Problem Set 3 Professor Nordhaus

Economics 154b Due: Wednesday February 8, 2006

Please put the name of your section leader and section time on your problem set. Make sure your answer is professional looking! Problem Set 3 (Ungraded) 1. Do Abel and Bernanke, Numerical problem 2, p. 562. 2. Do Abel and Bernanke, Numerical problem 3, parts a-c, p. 563. 3. Do Abel and Bernanke, Analytical problem 1, parts a-f, p. 563. 4. Money demand problem using the Baumol-Tobin model (see reading on web page and lecture notes). a. What is the Baumol-Tobin formula for optimal average money holdings? Define each variable carefully. Explain in a sentence the reason for each variable [e.g., “The reason that optimal money holdings (increase/decrease) as income increases is …”]. One careful sentence per variable will suffice. b. What is the interest elasticity of the demand for money? Explain what that means in English. c. Next, provide an estimate of the values of each variable† in the equation in 4(a) for yourself.‡ Then, for your data, solve for the optimal number of trips (n*) and the optimal money (M*) using the formula in 4(a). d. Extra credit: Part 4(c) assumed n* is continuous. Now, let’s solve the problem for integers. Calculate the total cost for the nlow and nup, where these are integers just above and just below n* from 4(c).§ What is the optimum for your data when n is an integer (call these nint* and M int*)? e. More extra credit: Because of the integer constraint, interest rates can move without M changing. Find the interest rate for your data for which the continuous n* exactly equals 1. How much can the interest rate change before the optimal becomes n*=2 (i.e., at which nint* changes from 1 to 2)?

Be very careful to note the units and time period for interest rates and payment period. If you feel the Y data are confidential, you may substitute an alternative hypothetical but reasonable number. All other numbers are presumably not confidential and should correspond to accurate estimates. † ‡

§

The symbol nlow is the integer just below n*, and nup means the integer just greater than n*. So

if n* = 1.414, nlow = 1 and nup = 2. Further, nint* is the optimal integer n (the integral value that minimizes costs). 1

Economics 154b Due: Wednesday February 8, 2006

Please put the name of your section leader and section time on your problem set. Make sure your answer is professional looking! Problem Set 3 (Ungraded) 1. Do Abel and Bernanke, Numerical problem 2, p. 562. 2. Do Abel and Bernanke, Numerical problem 3, parts a-c, p. 563. 3. Do Abel and Bernanke, Analytical problem 1, parts a-f, p. 563. 4. Money demand problem using the Baumol-Tobin model (see reading on web page and lecture notes). a. What is the Baumol-Tobin formula for optimal average money holdings? Define each variable carefully. Explain in a sentence the reason for each variable [e.g., “The reason that optimal money holdings (increase/decrease) as income increases is …”]. One careful sentence per variable will suffice. b. What is the interest elasticity of the demand for money? Explain what that means in English. c. Next, provide an estimate of the values of each variable† in the equation in 4(a) for yourself.‡ Then, for your data, solve for the optimal number of trips (n*) and the optimal money (M*) using the formula in 4(a). d. Extra credit: Part 4(c) assumed n* is continuous. Now, let’s solve the problem for integers. Calculate the total cost for the nlow and nup, where these are integers just above and just below n* from 4(c).§ What is the optimum for your data when n is an integer (call these nint* and M int*)? e. More extra credit: Because of the integer constraint, interest rates can move without M changing. Find the interest rate for your data for which the continuous n* exactly equals 1. How much can the interest rate change before the optimal becomes n*=2 (i.e., at which nint* changes from 1 to 2)?

Be very careful to note the units and time period for interest rates and payment period. If you feel the Y data are confidential, you may substitute an alternative hypothetical but reasonable number. All other numbers are presumably not confidential and should correspond to accurate estimates. † ‡

§

The symbol nlow is the integer just below n*, and nup means the integer just greater than n*. So

if n* = 1.414, nlow = 1 and nup = 2. Further, nint* is the optimal integer n (the integral value that minimizes costs). 1