Economics 402, Winter 2009
Problem Set 6
Suggested Solutions
1
The Baumol-Tobin Inventory Model of Money Demand (30)
month (notice that here Y denotes nominal income for the sake of notational simplicity, whereas usually
it denotes real income). Sarah is paid at midnight on the last day of the month, with a direct deposit into
her interest bearing bank account. She spends all $Y during the month, so at the end of the month she
has exactly zero dollars in her account. The account pays - at the end of the month - a nominal interest
rate of R on the AVERAGE cash holdings per month, L. Only cash is accepted for transactions, so Sarah
needs to walk to an ATM and pay a ±xed cost $F per trip to get cash. Sarah wants to economize on
trips, by withdrawing more than she needs for everyday use, but at the same time she does not want to
lose interest on her deposit. She turns to you, a professional economist, for advice. You will determine
for her the optimal number of trips to the ATM, N*, the optimal average cash holdings, L*, and how it
varies with her income and the nominal interest rate.
1.
If Sarah holds L units of cash in her pocket on average, what are her opportunity costs of holding
this amount of cash, given that the nominal interest rate on the AVERAGE cash holdings per month
is R? (1)
The opportunity cost of holding cash is the interest foregone, which is
RL:
2.
What are the total trip costs as a function of N, the total number of trips? (1)
Trips to the ATM cost $
F
per trip. If Sarah makes N trips, the total trip costs are FN.
3.
One can show that under certain assumptions the average money demand, L, in the Baumol-Tobin
inventory model as a function of the agent²s nominal income, Y, and the number of trips to the
bank, N, is: L=
Y
2
N
:
Express N as a function of L and Y. (1)
L
=
Y
2
N
=
)
2
N
=
Y
L
=
)
N
=
Y
2
L
:
4.
What are the total trip costs as a function of L, Y and F? (2)
The total trip costs are:
FN
=
FY
2
L
:
1