# Straightforward Keynesian Model

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2. Diagram. Three-Sector ModelTax Function T = f (Y)Consumption Function C = f (Yd)Government Expenditure Function G=f(Y)Aggregate Expenditure Function E = f(Y)Output-Expenditure Approach: Equilibrium National Income Ye. 3. Diagram. Components influencing YeExpenditure Multipliers k ETax Multipliers k TBalanced-Budget Multipliers k BInjection-Withdrawal Approach: Equilibrium National Income Ye.

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Slide 1

﻿Straightforward Keynesian Model National Income Determination Three-Sector National Income Model

Slide 2

Outline Three-Sector Model Tax Function T = f (Y) Consumption Function C = f (Yd) Government Expenditure Function G=f(Y) Aggregate Expenditure Function E = f(Y) Output-Expenditure Approach: Equilibrium National Income Ye

Slide 3

Outline Factors influencing Ye Expenditure Multipliers k E Tax Multipliers k T Balanced-Budget Multipliers k B Injection-Withdrawal Approach: Equilibrium National Income Ye

Slide 4

Outline Fiscal Policy (v.s. Money related Policy) Recessionary Gap Yf - Ye Inflationary Gap Ye - Yf Financing the Government Budget Automatic Built-in Stabilizers

Slide 5

Three-Sector Model With the presentation of the administration division (i.e. together with family units C , firms I ), total consumption E comprises of one more segment, government use G . E = C + I + G Still, the balance condition is Planned Y = Planned E

Slide 6

Three-Sector Model Consumption capacity is decidedly identified with discretionary cashflow Yd [slide 37 of 2-area model], C = f(Yd) C= C " C= cYd C= C " + cYd

Slide 7

Three-Sector Model National Income  Personal Income  Disposable Personal Income w/coordinate pay assess Ta and exchange installment Tr Yd  Y Yd = Y - Ta + Tr

Slide 8

Three-Sector Model Transfer installment Tr can be dealt with as adverse expense, T is characterized as immediate salary impose Ta net of exchange installment Tr T = Ta - Tr Yd = Y - (Ta - Tr) Yd = Y - T

Slide 9

Three-Sector Model The presumptions for the 2-segment Keynesian model are as yet legitimate for this 3-segment show [slide 24-25 of 2-division model]

Slide 10

Tax Function T = f(Y) T = T " T = tY T = T " + tY

Slide 11

Tax Function T = T' Y-intercept=T' incline of tangent=0 T = tY Y-intercept=0 slant of tangent=t T = T' +tY Y-intercept=T' slant of tangent=t

Slide 12

Tax Function Autonomous Tax T " this is a singular amount charge which is free of wage level Y Proportional Income Tax tY minor duty rate t is a steady Progressive Income Tax tY minimal expense rate t increments Regressive Income Tax tY peripheral duty rate t diminishes

Slide 13

Consumption Function C = f(Yd) C = C " C = C " C = cYd C = c(Y - T ) C = C " + cYd C = C " + c(Y - T )

Slide 14

Consumption Function C = C " + c(Y - T ) T = T " C = C " + c(Y - T " )  C = C " - cT " + cY  slant of digression = c T = tY C = C " + c(Y - tY )  C = C " + (c - ct)Y slope of digression = c - ct T = T " + tY C = C " +c[Y-(T " +tY) ] C = C " - cT " + (c - ct) Y slope of digression = c - ct

Slide 15

Consumption Function C = C " + c (Y - T " ) Y-capture = C' - cT' slant of digression = c = MPC slant of beam APC  when Y

Slide 16

Consumption Function C = C " + c (Y - tY) Y-block = C' slant of digression = c - ct = MPC (1-t) slant of beam APC  when Y

Slide 17

Consumption Function C = C " + c [Y - (T " + tY)] Y-catch = C' - cT' slant of digression = c - ct = MPC (1-t) slant of beam APC  when Y

Slide 18

Consumption Function C = C " - c T " + (c - c t )Y C "  OR T "    y-catch C " - c T "   C move upward t   c (1-t)   C compliment c   c (1-t)  C more extreme  y-catch C " - c T "  C move descending

Slide 19

Government Expenditure Function G just incorporates the piece of government use spending on products and enterprises, i.e. exchange installments Tr are prohibited. Typically, G is thought to be an exogenous/self-sufficient capacity G = G "

Slide 20

Government Expenditure Function Y-block = G' slant of digression = 0 slant of beam  when Y

Slide 21

Aggregate Expenditure Function E = C + I + G given C = C " + cYd T = T " + tY I = I " G = G " E = C " + c[Y - (T " +tY) ] + I " + G " E = C " - cT " + I " + G " + (c-ct)Y E = E " + c(1-t) Y

Slide 22

Aggregate Expenditure Function E = C " - cT " + I " + G " + (c - ct) Y E = E " + (c - ct) Y given E " = C " - cT " + I " + G " E " is the y-catch of the total use work E c - ct is the incline of the total use work E

Slide 23

Aggregate Expenditure Function Derive the total use work E if T = T " E = C " - cT " + I " + G " + c y-capture = C " - cT " + I " + G " slant of digression = c

