ecn 302-602 (4), the simple keynesian model

7/28/2019 ECN 302-602 (4), The Simple Keynesian Model

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Chapter 3 -- TheSimple Keynesian Model

Fundamental inflexibilityassumptions:

W -- inflexibleP -- inflexible

i -- inflexible

Overriding theme -- ProductionResponds to Economic Activity(focus on goods and servicesexpenditure)


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p )

Simplifying Assumptions

Business Saving = 0 (All private savingis personal saving)

Taxes dont depend upon income.

T = G (Balanced Budget)

NX = 0

Assumptions imply that the Magic

Equation is now S = I.


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Causes of Consumption (C)

Disposable Income (YD = Y - T)

YD CReal GDP, or Total Income (Y)

Y YD CNet Taxes (T)

T YD CConsumer Confidence (CC)

CC

C


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More Causes ofConsumption (C)

Real Interest Rate (r = i - e)r C

Nominal Interest Rate (i)i r C

Expected Inflation Rate (e)e r C

Real Wealth (A)

A

C


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Measures --YD C RelationshipAverage Propensity to Consume

(APC)

APC = C/YD

Marginal Propensity to Consume(MPC)

MPC = C/YD


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Handling MultipleCauses of Consumption

Causes of Consumption --

Y, T, CC, i, e, A.Autonomous Consumption (C0) --

changes in C due to causes otherthan Y.


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Causes of Investment (I)

Business Confidence (BC)

BC IBusiness Taxes (BT)

BT I


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More Causes of Investment

Real Interest Rate (r = i - e)r I

Nominal Interest Rate (i)i r I

Expected Inflation Rate (e)e r I

Note: Investment does not dependupon current income (Y)


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Government Purchases ofGood and Services (G)

Government purchases of goodsand services is a policy variable,

controlled by the government no causing variables.

The previous properties imply thatI and G are completely

autonomous.


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A Numerical Example

Y T YD C S I G

5 5 0 10 -10 10 5

25 5 20 25 -5 10 5

45 5 40 40 0 10 5

65 5 60 55 5 10 5

85 5 80 70 10 10 5

105 5 100 85 15 10 5

125 5 120 100 20 10 5


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The Saving-InvestmentRelationship

Recall -- macro identity

S + (T - G) + -NX = I

With simplifying assumptions:

S = I

Why doesnt S = I in numericalexample?


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Intentions Versus ActualOccurrences

Must distinguish betweenintended, desired, planned S and I

versus actual or realized S and I.Intended S and I -- strategies,

described by schedules andgraphs.

Actual S and I -- the numbers after

the period is over.


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Planned Expenditure (EP)

Planned Expenditure (EP) -- Thetotal intended spending for various

levels of income.In equation form,

EP = C + I + G.


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Planned Expenditure inthe Numerical Example

Y T YD C S I G EP

5 5 0 10 -10 10 5 25

25 5 20 25 -5 10 5 40

45 5 40 40 0 10 5 55

65 5 60 55 5 10 5 70

85 5 80 70 10 10 5 85

105 5 100 85 15 10 5 100

125 5 120 100 20 10 5 115


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An Equilibrium Levelof Real GDP: EP = Y

Y T YD C S I G EP

5 5 0 10 -10 10 5 25

25 5 20 25 -5 10 5 40

45 5 40 40 0 10 5 55

65 5 60 55 5 10 5 70

85 5 80 70 10 10 5 85

105 5 100 85 15 10 5 100

125 5 120 100 20 10 5 115


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Why is Y* = 85 anEquilibrium?

Example 1: Suppose Y = 105.

Intended Actual

C = 85 C = 85S = 15 S = 15

I = 10 I = 10 + 5 = 15

G = 5 G = 5

EP = 100

Note -- Actual S = Actual I

*


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Why is Y* = 85 anEquilibrium? (Continued)


Intended Actual

C = 55 C = 55S = 5 S = 5

I = 10 I = 10 + -5 = 5

G = 5 G = 5

EP = 70


Wh i Y* 8


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Why is Y* = 85 anEquilibrium? (Finally)


Intended Actual

C = 70 C = 70S = 10 S = 10

I = 10 I = 10

G = 5 G = 5

EP = 85



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Properties of Equilibrium

No unintended inventoryaccumulation or depletion.

