Question 1 (18 Points)

Consider the following situation faced by Jim, a regular salary man. He is looking to optimize his number of visits to the bank (annually), maximizing his return and minimizing his costs. The following shows his relevant parameters.

N : Number of trips to the bank annually. = $2 : Opportunity cost of Time (in minutes) t = 20 minutes: The time taken per visit to the bank F = $5 : Fixed fees charged by the bank per visit P = $50 : Price of consumption c = $20 : Annual Consumption R = 3% : Annual interest rate

Note: For each part first attempt it generically (without values of parameters) and then plug them in. a) Find the expression for total opportunity cost of going to the bank (denoted by ) (3 points)

b) Find the expression for annual real interest rate forgone annually and real average money hold- ings (denoted by i0 and m ) (2 points)

c) Using part a) and b), set up the minimization problem and calculate the optimal number of visits to the bank (4 points)

d) Using part c) find the optimal average holdings and an expression for real money demand (de- noted by ) (3 points)

e) Using your answers to part e) calculate the following comparative statistics and interpret

i) / R

ii) / c

iii) /