Friedman vs. Keynes

Friedman vs. Keynes

When comparing the money demand frameworks of Friedman and
Keynes, several differences arise Friedman considers multiple rates of return and considers
the RELATIVE returns to be important

Friedman viewed money and goods as substitutes.
Friedman viewed permanent income as more important than
current income in determining money demand

Friedman's money demand function is much more stable than
Keynes'. This is because permanent income is very stable, and

the spread between returns will also be stable since returns
would tend to rise or fall all at once, causing the spreads to
stay the same. So in Friedman's model changes in interest
rates have little or no impact on money demand. This is not
true in Keynes' model.

If the terms affecting money demand are stable, then money
demand itself will be stable. Also, velocity will be fairly
predictable (since Md is not affected by r).

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Friedman’s Modern Quantity Theory of Money

Friedman’s Modern Quantity Theory of Money

Milton Friedman developed a model for money demand based on
the general theory of asset demand.
Money demand, like the demand for any other asset, should be a
function of wealth and the returns of other assets relative to money.
As an asset (store of wealth) money must compete in an
individual’s wealth portfolio with other interest bearing assets.rb = interest rate or rate of return on bonds

Md is positively related to permanent income Yp (here we are
looking at the transaction demand for money); negatively related
to expected interest rates on bonds (rb), the expected rate of
return on equity (re) and expected inflation, (pie)e.

Tobin's theory 3

A higher interest rate will cause the expected return risk relationship line to rotate up (for any level of risk, the expected return is now higher since interest rate is
higher). When this happens, the new optimum point will depend
upon the expected yield-risk preference of the individual. Hence,
when interest rate increases, it could result in an increase or a
decrease in the demand for money.

An increase in the riskiness of holding bond, on the other hand,
causes the expected return risk relationship line to rotate
downward. And the maximum portfolio risk is now Rw1. There
are again two possible new optimums and this again depends on
the individual’s expected yield-risk preference. Hence, the impact
of an increase in risk may increase or decrease the demand for
money.
An increase in W will increase the demand for money if factors
affecting the composition of portfolio (the rate of interest and
the risk of holding bonds) are constant.

Still one problem with money demand remains. There are other
low risk interest bearing assets: money market mutual funds, U.S.
Treasury Bills, and others. So why would anyone hold money as a
store of wealth?

How is the portfolio determined?

How is the portfolio determined?

To determine the optimal portfolio allocation, we need to look at
the preference of the individual. Utility in this case is a function of
the expected return (Ye) and the risk (Rw). Since expected return is
a good and risk is a bad, the indifference curve in this case is
upward sloping, indicating that a person will be willing to accept
more risk provided it yields a higher return.

The highest indifference curve that is tangent to the expected
return risk relationship line shows the optimal expected return and
risk (K). Dropping a vertical line down from this position to the
lower diagram then indicates the optimal amount of bond holdings
(Bo). The wealth not held as bonds is held in money.

The demand for money is what Tobin terms as “behaviour toward
risk” – the result of attempting to reduce risk below what it would
be if all wealth were held in bonds. An all bond portfolio would
increase the risk to Rw* and an expected return of Ye*. The
individual would be on a lower indifference curve. People choose
to forgo a higher expected return in exchange for a decrease in risk.

Tobin's theory 2

Therefore if the individual holds all wealth (W) in money and none
in bonds, the portfolio would have zero expected returns and zero
risk (refer to the diagram). As the proportion of bonds increases,
expected portfolio returns and risk both rise. The terms on which
the individual investor can increase the expected return on the
portfolio (Ye) at the cost of increasing risk (Rw) is represented
by the line C.

By holding more bonds
a person increases his expected returns and also his risk.

Higher levels of risk is associated with higher proportions of bonds
in the portfolio.

Tobin’s theory

Tobin’s theory in a nutshell:

Total portfolio consists of bonds & cash (W)
W = money + bond

The expected yield on holding bonds (Ye) is the interest earning on
bonds :
Ye = B. r (1)

The total risk (Rw) that the individual takes depends on the
uncertainty concerning bond prices (i.e. the uncertainty concerning
future interest rate movements), as well as the proportion of the
portfolio placed in bonds, the risky asset
Rw = B . Rg (2)

From equation (1) and (2), we can see that an increase in B
increases both the expected yield (Ye) as well as the portfolio
risk (Rw).

