Investment Multiplier and Super multiplier

Investment Multiplier and Super Multiplier are very important concept of Macroeconomics to understand the effect of autonomous investment and induced investment in final increase in national income.

1. By: Khemraj Subedi Assistant Professor Far Western University PhD Scholar in Economics M.Phill (Economics) M.A. (Economics) M.Ed. (Economics) Simple Multiplier and Super Multiplier

2. Simple Multiplier and Super Multiplier The simple multiplier implies that investment is the central determinant of output . An  investment multiplier  similarly refers to the concept that any increase in public or private investment has a more than proportionate positive impact on aggregate income and the general economy.  The super multiplier combines the multiplier with the accelerator that indicates that investment is not autonomous, but is part of derived demand. Hence , the super multiplier indicates that capacity adjusted output is determined by autonomous demand.

3. Autonomous demand in the case of the super multiplier would correspond to government spending, exports and some elements of consumption (particularly the wealthy whose consumption is not constrained by income). The practical difference is that not only demand determines output in the short run, but also in the long run. The economic system is effectively demand driven and Keynes' Principle of Effective Demand substitutes Say's Law.

4. The concept of Multiplier occupies an important place in Keynesian theory of income, output and employment. It is an important tool of income propagation and business cycle analysis. According to Keynesian framework, employment depends upon effective demand, which in turn, depends upon consumption and investment(Y=C+I ). Keynes designed framework to show the relationship of a small increase in investment to final increase in income. It is very closely connected with the concept of the marginal propensity to consume(MPC ).

5. F. Kahn ," Multiplier is the ratio of the final change in income to the initial change in investment." Arithmetically, ∆Y = K. ∆I Where, ∆Y = Change in income. ∆I = Change in investment. K = Multiplier Therefore , we get K = ∆Y / ∆I

6. Example Suppose , initial investment is Rs.100 Million and multiplier coefficient is 5 ( MPC = 0.8) , then find out final increase in income. Solution: Given, ∆I = 100 Million Multiplier (K) = 5 (K= 1/1-MPC) We have, Final increase in income, ∆Y = K.∆I = 5 x Rs.100 Million ∆Y = Rs. 500 Million

7. Multiplier Formula Multiplier = K = 1/1-MPC or, K = 1/MPS Calculation of multiplier or Income propagation in multiplier ( MPC = 0.8) Period ∆I ( Rs. Crore ) ∆Y ( Rs. Crore ) ∆C ( Rs. Crore ) ∆S=∆Y-∆C ( Rs. Crore ) 1 2 3 4 - - (and so on) 100 - - - - - - - 100 80 51.2 40.96 - - - - 80 64 40.96 32.768 - - - - 20 16 12.8 10.24 - - - - Total 100 500 400 100

8. The concept of supermultiplier is the mathematical combination of multiplier of Keynes and accelerator of Aftalian . Prof. J.R. Hicks has interacted both multiplier and accelerator with a view to measuring the total effect of initial investment on income. The combined effect of the multiplier and the accelerator is also called the leverage effect. Super multiplier

9. The super multiplier is worked out by combining both induced consumption (MPC) and induced investment (MPI). Defined as; K’ = 1 / ( 1- MPC – MPI) The super multiplier is thus defined as the ratio of change in income to a change in autonomous investment when the induced investment is also present.

10. Concept of Super Multiplier The concept of super multiplier was developed J. R. Hicks in 1950 by combining the concept of multiplier and accelerator to give new concept of super multiplier. The concept of super multiplier is derived by combining both induced consumption ( ∆C/∆Y=MPC) and induced investment ( ∆I/∆Y=MPI).

11. The simple multiplier measures the effect of autonomous investment in the final increase in aggregate income where as accelerator measures the effect of induced investment in the final increase in aggregate income.

12. But, super multiplier measures the effect of both induced consumption and induced investment in the final increase in aggregate income .

13. Thus, super multiplier is combination of both simple multiplier and accelerator designed to measure the final effect of initial investment outlays to the final increase in income.

14. Derivation of Super multiplier Let, the equilibrium of a two sector economy be expressed as: Y = C+I .... ..... ..... ..... ...... ( i ) We know, I = I a + I i ∴ I = I a + V.Y ..... ...... ...... (ii) ( ∵ I i = V.Y) Similarly C = a + b Y............. ...... .......... (iii) Where, a = autonomous consumption b= ∆C/∆Y

15. Substituting (ii) and (iii) in equation ( i ) Y = a + b Y + I a + V.Y .... ..... ...... .....(iv) Let, I a changes by ∆I so that Y also changes by ∆Y, Y+∆Y=a +b(Y+∆Y)+ I a +∆ I a + V(Y+∆Y )...(V) Subtracting equation (iv) from (v), we get ∆ Y = b∆Y + ∆ I a + V∆Y

16. Dividing both sides by ∆Y, 1 = b + ∆ I a /∆Y +V or, 1 - b- V = ∆ I a /∆Y or, ∆Y/∆ I a = 1/1 - b- V ∴ Ks = 1/1-b-V Where, b= ∆C/∆Y = MPC V= ∆I/∆Y =MPI or Accelerator coefficient.

17. If V = 0, Ks = 1/1-b-0 = 1/1-b =K Where, K = Simple multiplier Let, b = 0.5, V= 0.4 ∴ K = 1/1-b = 1/1-0.5 = 2 ( i.e. V= 0) ∴ Ks = 1/1-b-V = 1/1-0.5-0.4 = 10

18. Period Initial Investment Induced consumption (MPC = 0.50) Induced Investment (MPI ( I i )= 0.4) Increase in income (Delta Y = MPC + MPI) Total increase in income 1st -   - - - 2nd 50.00 - - 50.00 50.00 3rd   25.00 20.00 45.00 95.00 4th   22.50 18.00 40.50 135.50 5th   20.25 16.20 36.45 171.95 6th   18.23 14.58 32.81 204.76 7th   16.40 13.12 29.52 234.28 8th   14.76 11.81 26.57 260.85 9th   13.29 10.63 23.91 284.77 10th   11.96 9.57 21.52 306.29 11th   10.76 8.61 19.37 325.66 12th   9.69 7.75 17.43 343.09 13th   8.72 6.97 15.69 358.79 14th   7.85 6.28 14.12 372.91 .   . . . . .   . . . .     500.00             K' = 1 / (1-0.5-.4) K' = 10 Note: When K' is 10, the initial investment grow equivalent to 10 fold in terms of national income SUPERMULTIPLIER PROCESS

19. When we introduce the induced investment in autonomous investment, the total investment will have two components: autonomous investment( Ia ) and induced investment(I i ) I = I a + I i

20. The simple multiplier implies that investment is the central determinant of output. The super multiplier combines the multiplier with the accelerator that indicates that investment is not only autonomous, but is part of derived demand. Hence, the super multiplier indicates that capacity adjusted output is determined by autonomous demand. What are the practical differences between simple multiplier and super multiplier?