4. An economic agent earns an income of $1,600 a month and has a non-interest bearing chequing account which allows him to write cheques for transactions. He can earn 6% pa. on a bond, and the brokerage fee on redeeming the bond is $1 per transaction. a). Determine the economic agent's optimal cash management strategy according to Baumol's inventory-theoretic model. State explicitly the optimal amount of bond redemption, average balance of his chequing account and the average balance of bond holding over the year. b). Suppose the economic agent's income rises to $1,800 a month. What percentage would his demand for cash rise? c). Suppose the original condition as stated above hold (i.e., income $1,600 a month, 6% interest on a bond and $1 transaction fee) except that, because of nancial innovation, the chequing account pays deposit interest at 1% pa. Determine the economic agent's optimal cash management strategy in this case. (I). Show formally that in Baumol's model of transaction demand for money, the optimal cash balance is homogenous of degree n in both income and the interest rate. Determine the value of n. Give economic interpretations to this result