1.
hbj
Cash Balance Approach
of Quantity Theory of
Money

2.
Introduction:
• The Cambridge cash balance approach is a version of quantity
theory of money.
• It is popular in Europe especially in England.
Quantity theory of money:
• Developed in 19th and 20th centuries.
Cambridge Cash balance approach:
• It is explained and developed by four Cambridge economists.

3.
Cambridge Equation of Cash Balance
Approach:
• Equation of Marshall :
M=kPY
• Equation of Pigou:
P=kR/M
• Equation of Robertson:
P=M/kT
• Equation of Keynes:
n=pk

4.
Fisher’s transactions approach:
This approach emerged in fishers book the
purchasing power of money
𝑀𝑉𝑡 =PT
Pigou’s illustration of the quantity theory:
A.C Pigou formally introduce for the first time
(collared,2002,p,xxv), the Cambridge equation for the
demand for real cash balance.

5.
Continued…
The simplified fisher`s equation
Mv = 𝑃𝑛 T----------(1)
But Pigou’s notion of price does not concern the
national price level.
Pigou’s also present the real price of money as the
dependent variable
𝑃 𝑤 = 𝑇/𝑉𝑀-----------(2)

6.
Continued..
But Pigou’s basic contention is that 𝑃^𝑤 depends on
the demand for real balances
𝑃 𝑤= (𝐾𝑅 𝑤)/𝑀----------(3)
Pigou suggested that the right hand side of equation 2
& 3 both represent the value of real balances
When equation 2&3 are expressed as percentage
changes and we get
%∆𝑃 𝑤= -%∆M-------(4)

7.
Graphical Presentation of Pigou’s
Theory:

8.
Advantages of Cambridge Equation
of Cash Balance Approach:
• Basis of liquidity preference
• Complete theory
• Discards the velocity of money
• Based on macroeconomic factors
• Simple equation
• Applicable under all circumstances

9.
Keynes’s cash balance approach:
• Value of money depends on supply and demand of
money
• Liquidity preference
• Keynesian theory of demand for money
• Keynes quantity theory of money

10.
Cash Balance Plan:
• Sections of cash balance approach
-Cash balance method and Cash balance plan
• Functions of cash balance plan
A cash balance plan provides a participant with a periodic
pay credit and prescribes an interest crediting rate, usually
tied to a constant maturity bond or a Consumer Price Index,
that defines how the accumulation of pay credits will
evolve over time

11.
Cash balance plan for organizations:
Cash balance plans are easier than traditional
defined benefit plans for employees to understand,
they have been well received by many
organizations.
• Applicability of cash balance plan
• Inapplicability of cash balance plan

12.
Traditional benefit in Cash balance
plan:
The cash balance plan is not suitable for every employer.
Several considerations from the point of view of an
employer and employee are-
• Employee advantages
• Employer advantages

13.
Deciding if a cash balance plan is right for
certain organizations:
• Employer with younger, more mobile workforce
• Cost control
• Acquisition tool

14.
Traditional defined benefits plan:
Understanding cash balance plan
• A benefit plan
• Having plan feature characteristics
• A defined contribution plan
Traditional defined benefits plans
• Normal retirement age 65

15.
Comparison among traditional defined
benefit, cash balance and defined contribution
plan designs:
• Amount of benefit
• Guaranteed benefits by employer
• Responsibility for benefits
• Form of payment
• Investment risk

16.
Cost Method:
Cost method define the rate of growth of the cash
balance account and the accrued pattern. Cost method
have been used to calculate the plans normal cost and
accrued liability

17.
Entry age normal method:
Entry age normal method is a level of percentage of salary entry age
until retirement age.
When, Accrued liabilities =Accumulated value of normal cost

18.
When,
Cash balance age in ‘w’ =Accumulated value of pay
credit
At age w,
Lump Sum Cash balances=Accrued liability at age w

19.
Pros & Cons:
• Cash balance plan is more frontloaded this appeal to
the younger and more mobile workforce
• Cash balance plan will cost more than traditional
design
• When many companies shift traditional plan to cost
balance plan may adversely affect on mid and later
career employees

20.
Money-Back Guarantee:
The money-back guarantee can be viewed as equivalent to
a put option that is owned by the plan participant and
underwritten by the plan sponsor

21.
Enhanced
Money-Back Guarantee:
The enhanced money back guarantee can also be viewed as
equivalent to a put option except that the strike price is
slightly different because the guarantee compounds over
time

22.
Minimum Annual Interest Rate
Guarantee:
• In this guarantee, participants must receive at
least the sum of their pay credits with up to 3.0%
interest
• Applied each year until benefit commencement

23.
Money supply and demand framework:
Marshall in his book, Economics of Industry, he
accomplished two tasks. These are:
• The theory of price level determination as a part of the
general theory of value
• He adopted coordinated and refined quantity theory
namely some core proposition essential to the theory

24.
Money supply and demand framework:
These referred to:
• Equal proportionality of money and prices
• Long run neutrality
• short run non neutrality of money
• Money stock exogeneity

25.
The Transmission Mechanism:
The transmission mechanism depends on the change in stock of
money .Generally for the change in money supply price level
will change. There are direct and indirect mechanism of this
change
Direct mechanism:
PT = MV + M`V`
Bank deposit is a direct mechanism of raising price level

26.
Indirect mechanism:
Fisher demonstrated that the emergence of inflation
would result in a divergence between the real and
nominal rates of interest
𝑅 𝑡 = 𝑟 𝑡 + ∆ 𝑝 𝑒t
In short run mechanism may increase only the number of
transaction. But in long run price level will rise for both
direct and indirect mechanism

27.
Optimal Cash Balance Approach:
The optimal cash balance c* is defined as;
Where,
c*=optimum amount of cash to be raised by selling
marketable securities or by borrowing

28.
Superiority of Cambridge Quantity theory:
Theme of Difference Cambridge Version Fisher’s Version
1. Humanistic approach It emphasize K or cash balance and
consider human motives as an
important factors affecting the price
level.
It does not explain how changes
in the volume of money bring
about
2. Mode of thinking It is concerned with the level of
income.
It is concerned with the total
number of transaction
3. Realistic approach It emphasizes the psychological
factors or subjective valuation as
chief determinants of demand for
money
It emphasizes on the institutional
objective and technological
factors only.
4. Convenience of equation Cambridge equation p=KT/M The cash transaction approach p=
MV/T
5. Foundation of theory The cash balance theory has shown
the seeds of the Keynesian liquidity
preference.
It only shows the precautionary
and transaction motives.

29.
Pitfalls of Cash Balance Approach:
• Price Level does not Measure the Purchasing
Power
• More Importance to Total Deposits
• Neglects other Factors
• Neglect of Saving Investment Effect
• k and Y not Constant
• Fails to Explain Dynamic Behavior of Prices

30.
Pitfalls of Cash Balance Approach:
• Neglects Interest Rate
• Neglect of Goods Market
• Neglects Real Balance Effect
• Elasticity of Demand for Money not Unity
• Neglects Speculative Demand for Money

31.
Conclusion:
• The popularity of cash balance approach is attributable, in
part, to the simplicity of the benefit accrual.
• Corporate sponsors are increasingly turning to cash balance
plans as a means of providing attractive retirement benefits
to employees while avoiding the drawbacks of traditional DB
plans.
• It is very easy for employees to understand the annual
growth in their account balance.
• The cash balance funding method would apply the same
• Commonsense approach to the funding and expensing of the
pension plan.