1 The Cost of Holding Money Consider an individual who needs to obtain money in order to purchase a set of goods from which he derives utility. The individual's monthly salary, which we denote Y , is direct depoi-dterl into his bank account. He earns a nominal interest rate of 1'. percent on the amount deposited, but foregoes it on the amount withdrawn, which we denote W. The individual, therefore faces two types of costs associated with holding cash: direct costs and opportunity costs: a Direct costs: the individual miJSt pay a xed cost equal to F dollars every time he uses the ATM machine [this is the only way he can access his money]. We will interpret this cost as a. brokerage fee. In general, it also includes the cost of the individual's time in going to the ATM machine. a Opportunity cost: the individual foregoes the interest on his cash balances. We assume that the individual spends his cash, W, at a. constant rate, therefore, his average holdings are equal to %. If we assume that the individual spends his money at a constant rate, then on average he holds 1 M' =W"' 2 dollars in his pocket. the will refer to the quantity M" as the individual's money demand function. Please answer the following questions : 1. White out the cost minimization problem under the assumption that the individual withdraws the same amount of cash every time he goes to the bank. Compute, in additionI the total cost paid to the individual. 2. Explain clearly how you computed the individual's direct costs and his opportunity costs and discuss the nature of the trade-off he faces. 3. How much money does the individual withdraw every time he goes to the bank? What is his money demand function? 4. How is the demand for money related to the {nominal} interest rate? Compute the elasticity of money demand with respect to the {nominal} interest rate and explain the intuition. Does the result make intuitive sense? Please comment on the magtude of the elasticity and its sign