All intentions are realized.

Intended Saving = Intended

Investment (only at equilibrium).EP = Y

E ilib i d th


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Equilibrium and theNatural Level of Real GDP

Fundamental Prediction ofKeynesian models -- Y* is not

necessarily equal to YN.

Classical Prediction: Self-correcting economy Y* = YN.(Business cycle represents

deviations from equilibrium)

K i P di ti


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Keynesian Prediction --State of the Economy

Y* < YN (sluggish economy)

Y* > YN (accelerating inflation)

Y* = YN (desired state ofeconomy)

If Y* YN, then one needseconomic policy to achieve a new

equilibrium closer to YN.


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The Keynesian Prescription

Achieve a new equilibrium byshifting the Ep curve.

If Y* < YN, seek to increaseexpenditure, described by shiftingthe E

P

curve upward.

If Y* > YN, seek to decreaseexpenditure, described by shifting

the EP curve downward.


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Shifting the EP Curve

Key -- Change AutonomousConsumption, Autonomous

Investment, or GovernmentPurchases (or, later,Autonomous Net Exports).

Change C0 -- change T, CC, i, e, AChange I0 -- change BC, BT, i, eChange G0.


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Economic Policy

Purpose -- to move Y* closer to YN.

Method -- change autonomous

expenditure (C0, I0, G0).

If economy is sluggish (Y* < YN),

increase autonomous expenditure.If economy has accelerating

inflation (Y* > YN), decrease

autonomous expenditure.


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Strategies for Policy

Expansionary Policy -- Policydesigned to address a sluggish

economy (Y* < YN).Contractionary Policy -- Policy

designed to address anoverstimulated, or acceleratedinflation economy (Y* > YN).

Q tit ti Eff t


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Quantitative Effects --Changes in C0, I0, or G0

Y T YD C S I G EP

5 5 0 10 -10 10 5 25

25 5 20 25 -5 10 5 4045 5 40 40 0 10 5 55

65 5 60 55 5 10 5 70

85 5 80 70 10 10 5 85

105 5 100 85 15 10 5 100

125 5 120 100 20 10 5 115


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Note: MPC = C = 25 - 10 = 0.75YD 20 - 0

Example -- If autonomous

government purchases arechanged by 5, how much will Y*change as a result?

S l ti N i l


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Solution -- NumericalExample

Y EP EP (G0 = 5)5 25 30

25 40 45

45 55 60

65 70 75

85 85 90

105 100 105

125 115 120


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The Multiplier Effect

The Multiplier Effect -- Given aninitial change in autonomous

consumption, autonomousinvestment, or governmentpurchases of goods and services,

the resulting change in equilibriumoutput will be a multiple oftheinitial change.

The M ltiplier Effect


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The Multiplier Effectin Equation Form

Y* = m (C0, I0, G0, orNX0),where m = the multiplier.

m = 1/(1 - MPC)

Our Example: (G0 = 5 Y* = 20)(20) = (4)(5)

MPC = 0.75 m = 1/(1 - 0.75) = 4

Tracing the Effect on Y*:


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Tracing the Effect on Y*:G0 = 5, with MPC = 0.75Added Added

Round Spending Income

1 5 52 5(0.75) 5(0.75)

3 5(0.75)2 5(0.75)2

... ... ...

Y* 20 20


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Properties: Multiplier Effect

The multiplier varies positivelywith the MPC, i.e. MPC m.Applies for either increases or

decreases in C0, I0, G0, or NX0.

Applies to changes both policy-

induced and otherwise.Changes in autonomous net taxes

(T0) have a multiplier effect, but not

the same multiplier.

