(5.4) This exercise deals with a transaction-based motivation for money demand. The model considered here is...

 

Transcribed Image Text:

(5.4) This exercise deals with a transaction-based motivation for money demand. The model considered here is also referred to as Baumol-Tobin model. Consider an econ- omy with two assets only: money which pays no interest and bonds which pay an interest rate of i. Let Md denote average money holdings per period, PY nominal income per period, n the number of transaction per period and PC nominal fixed cost per transaction and period, with n, i, P, C, Y, Md > 0. Households choose Mª and n such that the cost of transactions are minimal: (1) (a) Explain both the objective function and the constraint in the optimization prob- lem (1). min nPC + iMd subject to Mª namd EMd.i (b) Solve the constrained optimization problem, i. e., find the optimal number of transactions and money holdings. Hint: Insert the constraint into the objective function and solve the resulting unconstrained optimization problem.5 (c) Calculate the money demand elasticity of interest rate and the money demand elasticity of (real) income, i. e., compute:6 = Əln Md Əln i ƏMd di Md PY 2n = and EMY = Əln Md Əln Y = ƏMd ƏY Md Y (d)* Solve the constrained optimization problem in (1) using the Lagrangian method. Interpret the Lagrange multiplier.7 (5.4) This exercise deals with a transaction-based motivation for money demand. The model considered here is also referred to as Baumol-Tobin model. Consider an econ- omy with two assets only: money which pays no interest and bonds which pay an interest rate of i. Let Md denote average money holdings per period, PY nominal income per period, n the number of transaction per period and PC nominal fixed cost per transaction and period, with n, i, P, C, Y, Md > 0. Households choose Mª and n such that the cost of transactions are minimal: (1) (a) Explain both the objective function and the constraint in the optimization prob- lem (1). min nPC + iMd subject to Mª namd EMd.i (b) Solve the constrained optimization problem, i. e., find the optimal number of transactions and money holdings. Hint: Insert the constraint into the objective function and solve the resulting unconstrained optimization problem.5 (c) Calculate the money demand elasticity of interest rate and the money demand elasticity of (real) income, i. e., compute:6 = Əln Md Əln i ƏMd di Md PY 2n = and EMY = Əln Md Əln Y = ƏMd ƏY Md Y (d)* Solve the constrained optimization problem in (1) using the Lagrangian method. Interpret the Lagrange multiplier.7