Chapter # 4 MULTIPLIER and ACCELERATOR

Chapter`s Outlines Introduction and History of Multiplier Investment Multiplier Numerical & Graphical Presentation Consumption Multiplier Government Multiplier Tax Multiplier Accelerator Numerical Explanation of Acceleration Principle

Introduction of Multiplier The concept of Multiplier was first developed by R.F. Kahn in early 1930`s. He traced the effect of an increase in investment on employment. Then J.M. Keynes used it for income analysis. Keynes believe that an increase in investment causes a much bigger increase in national income.

Introduction of Multiplier When we change investment, it will bring a multiple change in national income, but the question arise to what extent NI changes as a result of change in investment.

Definition of Multiplier An initial change in aggregate demand will lead to greater increase in the final level of equilibrium National Income.

Investment Multiplier Multiplier shows that how an initial change in investment brings a multiple change in income. OR Multiplier is the ratio of change in the National Income to a change investment.

Example: The government decides to build new roads across the Afghanistan. They pay a contractor $300m to do this. This creates a $300 million increase in spending in the Afghan economy.

This will create a chain reaction of increases in expenditures. The firm who gets the contract to build the roads will spend this $300m on materials, equipment, wages & profits. This will create additional incomes for other firms and households If they spend approx 60% of that additional income, then $180m will be added to the incomes of others. At this point, total income has grown by ($300m + (0.6 x $300m).

The sum will continue to increase as the producers of the additional goods and services gain an increase in their incomes, of which they in turn spend 60% on even more goods and services. The increase in total income will then be ($300m + (0.6 x $300m) + (0.6 x $180m). The process can continue indefinitely. But each time, the additional rise in spending and income is a fraction of the previous addition to the circular flow.

Size of Investment Multiplier...?? The final increase in national income (Y) will be greater than the initial injection. The size of the multiplier depends on how much of an increase in income is spent in Afghanistan economy.

Size of Multiplier…… cont`d The Multiplier Effect Size of Multiplier…… cont`d Marginal Propensity to Consume determine the size of multiplier. MPC = change in consumption change in income For example if the MPC is 0.8 it means 80% of the increase in income is spent. Unit 3 Economics

Size of Multiplier…… cont`d The investment multiplier is the direct function of marginal propensity to consume (MPC). The size of multiplier depends upon how large or small is the MPC. If MPC is high, the value of the multiplier will also be high. If MPC is small, the value of the multiplier will also be small.

Size of Multiplier…… cont`d The value of Multiplier can be obtained by following formula K= 1 . For example if mpc is 0.80 then multiplier will be K= 1 = 1 K = 5 1-mpc 0.2 1-0.8

Alternate way to find K…??? Another way to find out the multiplier is that it is the reciprocal of MPS, For example if MPC is 0.8 then we can easily find MPS , as we know that MPS = 1- MPC So K = 1/MPS K = 1/0.2 K=5

Conclusion The size of the multiplier depends on marginal propensity to consume or propensity to save. The larger the MPC, the larger the multiplier. The larger the MPS, the smaller the multiplier.

Numerical Example for Multiplier Action The investment multiplier tells us that an increase in investment brings about a multiple increase in aggregate income. Let us assume that MPC is 0.8 and an increase in investment is $100 mn The MPC being 0.8 means that the multiplier (K) will be (1/1-0.8) = 5 So the new investment of $100 mn will increase the aggregate income by $ 500 mn.

Graphical presentation of multiplier effect C+S C+I+ ΔI Y B C+I } 100 E . 500 2500 x 2000 National income

Explanation of Graph In this figure the curve C+I intersects the aggregate production curve line at point E at 2000, the equilibrium level of the income. The new curve showing the additional investment curve (C+I+∆I), intersects the total production line at B. The equilibrium income eventually increases from 2000 to 2500 in time periods (t). Thus the total increase in equilibrium income is equal to 500

Assumptions of Multiplier MPC is constant. There is no changes in prices of commodities. There is closed economy unaffected by foreign influence. There is no change in autonomous investment

Consumption multiplier In consumption multiplier we want to show the effect of consumption on National Income. Y=f (c ), that is NI will change many a time more than the change in consumption. Change in consumption will have a multiple effect on income.

Consumption Multiplier …. How much income change as a result of change in consumption depends on consumption multiplier (Kc) Consumption Multiplier is a ratio of change in NI (ΔY) to change in consumption (Δc)

Numerical example of consumption multiplier Y=C+I, C= 40 + 0.60Y I0=80 Y=Co+ cY+ I0 Y=40+0.60Y+80 Y- 0.60Y=120 0.40Y=120 dividing both sides by 0.40 Y= 300 is initial equilibrium level of income

Numerical example of consumption multiplier Now suppose that autonomous consumption increases from 40 Afs to 100 Afs Y=Co+ cY+ Io Y=100+0.60Y+80 Y-0.6Y=180 0.4Y=180, dividing both sides by 0.4 Y1=450 so Y1 is the new equilibrium level of income after change in consumption

