Consider the following model of the reserves averaging scheme. The total number of days during the maintenance period is denoted by T. Let X, denote the target reserves balances at the end of the maintenance period for a bank, indexed by i. At the end of each day during the mainte- nance period (t = 1,2,..., T), bank i's reserves balances are recorded as, it, and thus the av- erage reserves balances up to the end of Day h is calculated as Xih= (hi)/h. Therefore, the average reserves balance for the maintenance period for period 1 to T is calculated as X₁T = (it)/T. If aX ≤XT ≤ bX₁, where 0 ≤ a ≤ b, bank i will get a payment Rr > 0. If X₁T bX¡, bank i will not get any payment, therefore RT = 0. a) Suppose a = b = 1.0, X₁ = 1.0, and XT-2= 1.0. Suppose bank i finishes Day T-1 with reserves balances T-1 = 0.99. In order to receive Rr>0 at the end of Day T, what should (i.e., bank i's optimal reserves balances at the end of Day T) be? [5 marks] b) At the start of Day T, suppose bank i's reserve balances are . Let T be the optimal reserves balances for bank i at the end of day T. Denote =-. Consider a large number of banks in the interbank market with each bank indexed by i = 1,...N. Explain the meaning of ZT = r. If the central bank can observe the fact that Zr> 0, how can this information be used for open market operations? [5 marks] c) At the start of Day T, suppose bank i's expected reserve balances at the end of Day T are ExT | XT-1] = (T-1) XT-1 + Er, where ~ N(0,0²). Suppose a = 0.9, b = 1.1 and X₁T-1 = 1.0. Is o irrelevant for for the implementation of monetary policy? Answer with either True or False, and support your answer by providing a concise explanation with derivation where necessary. [10 marks]