A treasurer has to manage the cash position of a small London college. At the beginning of the year the college receives 5 million in tuition fees. The college is expected to spend all that money in the year, at an approximately constant daily rate. The treasurer can either hold the financial wealth of the college in bonds, yielding an interest rate of 4% or in cash, which is assumed to not receive any interest. The accrued interest on the bond holdings is received at the end of the year and is not compounded in between. The brokerage fees of exchanging bonds for money are 1,000 per transaction. Note that the first transaction takes place at the beginning of the year, when the treasurer buys bonds, the transactions during the rest of the year will compose of selling bond holdings. The treasurer wants to minimize the costs of cash management, C, which are composed of the interest foregone on the cash holdings and the brokerage fees.

a) Set up the cost minimization problem for the treasurer and calculate the how much money, Z, should be transferred each time the treasurer sells off bonds.

b) Calculate the interest elasticity of money demand.