Coursework: MPP IMT Ghaziabad

By

Dr. Manas Paul

Term II PGDM 2015-17

Keynesian Multipliers

• Keynesian model of income determination

• Consumption function

• Multipliers…impact of autonomous spending on output

• Impact of income tax on multipliers

• Effect of Govt purchases and tax changes on govt finances/govt budget

Post crisis fiscal boost

Source: Pg. 08 of “IMF Macroeconomic Policy Advice in the Financial Crisis Aftermath”, Independent Evaluation Office, IMF, BP/14/7 , by Sanjay Dhar , 08 Oct, 2014

US plan for a boost of $787bn; China boost of $586bn, EU a boost of $200bn

Autonomous Spending TRTAYYD

)( TATRYcCcYDCC

cYA

cYNXGITRTAcC

NXGITRTAYcC

NXGICAD

)(

)(

“A bar” is independent of the level of income or autonomous. In equlbm Y = AD i.e. Solve for Y to find the eqlm output

cYAY

Ac

Y

AcY

AcYY

)1(

1

)1(

0

Making C a function of disposable income

])([ NXGITRTAcCA

Got to excel Sheet Example Example 1

• What is the slope of Consmption fn?

• What is the slope of Agg DD fn?

Consumption, AD & autonomous spending

The Government Sector • The government affects the level of

equilibrium output in two ways:

1. Government expenditures (component of AD)

2. Taxes and transfers

• Fiscal policy is the policy of the government with regards to G, TR, and TA

– Assume G and TR are constant, and that there is a proportional income tax (t)

– The consumption function becomes: YtccTRC

tYTRYcCC

)1(

)(

The MPC out of income

becomes c(1-t)

9-7

The Government Sector

• Combining with AD:

• Using the equilibrium condition, Y=AD, and equation the

equilibrium level of output is:

• The presence of the government sector flattens the AD curve and reduces the multiplier to

YtcA

NXGIYtccTRC

NXGICAD

)1(

)1(

)1(1

)1(1

)1(

)1(

0tc

AY

AtcY

AYtcY

YtcAY

))1(1(

1

tc

9-8

Effects of a Change in Fiscal Policy

• Suppose government expenditures increase – Results in a change in

autonomous spending and shifts the AD schedule upward by the amount of that change

– At the initial level of output, Y0, the demand for goods > output, and firms increase production until reach new equilibrium (E’)

• How much does income expand? The change in equilibrium income is

[Insert Figure 9-3 here]

GGtc

Y G

)1(1

10

Effects of a Change in Fiscal Policy

• A $1 increase in G will lead to an increase in income in excess of a dollar – If c = 0.95 and t = 0.25, the

multiplier is 3.5

A $1 increase in G results in an increase in equilibrium income of $3.50

G and Y shown

[Insert Figure 9-3 here] GG

tcY G

)1(1

10

Expansionary fiscal policy measure

Effects of a Change in Fiscal Policy

• Suppose government increases TR instead – Autonomous spending would increase by only cTR,

so output would increase by G cTR – The multiplier for transfer payments is smaller than

that for G by a factor of c • Part of any increase in TR is saved (since considered income)

• If the government increases marginal tax rates, two things happen: – The direct effect is that AD is reduced since disposable

income decreases, and thus consumption falls – The multiplier is smaller, and the shock will have a

smaller effect on AD

Effects of Government Purchases on Budget Surplus

– An increase in G reduces the surplus, but also increases income, and thus tax revenues

Does there exist a Possibility that increased tax collections overwhelms the increase in G????

• The change in income due to increased G is equal to

, a fraction of which is collected in taxes

– Tax revenues increases by

– The change in BS is

GY G 0

Gt G

Gtc

tc

GGt

GTABS

G

)1(1

)1)(1(

The change is

negative OR

reduces the surplus

• When the tax rate remains unchanged, an increase in Govt spending can not generate tax revenues more than it…..

Balanced budget multipliers We have seen earlier:

• In the case of (proportional) tax rate remaining unchanged, tax revenues earned from

multiplied income (fiscal multiplier effect) at the back of a rise in govt spending would always fall short of the govt spending made.

• So what if along with Govt spending the tax rate also changes?

