This question examines the Baumol-Tobin model of money demand. Suppose that a household earns PQ at the beginning of each month and spends it all at a constant rate throughout the month. The household keeps money in a bank account earning interest at nominal rate i, but to make purchases must use non-interest bearing money. Each time it visits the bank to withdraw money, it incurs a fixed cost, Pb. It visits the bank N times each month, and withdraws an amount PQ/N each time

(a) Explain verbally and diagrammatically why the total cost of holding money is given by TC = Pb(PQ/M*) + i(M*/2). (1)

(b) By differentiating (1) with respect to M*, setting the resulting expression to zero and rearranging, show that the demand for real money balances is M*/2P = (1/2)(2bQ/i)1/2. (2)

(c) Show that the elasticity of money demand with respect to real income, interest and the fixed cost of withdrawals are respectively 0.5, -0.5 and 0.5. Explain what is going on.