Changing G Versus


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Changing G0 VersusChanging T0, MPC = 0.75

Added Spending

Round G0 = 5 T0 = -51 5 5(0.75)2 5(0.75) 5(0.75)2

3 5(0.75)2 5(0.75)3

... ... ...

______________________________

Y* 20 15

Th N t T M lti li


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The Net Taxes Multiplier

Y* = -MPC T01 - MPC

The Net Taxes Multiplier is smallerthan the regular multiplier (less ofan impact on Y* for the same initial

change).Tax or transfer policy is not as

powerful as G policy, but less

likely to overshoot YN.

A li ti


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Application:The Obama Stimulus Plan

The Obama Stimulus Plan A $787 Bstimulus package passed in February2009, to address sluggish US economy.

-- Tax Cuts = $288 B

-- Extended unemployment benefits,

education and health care = $224 B

-- Federal contracts, grants, and loans

= $275 B (Infrastructure

improvements = $83 B)

The Simple Keynesian


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The Simple KeynesianModel -- The Algebra

The model in equation form.

(1) EP = C + I + G,

(2) C = C0 + b(Y - T),

(3) I = I0,

(4) G = G0,(5) T = T0,(6) At equilibrium, E

P

= Y*.


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Solving for Y*

Substitute equations (2), (3), (4),(5), and (6) into (1)

Y* = C0 + b(Y* - T0) + I0 + G0.

Solve for Y* Y* = 1 {C0 + I0 + G0} + -b T0.(1 - b) (1 - b)

Removing the


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Removing theSimplifying Assumptions

Investment depends upon currentoutput or income (Y).

I = I0 + dY,d = marginal propensity

to invest

Income Tax

T = T0 + tY,

t = marginal tax rate

Causes of Net Exports


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Causes of Net Exports(NX = Exports - Imports)

Foreign output or income (Yf)

Yf Exports NXUS output or income (Y)

Y Imports NXBarriers to TradeReal exchange rate (e)

e NX

A Model for Net Exports


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A Model for Net Exportsin Equation Form

NX = NX0 - fY

NX0 = Autonomous Net Exports

(made up of causes other

than Y)f = marginal propensity to import


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The Model Without the

Simplifying Assumptions:What Results Are The

Same?Answer -- All the qualitative

results are the same!!


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Same Results

Equilibrium occurs where Ep = Y.

True equilibrium, guided by unintendedinventory changes.

Y* may be , or = YN.Need for policy if Y* is different from

YN.

Policy change autonomousexpenditure (expansionary orcontractionary).


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More of the Same Results

Same options as before(C0, I0, G0).Multiplier effect exists.

Tax multiplier is smaller than the

autonomous spending multiplier.

The Model Without the


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The Model Without theSimplifying Assumptions:

What Results Are Different?More possibilities for policy.

-- autonomous net taxes (T0)-- marginal tax rate (t)

-- trade policy (NX0)

Different multipliers forautonomous spending and net

taxes.

The Expanded


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The ExpandedSimple Keynesian Model

(1) EP = C + I + G + NX,

(2) C = C0 + b(Y - T),

(3) I = I0 + dY,(4) G = G0,

(5) NX = NX0 fY,

(6) T = T0 + tY,(7) At equilibrium, EP = Y*.


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More Realistic Multipliers

Substitute equations (2)-(7) into (1),solve for Y*.

Y* = 1 [C0 + I0 + G0 + NX0]

(1 b(1t) d + f)

- b [T0].

(1 b(1t) d + f)

The Economy and the


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The Economy and theFederal Budget

Recall that the Federal Budget isgiven by

Budget = T - G.Substitute income tax function for

T (with Y = Y*):

Budget = (T0 + tY*) - G.

Note that Y*

Budget

The Economy and the


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The Economy and theBalance of Trade

Recall that the Balance of Trade(BOT) is approximated by NetExports (NX).

Also recall that the Net Exportsequation is (Y = Y*):

NX = NX0 - fY*.

Note that Y* BOT

ecn 302-602 (4), the simple keynesian model

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