rs. Reserves pay 0 net interest rate. At period 1, the bank faces w x D deposit withdrawals, of which w is drawn from uniform distribution over [0,] with @ 0, then the reserve requirement ratio for this bank drops from * to Ks. (c) Explain (using words or maths) why the optimal fraction of a bank's lending to quali- fied firms Ls/(LN + Ls) will never exceed y given that r > rs. The large bank's profits also include direct monopolistic profits from lending out reserves, which we omit here.. (d) Write down the equation that determines the cutoff * as a function of other model parameters such that if y y*, the optimal fraction of a bank's lending to qualified firms is exactly y; if y> y*, the bank lends 0 to qualified firms. Interpret the results. (Hint: assume the bank just lends fraction to qualified firms, compare the expected profits to the case not lending to qualified firms at all and determine *). (e) How does y vary with rs and xs? What does it say about the effectiveness of the structural monetary policy? Intuitively, how does your answer change if we allow the bank to optimally choose reserve C? 3. (Loan allocations with structural monetary policy). Consider the bank's liquidity manage- ment problem in a three-period model. At period 0, the bank's liabilities and equity consist of deposits D and paid-in capital E. The bank has made the decision to allocate C rs. Reserves pay 0 net interest rate. At period 1, the bank faces w x D deposit withdrawals, of which w is drawn from uniform distribution over [0,] with @ 0, then the reserve requirement ratio for this bank drops from * to Ks. (c) Explain (using words or maths) why the optimal fraction of a bank's lending to quali- fied firms Ls/(LN + Ls) will never exceed y given that r > rs. The large bank's profits also include direct monopolistic profits from lending out reserves, which we omit here.. (d) Write down the equation that determines the cutoff * as a function of other model parameters such that if y y*, the optimal fraction of a bank's lending to qualified firms is exactly y; if y> y*, the bank lends 0 to qualified firms. Interpret the results. (Hint: assume the bank just lends fraction to qualified firms, compare the expected profits to the case not lending to qualified firms at all and determine *). (e) How does y vary with rs and xs? What does it say about the effectiveness of the structural monetary policy? Intuitively, how does your answer change if we allow the bank to optimally choose reserve C