IS YOUR ANSWER CORRECT..?? VERIFY K = 1 . 1-mpc K= 1/1-0.60 = 1/0.4 K= 2.5 Now verify your answer Y0= 300 & Y1 = 450 ∆Y = 450-300= 150 C= 40, C1 = 100, ∆C =100-40= 60 K = ∆Y/ ∆C K= 150/60 = 2.5

Consumption Multiplier Effect (cont….) Graphical presentation of multiplier effect AS=C+S C+I C+S C+ΔCo +I E2 C+I E1 ΔCo=60 ΔY=150 x 300 450

Government Expenditure Multiplier Like a change in autonomous investment, change in government expenditure also has a multiple change in National Income Now our NI, Y will be equivalent to AD = C+I+G , AS=C+I+S Where C= Co+cYd ,where Yd is personal disposable income which is equal to Y-T

Government Expenditure Multiplier….. Investment is equal to autonomous investment i.e. Io The saving equation is S=-So+sYd Government expenditure is autonomous expenditure i.e. Go Taxes are also autonomous i.e. To

Government expenditure multiplier (cont..) How much income changes as a result of change in Government expenditure is known as Government Expenditure Multiplier (KG) OR It is the ratio of change in NI (ΔY) to change in Government expenditure (ΔG)

Numerical example of government expenditure multiplier Y=C+ I0+ Go C=Co+ c Y C = 40+0.60Y, I0 =80, Go=60 Putting the values in income equation Y = 40+0.60Y+80+60 Y-0.60Y=180 Y=450 Now we assume that government expenditure increases her expenditure from 60 Afs to 100 Afs, theory suggests that change in government expenditure has multiple effect on NI, now we will prove it

Numerical example of government expenditure multiplier Y=C+ I0+ Go C=Co+ c Y C = 40+0.60Y, I0=80, Go=100 Putting the values in income equation Y = 40+0.60Y+80+100 Y-0.60Y=220 Y1 =220/.40 =550 Y1=550, so change in GOVT expenditure is 40 Afs ,where as change in NI is 100 Afs

VERIFY YOUR ANSWER..?? As we know that K = 1 . 1-mpc K= 1/1-0.60 = 1/0.4 K= 2.5 Now verify your answer Y0= 450 & Y1 = 550 ∆Y = 550-450= 100 G= 60, G1 = 100, ∆G =100-60= 40 K = ∆Y/ ∆G K= 100/40 = 2.5

Government expenditure multiplier (cont..) Graphical presentation of GEM AS AD2=C+I+G2 E2 AD,AS AD1=C+I+G1 E1 ΔGo=40 Y 450 550

Tax multiplier Like a change in autonomous investment, the change in autonomous taxes has a multiple effect on level of national income However there is a negative effect on level of national income When tax rate increase, consumption decrease and it leads to decrease in investment and ultimately decrease the national income.

Tax multiplier (cont…) As a result, NI decrease many a time depending upon the value of Kt Through KT we find How much income change as a result of change in Tax (Kt) Tax Multiplier is a ratio of change in NI (ΔY) to change in Tax (ΔT)

Numerical example of Tax Multiplier Y=C+ I0+ Go C=Co+ c Yd , Yd =(Y-T) C = 40+0.60Yd, I0=80, Go=60, T= 20 Putting the values in income equation Y = 40+0.60Yd+80+60 Y=40 + 0.60Y - 0.6(20) +80 + 60 Y=40 + 0.6Y -12 + 60 + 80 Y-0.60Y=168, => 0.4Y=168 => Y= 420 Now we assume that government increases Tax from 20 Afs to 30 Afs

Numerical example of Tax Multiplier…… C = 40+0.60Yd, I0=80, G0=60, T0= 30 Putting the values in income equation Y = 40+0.60Yd+80+60 Y=40 + 0.60Y - 0.6(30) +80 + 60 Y=40 + 0.6Y -18 + 60 + 80 Y-0.60Y=162 0.4Y=162 Y= 405

Introduction to Acceleration Principle Carver was the first economist who recognized the relationship between changes in consumption and net investment in 1903 The term “acceleration principle” itself was first introduced into economics by J.M Clark in 1917. It was further developed by Hicks, Samulson and Harrod

Acceleration The principle of acceleration The principle of acceleration is based on the fact that demand for capital goods is derived from the demand for Consumer goods, it means that if there is demand of consumer goods in market, investment will take place and demand for capital goods will increase.

Acceleration (cont…) Acceleration principle explains the process by which an increase or (decrease) in demand for consumption goods leads to an increase or decrease in investment or capital goods In words of Kurihara “ acceleration coefficient is the ratio between induced investment and initial change in consumption expenditure.

Acceleration (cont…) Symbolically β = ΔI/ ΔC Where β is accelerator coefficient , ΔI is net change in investment, and ΔC is change in consumption expenditure If the increase in consumption expenditure of 10 million Afs leads to an increase in investment of 30 million Afs the accelerator coefficient is 3.

This means that when the income of a community rises the purchasing power of the people increases. They begin to buy more commodities. The higher the demand for consumer goods leads to greater investment. The rise in investment is proportionately more than the rise in demand for consumption.

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