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Cash Balance Approach

of Quantity Theory of

Money

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.

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

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.

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

𝑃𝑤 = 𝑇/𝑉𝑀-----------(2)

Continued..

But Pigou’s basic contention is that 𝑃^𝑤 depends on

the demand for real balances

𝑃𝑤= (𝐾𝑅𝑤)/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

%∆𝑃𝑤= -%∆M-------(4)

Graphical Presentation of Pigou’s

Theory:

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

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

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

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

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

Deciding if a cash balance plan is right for

certain organizations:

• Employer with younger, more mobile workforce

• Cost control

• Acquisition tool

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

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

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

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

When,

Cash balance age in ‘w’ =Accumulated value of pay

credit

At age w,

Lump Sum Cash balances=Accrued liability at age w

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

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

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

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

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

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

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

Indirect mechanism:

Fisher demonstrated that the emergence of inflation

would result in a divergence between the real and

nominal rates of interest

𝑅𝑡 = 𝑟𝑡 + ∆ 𝑝𝑒t

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

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

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.

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

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

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.