Tobin’s Portfolio Diversification Model

Tobin’s Portfolio Diversification Model

Tobin developed a model to explain portfolio diversification that
did not require individuals to have an idea of a ‘normal’ interest
rate.

Basic idea:
This model is based on the idea that people are risk averse and
therefore choose to diversify their assets

Assumptions:
There is no ‘normal’ interest rate in Tobin’s model;
The returns on bonds = r + G.
Capital gains on bonds (G) can be positive or negative
The individual believes that gains and losses are equally
likely so that the expected capital gain is zero. Therefore the
best expectation of the total return on bonds is just the
interest rate, r. Bonds it must be noted are risky assets as
there is a possibility of capital loss when bond prices fall.

Money, on the other hand, is a safe asset by has zero
returns.

There is therefore a trade-off between bonds and money. By
holding more bonds, a person will enjoy higher returns but there
is also the risk of holding one’s wealth in bonds. Hence, a risk
averse person is willing to give up some of this possible return for
the security of holding some money.

Theory assumption

Let’s generalize what we have discussed. Assume that the
individual makes N trips to the bank over the period. On each trip
he will withdraw Y/N dollars and he then spends the money
gradually over the period. Money holdings therefore vary from Y/N
to zero and this averages to Y/(2N).

The question that we need to answer is what is the optimal choice
of N bearing in mind that the greater N is, the less money he holds
on average and therefore the less interest he forgoes. But at the
same time the greater N is, the more trips he has to make to the
bank, which increases his inconvenience.

Let’s assume that
the cost of going to the bank is a fixed amount of $F;
and
r, represent the interest foregone or the opportunity cost
of holding money.


For any N, the average amount of money held is Y/(2N). Therefore
the forgone interest is rY/(2N). The cost of making trips to the bank
is FN. Therefore, the total cost the individual bears is :
Total cost (C) = rY/(2N) + FN

The greater is N, the smaller is the cost of interest forgone but the
greater is the cost of the trips.


The individual holds more money:
if the fixed cost of going to the bank increases;
if expenditure (Y) is higher; and
when r is lower.

So contrary to the classical economist and Keynes, in Baumol’s
model, transaction demand for money is inversely related to interest
rate.

Baumol’s Inventory Approach Theory

This theory suggests that the level of inventory holding of money
depends on two factors:

the carrying cost of holding money, i.e. the interest
foregone by holding money and not bonds; and

the cost of making a transfer between money and bond
- transaction cost.

Alternatively the individual could invest a proportion of the initial
income payment in bonds and then sell the bonds when additional
money is needed for transactions. If the individual invested
his income payment in bonds at the beginning of the month,
the time profile of his money holdings will be as follows.


Money holdings at the beginning of the month is Y/2 and money
holdings are run down to zero by the midpoint of the period at a
uniform rate. Average money holding for the first half of the
period is therefore Y/4. At the mid point of the period, bonds are
sold causing money holdings to return to Y/2. This is then
spent at a uniform rate over the remaining half of the period. The
average money holding for the second half of the period is Y/4.
Thus the average money holding for the whole period is Y/4,
which is lower than Y/2 (the case where no bonds are held). The
advantage of this option is that he forgoes less interest since he is
holding less money on the average but the disadvantage is that he
has incurred some transaction costs.

Question

Question: How much money will an individual hold to make
payment for the things he buys?

Assuming that:
an individual receives an income of Y at the beginning of
the period (t=0 e.g. start of the month);
(ii) the individual spends this income at a constant rate such that he has exactly no money left at the end of the month (t=1);

Therefore, the average inventory money held during the
period = Y/2 , which is also the amount that will be held at the
midpoint of the period t/2.

