Lesson 14: Cambridge Equation

Objectives:

After studying this lesson, you will be able to understood,

The importance of demand for money

The Cambridge approach to demand for money

Marshall equation

Pigou’s equation

Robertson’s equation

13.1 Introduction

13.2. Cambridge approach to demand for money

13.2.1. Marshall Equation

13.2.2 Pigou’s Equation

13.2.3 Robertson’s Equation

13.3 Summary

13.4 Check your progress

13.5 Key concepts

13.6 Self Assessment questions

13.7 Answers to check your progress

13.8 Suggested Readings

13.1 Introduction:

The present lesson is concerned with the one of the approaches to quantity theory of

money i.e., Cambridge quantity theory of money. As you aware, the quantity theory of

money is, indeed, a very old theory. It was first propounded in 1588, by an Italian

economist, Davanzatti. Later, the classical economists explained the value of money in

terms of the quantity theory of money. The quantity theory of money aims at explaining

the factors that determine the general price level in a country. In other words, it pinpoints

those causes which bring about changes in the value of money. In its unrefined form, the

theory states that the price level or the value of money is determined by the supply of

money. The value of money, according to this theory, varies inversely as the supply of

money; the price level, on the contrary, varies directly as the quantity of money.

13.2. The Neo-classical quantity theory of money or Cambridge Equation:

Neo-classical quantity theory of money also known as ambridge cash balance theory of

demand for money, because it was put forward by Cambridge economists like Marshall,

Pigou, and Robertson. It places emphasis on the function of money as a store of value or

wealth instead of Fisher’s emphasis on the use of money as a medium of exchange.

Marshall, Pigou and Robertson focussed their analysis on the factors that determine

individual demand for holding cash balances. Although, they recognised that current

interest rate, wealth owned by the individuals, expectations of future prices and future

rate of interest determine the demand for money, they however believed that changes in

these factors remain constant or they are proportional to changes in individual’s income.

Thus, they put forward a view that individual’s demand for cash balances is proportional

to the nominal income. Thus, according to their approach, aggregate demand for money

can be expressed as

Md = kPY ------------(1)

Where Y=real national income; P = average price level of currently produced goods and

services; PY = nominal income; k = proportion of nominal income (PY) that people want

to hold as cash balances

Demand for money in this equation is a linear function of nominal income. The slope of

the function is equal to k, that is, k = Md/Py, thus important feature of cash balance

approach is that it makes the demand for money as function of money income alone. A

merit of this formulation is that it makes the relation between demand for money and

income as behavioural in sharp contrast to Fisher’s approach in which demand for money

was related to total transactions in a mechanised manner.

The Cambridge economists have attempted to express the relationship between the

supply of and the demand for money by formulating cash balance equations known as

‘Cambridge Equations’. We shall discuss now some of the important equations.

13.2.1 Marshall’s Equation:

The Marshallian cash balance equation is expressed as follows:

M = KY ----------------(2)

Where,

M is the quantity of money,

Y is the total money income and

K is the co-efficient whole function is to bring the two sides into balance.

The value of money in terms of this equation, can be found out by dividing the total

quantity of goods which the public desires to hold out of the total income by the total

supply of money thus,

P= KY/M

Where,

P represent the purchasing power of money.

According to Marshall’s equation, the value of money is influenced not only by changes

in M, but also by changes in K. K is rather a more important influence on P than M. for

example, a sudden change in K may greatly influence P even though the supply of money

remains constant.

13.2.2 Pigou’s Equation:

Pigou expresses the form of an equation as:

P= KR M

------ or ------ ----------------(3)

M KR

Where,

P stands for the value of money or its inverse the price level (M/KR),

M represents the supply of money, R the total national income and

K represents that fraction of R for which people wish to keep cash.

Pigou presents the equation in an extended form by dividing cash into two parts: cash

with the public and, deposits which the people consider as cash, therefore:

P = KR/M{C+h (1-c)} -----------------(4)

Where,

C denotes cash with the public

(1-c) stands for bank deposits and

H denotes the percentage of cash reserve against bank deposits.

If we assume the total amount of money in the community as 1, the public as cash holds

the public holds part of it and balance as deposits in banks. Banks do not keep the entire

deposits as cash only a portion or a part of it is kept as cash and is denoted by ‘h’.

Therefore, C+h (1-c) shows the amount of money in the economy at any time denoting

the proportion of cash and h(1-c) denoting it proportion of bank deposits.

13.2.3 Robertson’s Equation:

Prof D H Roberstson’s equation is similar to that of Prof Pigou’s with a little difference.

Roberson’s equation is:

M = PKT or P = M/KT -----------------(1)

Where P is the price level, T is the total amount of goods and services K represents the

fraction of T for which people wish to keep cash. Robertson’s equation is considered

better than that of Pigou as it is more comparable with that of Fisher. It is the best of all

the Cambridge equations, as it is the easiest.

Glay writes,’ Cambridge approach is conceptually richer than the transactions approach,

the former is incomplete because it does not formally incorporate the influence of

economic variables must mentioned on the demand for cash balances, Keynes attempted

to eliminate this shortcoming.

Another important feature of Cambridge demand for money function is that the demand

for money is proportional function of nominal income. Thus, it is proportional function of

both price level and real income. This implies tow things, first income elasticity of

demand for money is unity and secondly price elasticity of demand for money is also

equal to unity so that any change in the price level causes equal proportionate changes in

the demand for money.

13.4 Summary

Quantity theory of money seeks to explain the value of money in terms of changes in its

quantity. In other words, quantity theory of money says that the level of prices varies

directly with quantity of money. In this regard there are three theories, one is cash

transactions theory which was developed by considering medium of exchange is a

function of money, second one is cash balances approach based on the store value as a

function of money and, thirdly Keynes theory of liquidity preference.

13.9 Check your progress

State whether the following statements are true or false

a) Cash balances and transactions are one and same

b) The purchasing power of money depends on the existing price level

c) The quantity theory states the there is a positive association between money

supply and changes in price.

d) Md = Ky Equation is given by Classicals

13.10 Key concepts

Quantity theory of money

Marshall equation

Pigou equation

Robertson’s equation

Cash balances

Demand for money

13.11 Self Assessment questions

Short Answer type questions:

a) What are the deficiencies in the cash balances approach?

b) What is the basic difference between Marshal and Robertson equation?

Essay type questions:

a) Explain, in what respects Cash Balances approach superior to the traditional

approach?

b) Critically examine the quantity theory of money?

c) What are the objections raised against the Cambridge approach to money?

13.12 Answers to check your progress

a) False b) True c) True d) True e) false

13.13 Suggested Readings

Ackley Gardner : Macro economic theory

Ward R A: Monetary theory and policy

Rana & Verma : Macro economic analysis

Hajela TN: Monetary economics

Ghatak : Monetary economics in developing economies