Assume that you earn $1500 per month, a trip to the bank takes 0.50 hours and your wage is $10/hour. The interest rate paid on your money left in the bank is 6%.

a) Use the Baumol-Tobin result to determine your optimal number of trips to the bank per month. b) Now suppose that youre worried about the solvency of your bank. In particular, you believe that there is a 5% chance the bank could fail during any month and if it does you will lose everything you kept in it. Reformulate the Baumol-Tobin cost equation (for holding money) and determine your new optimal number of transactions. Do you hold anything in the bank now? c) Now suppose that average money holdings can be written as M=PY/2n where PY is the nominal value of expenditure. Use this expression combined with the quantity equation (MV=PY) to derive an expression for the velocity of money. d) Finally, combine your expression in part (c) with the expression for optimal trips to the bank (used in part (a) to show and explain: i. the relationship between interest rates and velocity. ii. The relationship between the price level and velocity iii. The relationship between income and velocity.