Baumol’s Inventory Approach

Baumol’s Inventory Approach (Baumol-Tobin Model of
Cash Management)

Later economists further developed the Keynesian approach
to the demand for money. The transaction demand for money
according to them is also sensitive to interest rate.
The transaction demand for money arises because of the lack of
synchronization between receipts and payments. Hence, there is
a need to keep some money at hand to pay for the things we
buy.

Speculative Demand for money 3

If people are plungers and they believe that the normal interest
rate re, they will hold either all bonds or all money. Therefore the
speculative demand for money is discontinuous. A discontinuous
money demand function can only happen if people are plungers,
i.e. they will put all or none of their money into bonds.

As different individuals have different expectations regarding
interest rate and aggregation of the demand for money will yield a
demand for money curve that slopes continuously downwards.

Taking both his concepts of transaction demand and
speculative demand for money together, the Keynesian money
demand function can be represented as:
Md / P = f( r , Y)

Speculative Demand for money 2

Taken together, when interest rate is high, the high interest
payment foregone as well as a likely capital gain on bonds means
that demand for money (as a store of value) will be low. As
interest rate falls, the demand for money as an asset would increase.
Therefore according to Keynes, the demand for money as a store
of value is inversely related to interest rate. This is Keynes
speculative demand for money.

If current interest rate is higher than re, people would
rather hold all their extra money in bonds in the hope of making
capital gains when interest rate returns to the normal level. If
current interest rate is lower than re, people would prefer to hold
money in idle cash, so as to avoid capital losses when interest
rate returns to the normal level.

Speculative Demand for Money

Speculative Demand for Money

The most important contribution of Keynes is that
he added the idea that since money is a store of value it is therefore
an asset that people can hold as wealth. He therefore viewed money
as one asset in an individual’s portfolio and considered how an
individual divides his wealth between money and alternative interest
earning assets.

The important variable according to Keynes that determine the split
of an individual’s portfolio between money and bonds was the
interest rate on bonds. At high interest rate, the opportunity cost of
holding money is high (the forgone interest payments). Added
to this according to Keynes is the fact that when interest rate is
high relative to some fixed view of the normal level, the public
would expect interest rate to fall. A decline in interest rate will
mean a capital gain on bonds.

Keynes Liquidity Preference Theory

Keynes Liquidity Preference Theory

Keynesian theory considered money as a store of value in
addition to a medium of exchange.

Transaction and Precautionary Demand for Money
Keynes, like the classical economists, held the view that real
income was the most important determinant of the transaction
demand and precautionary demand for money.
Therefore, according to Keynesian theory, both the transaction and
precautionary demand for money are proportional to income.

Mechanism of Money Demand

To understand how money affects the economy, it is useful to
express the quantity of money in terms of the quantity of goods
and services it can buy which is the concept of real money
balances (M/P). Real money balances measure the purchasing
power of the stock of money.


Since V is rather stable, we can represent it as k = 1/V, and
therefore M can be written as:

M = k PY
The quantity theory of money is also a theory of the demand for
money. When the money market is in equilibrium, quantity of
money supplied (M) equals the quantity of money demanded
(Md)

Therefore:
Md = kPY


This means that the real demand for money (Md/P) is proportional
to real income or the level of output. Therefore according to the
Classical school, the demand for money is purely a function of
income.

Classical Quantity Theory of Money

Classical Quantity Theory of Money

Classical economists saw money’s role only as a medium of
exchange.
The relationship between transactions and money is expressed in
the following identity, called the quantity theory of money.
MV= PY

It relates the nominal money supply (M) and income velocity of
money (V) to the price level (P) and real GDP (Y ).


Fisher viewed velocity as constant in the short run. This is because
velocity is affected by institutions and technology that change
slowly over time.

Demand for money

Money serves as a medium of exchange, a unit of account and
a store of value.

People hold money for different reasons and our objective is to
find the factors that affect the different reasons for holding money
and then proceed to derive the aggregate demand for money
function for the economy as a whole. In identifying the factors that
affect the demand for money we shall look at the different theories
that have evolved over time. Generally, the theories of money
demand are built around a trade-off between the benefits of holding
more money versus the interest costs of doing so.