Boumal-Tobin Demand for Money, Portfolio Management

Assignment Help:
The Baumol-Tobin model is a model that explains money holdings in terms of a
transactions demand. That is, money is needed as a medium of exchange to purchase goods and
services. This note explains the algebra of optimal money demand in this model.
Jean earns Y per year, which is deposited at the beginning of the year. If Jean leaves all
the salary in money for the entire year, then Figure 1 shows that average money balances are
Y/2.
Jean realizes that this may not be a good strategy, for bonds have a higher return than
money. So Jean instead makes N trips to the bank over the course of the year. On each trip, Jean
withdraws Y/N dollars; Jean then spends the money evenly over the following 1/Nth of the
year.
How does Jean decide how many trips to make to the bank? Suppose that the cost of
going to the bank is some fixed amount F. We can view F as representing the value of the time
spent traveling to and from the bank, waiting in line to make the withdrawal, and so forth. Also,
let i denote the interest rate on bonds (or savings); because money has a zero interest rate, i
measures the opportunity cost of holding money.
If N = 1, then Figure 1 shows that average money holdings are Y/4. For any N, the
average money balances are Y/(2N), so the forgone interest is iY/(2N). Because F is the cost per
trip to the bank, the total cost of making trips to the bank is FN. The calculation then is that the
total cost is the sum of the forgone interest and the cost of trips to the bank:
Total cost = C(N) = Forgone Interest + Cost of Trips
= iY/(2N) + FN
More trips, less interest foregone and more trip cost; fewer trips, the opposite.
The optimal N, denoted N*, can be found by calculus as
dC/dN = 0 = - iY/(2N*2) + F
N* = (iY/2F)½
Optimal average money holding are
(1) M* = Y/(2N*) = (YF/2i)½
The major result here is that money demand is increasing in Y and F and decreasing in i.
Moreover, the elasticities are all one-half.
Note on inflation: We haven’t worried about prices. Assume that Y and F are real income
and cost, respectively. Further, suppose that the price of each is p. Then we can rewrite (1) with
the price level as:
(2) M*/p = Y/(2N*) = (YF/2i)½
This shows that the real money demand has an elasticity of ½ with respect to real income and
the real price of trips, and an elasticity of -½ w.r.t. the nominal interest rate.

Related Discussions:- Boumal-Tobin Demand for Money

American land title association - alta, A trade association presenting the ...

A trade association presenting the title insurance sector. It was founded in 1907. The American Land Title Association also focuses on a property's abstract of title, which binds t

Corporate investment, what is the first step in the investment process in t...

what is the first step in the investment process in the development

Case study, you have to study case and than you have to fill the table that...

you have to study case and than you have to fill the table that teacher had given.

American opportunity tax credit, A tax credit that allow more student and p...

A tax credit that allow more student and parents to pay for portion of their college expenses in the 2009 and 2010 tax years by increasing the existing Hope tax credit. The highest

Financing, #questYou have the following limited information upon which to b...

#questYou have the following limited information upon which to base your decision as to which is the better of two alternative funding arrangements: • Alternative 1 is to arrange f

MASTER ., 1. What are basic assumptions of CAPM? What are the advantages of...

1. What are basic assumptions of CAPM? What are the advantages of adopting CAPM model in the portfolio management?

Adjustable-rate preferred stock - arps, It is a kind of preferred stock whe...

It is a kind of preferred stock where the dividends issued will change with a benchmark, most often a T-bill rate. The price of the dividend from the preferred share is set by a fi

Abcd, Ask question$100 par of a 0.5-year 10%-coupon bond has a price of $10...

Ask question$100 par of a 0.5-year 10%-coupon bond has a price of $102. $100 par of a 1-year 12%-coupon bond has a price of $105. a. What is the price of $1 par of a 0.5-year zer

Derivatives, 2. The futures price for the June 17, 2009 CBOT bond futures c...

2. The futures price for the June 17, 2009 CBOT bond futures contract is 118-23. (a) Calculate the conversion factor for a bond maturing on Jan 1, 2025, paying a coupon rate of 9

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd