Accelerator is the ratio between induced investment and an initial change in consumption.
(β) = \(\frac{ΔI}{ΔC}\)

Muliplier is the ratio of the change in national income to change in Investment.
K = \(\frac{ΔY}{ΔI}\)

MPS is the ratio of change in saving to a change in income
MPS = \(\frac{ΔS}{ΔY}\)

S. No Accelerator Effect Multiplier Effect 1. First developed by R. F. Khan redefined by Keynes Developed by J.M. Clark. Further developed by Hicks, Samuelson 2. It is the ratio of the change in national income to a change in investment.
\(K=\frac{\Delta Y}{\Delta I}\) It is the ratio between induced investment and an initial change in
consumption
\(\beta=\frac{\Delta \mathrm{I}}{\Delta \mathrm{C}}\)

S. No	Autonomous Investment	Induced Investment
2.	Independent	Planned
3.	Income inelastic	Income elastic
4.	Welfare motive	Profit motive

(i) When income incrcases, consumption expenditure also incrcases but by a smaller amount.
(ii) The increased income will be divided in some proportion between consumption expenditure and saving.
(iii) Increase in income always leads to an increase in both consumption and saving.

S. No	Marginal Efficiency of Captial (MEC)	Marginal Efficiency of Investment (MEI)
1.	It is based on given supply price for capital.	It is based on the induced change in the price due to change in the demand for capital.
2.	It represents the rate of return on all successive unit of capital without regard to existing capital.	It shows the rate of return on just those units of capital over and above the existing capital stock
3.	The capital stock is taken on the X axis of diagram.	The amount of investment is taken on the X axis of diagram.
4.	It is a 'Stock' concept.	It is a 'Flow' concept.
5.	It determines the optimum capital stock in an economy at each level of interest rate.	It determines the net investment of the economy at each interest rate given the capital stock.

Introduction
The concept of multiplier Was first developed by R.F. Khan in terms of employment. J.M Keynes redefined it as investment multiplier.
Definition
Multiplier is defined as the ratio of the change in national income to change in investment.
\(K=\Delta Y / \Delta I\)
The value of multiplier depends on MPC.
\(\mathrm{K}=\frac{1}{1-\mathrm{MPC}} \text { since } \mathrm{MPC}+\mathrm{MPS}=1\)
\(k=\frac{1}{N 118}\)
Multiplier is inversely related to MPS and directly with MPC.
If MPC is, 0.75, MPS is 0.25 then K=4.00
\(\frac{1}{1-0.75} \text { or } \frac{1}{0.25}=4\)

MPC	MPS	k
0.00	1.00	1
0.10	0.90	1.11
0.50	0.50	2.00
0.75	0.25	4.00

Working
(i) Suppose government undertakes investment expenditure equal to र100 cr on public works.
(ii) Income of labourers and suppliers of materials increases by र100 cr
(iii) If MPC is 0.8 that is 80 %. र80 cr is spent on consumption र20 cr salved
(iv) Suppliers of goods get an income of र80 cr. They spend र64 cr (ie 80% of र80 cr).
(v) In this manner consumption expenditure and increase in income act in a chain like manner.