Can we get a solution where the increase in tax collection at the back of multifold rise in ‘Y’ and an increase in tax rate ‘t’ can match the increase in government spending? If so happens then we arrive at the situation of balanced budget multiplier.. We do this in terms of lump-sum taxes where balanced budget implies:

TAG

Balanced Budget implies:

G = TA Hence,

∆𝐺 = ∆𝑇𝐴

Now we have seen earlier that in such a case Y = A +cY

∆𝑌 = ∆𝐴 + 𝑐 ∗ Δ𝑌

Now change in autonomous spending will have two components. 1. First increase in Govt spending ΔG. 2. Second the reduction in disposable income due to taxes will lead to a

reduction in domestic consumption ∆𝐴 = ∆𝐺 − 𝑐 ∗ ∆𝑇𝐴

Replacing ΔA in the equation above for ΔY: ∆𝑌 = ∆𝐺 − 𝑐 ∗ ∆𝑇𝐴 + 𝑐 ∗ ∆𝑌

Balanced budget multipliers: Using Lump sum taxes

Since ΔG = ΔTA : ∆𝑌 = ∆𝐺 − 𝑐 ∗ ∆𝐺 + 𝑐 ∗ ∆𝑌 ∆𝑌(1-c) = ∆𝐺(1-c) => ∆𝑌 = ∆𝐺

• What is the value of balanced budget multiplier?

Balanced budget multipliers: Cute construct but unlikely to be so relevant

• Political difficulty to use the balanced-budget multiplier …..people are bound to notice that the benefits of the plan go disproportionately to the unemployed, while most of the costs are borne by the majority who are working…..

• Pursuing balanced-budget stimulus requires raising taxes…. voters are extremely sensitive to the very words “tax increase.”

What are they?

• Automatic Stabilizers: Factors /arrangements those reduces the impact of short-run fluctuations…hence dampens the multiplier impact without additional government intervention… i.e. Proportional taxation: Reduces the multiplier…. Hence dampens the rise in Income during expansions and similarly it makes any downturn less severe. Unemployment benefits: During and after recession as more an more people loose jobs, they automatically come under the unemployment benefit which reduces the impact of income loss at back of job losses. Similarly as during a recovery as more and more job gains happens people start exiting from the unemployment benefit programs.

What do they do? They reduces the severity of downturn and at the same time prevents the economy from overheating during recovery.

Automatic Stabilizers

We have an economy described by the following functions:

20.0

100

200

70

8.050

_

_

_

t

TR

G

I

YDC

a. Calculate the equilibrium level of income and multiplier in the model b. Calculate the budget surplus/deficit c. Suppose ‘t’ increases to 0.25, what would be the equilibrium income and new multiplier? d. Calculate the change in the budget surplus/deficit. Would you expect the change in surplus/deficit to be more or less if c=0.9 rather than 0.8? e. Can you explain why the multiplier is 1 when t=1?

Example:

You as a part of IMF Mission have been deputed to analyse and suggest possible fiscal boosters to two island economies run down by financial crisis. These two economies were hit by economic crisis in the previous year. Economy 1 had a nominal GDP of USD 700 and Economy 2 had a nominal income of USD 800, while their GDP deflator declined by 5% and 7% respectively from the base year. The two economies are characterised by:

Assignment 1:

These are in real terms

Economy 1

C=50 +0.8YD

I bar = 70

G bar = 200

TR = 100

t=0.2

These are in real terms

Economy 2

C=50 +0.85YD

I bar = 70

G bar = 200

TR = 100

t=0.15

1. Find yoy growth in real GDP in both these economies. 2. What are the value of autonomous spending in both these economies? 3. Apparently there is hardly any difference in autonomous spending between these two economies? What could be the

reason for higher growth in one of these economies? 4. Because of rising dissent at the back of increased economic difficulties, finance ministers in both these economies are

advocating transfers to the masses over government spending? Explain to what extent you would veto their recommendation?

5. Finance ministers of both these countries were of the view that they can fund an increase in government spending through rising tax collections even if there is no increase in tax rate… just because of the manifold rise in income at the back of multiplier effect. Can you find that level of government spending for these countries that can be funded through rising tax collections just because of the multiplier effect?

6. Now along with a rise in government spending the government also has the option of raising the tax rate. Can you find a combination rise in taxes and government spending for both these countries when the entire rise in government spending can get funded through the rising tax revenues?

Assignment 2: Suppose tax revenue take the functional form 𝑇𝐴 = (𝜏 + 𝑡𝑌), where 𝜏 is autonomous tax independent of income. Consumption function takes the form given below, while I, G, (X-M) are autonomous.

1. Find the formula for multiplier… is it different from the multiplier where you had only proportional tax without any autonomous element?

2. What is the value of equilibrium Y, is it lesser or more than the case without proportional income? Can there

be an explanation for the same? 3. Can you prove the case of balanced budget multiplier with a change in autonomous component of of the tax?

))((()( tYTRYcCTATRYcCcYDCC