Slide 24

Aggregate Expenditure Function Derive the total consumption work E if T = tY E = C " + I " + G " + (c-ct ) y-block = C " + I " + G " slant of digression = (c-ct )

Slide 25

Aggregate Expenditure Function Derive the total use work E if T = T " and I = I " + iY E = C " - cT " + I " + G " + (c + i ) y-catch = C " - cT " + I " + G " slant of digression = (c + i )

Slide 26

Aggregate Expenditure Function Derive the total use work E if T = tY and I = I " +iY E = C " + I " + G " + (c - ct +i ) y-catch = C " + I " + G " slant of digression = (c - ct +i )

Slide 27

Aggregate Expenditure Function Derive the total use work E if T = T " + tY and I = I " +iY E = C " - cT " + I " + G " + (c - ct +i ) y-block = C " - cT " + I " + G " slant of digression = (c - ct +i )

Slide 28

Output-Expenditure Approach w/T = T " + tY w/C = C " + cYd C 2-Sector C = C' + cYd = C' + cY Slope of digression = c = MPC = C/Yd Slope of digression = c (1-t) = (1-t)*MPC  MPC C = C' - cT' + c(1-t)Y 3-Sector C' C' - cT' Y

Slide 29

I , G , C , E , Y Y=E Y Planned Y = Planned E

Slide 30

Output-Expenditure Approach I = I " exogenous capacity E = E " + (c - ct) Y [slide 21-22] In balance, arranged Y = arranged E Y = E " + (c - ct) Y (1-c + ct) Y = E " Y = E " E " = C " - cT " + I " + G " k E = 1 - c + ct 1 - c + ct

Slide 31

Output-Expenditure Approach I= I " +iY endogenous capacity E = E " + (c - ct + i) Y [slide 27] In harmony, arranged Y = arranged E Y = E " + (c - ct + i) Y (1-c + ct - i) Y = E " Y = E " E " = C " - cT " + I " + G " k E = 1 - c - i + ct 1 - c - i + ct

Slide 32

Output-Expenditure Approach T = T " exogenous capacity I = I " + iY E = E " + (c + i) Y [slide 25] In balance, arranged Y = arranged E Y = E " + (c + i) Y (1 - c - i) Y = E " Y = E " E " = C " - cT " + I " + G " k E = 1 - c - i 1 - c - i

Slide 33

Factors influencing Ye = k E * E " In the Keynesian model, total use E is the determinant of Ye since AS is flat and cost is unbending. In balance, arranged Y = arranged E = C " - cT " + I " + G " + (c - ct + i) Y Any change to the exogenous factors will bring about the total consumption capacity to change and thus Ye

Slide 34

Factors influencing Ye Change in E " If C "  I "  G "   E "   E  Y  If T "  C " - c T "   E "  by - c T "  E Y Change in k E/incline of digression of E If c  i   E more extreme  Y If c   C " - c T "   E "   E   Y  If t   E more extreme  Y 

Slide 35

I , G , C , E , Y Y=E Y

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I , E , Y  I'  E' = I'  I' Y  Ye = k E E'

Slide 37

G , E , Y  G' Y

Slide 38

C , E , Y  C' Y

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C , E , Y  T' C  by - cT' Y

Slide 40

I, E , Y  i Y

Slide 41

Digression Differentiation y = c + m x separate y as for x dy/dx = m

Slide 42

Expenditure Multiplier k E Y = k E * E " E " = C " - cT " + I " + G " k E = if I=I " & T=T " +tY k E = if I=I " +iY & T=T " +tY k E = if I=I " +iY & T=T " 1 - c + ct 1 - c + ct - i 1 - c - i

Slide 43

Expenditure Multiplier k E Whenever there is an adjustment in the self-governing spending C " I " or G " the national wage Ye will change by a various of k E . It really measures the proportion of the adjustment in national salary Ye to the adjustment in the self-ruling consumption E " Ye/E " = k E

Slide 44

Tax Multiplier k T Y = k E * ( C " - cT " + I " + G " ) k T = if I=I " & T=T " +tY k T = if I=I " +iY & T=T " +tY k T = if I=I " +iY & T=T " - c 1 - c + ct - c 1 - c + ct + i - c 1 - c - i

Slide 45

Tax Multiplier k T Any adjustment in the single amount duty T " will prompt to an adjustment in the national pay Ye by a different of k T the other way since k T goes up against a negative esteem Besides, the total estimation of k T is not as much as the estimation of k E .

Slide 46

Balanced-Budget Multiplier k B G "   E "   E   Ye  by k E times T "   E "   E   Ye  by k T times If G "  = T "  , the change in Ye can be measured by k B Y/G " = k E Y/T " = k T k B = k E + k T k B = + = 1-c - c 1-c

Slide 47

Balanced-Budget Multiplier k B The adjusted spending multiplier k B = 1 when t=0 & i=0 What is the estimation of k B if t  0 ? On the off chance that k B = 1 an expansion in government use of \$1 which is financed by a \$1 increment in the single amount salary charge, the national wage Ye will likewise increment by \$1

Slide 48

Injection-Withdrawal Approach In a 3-division mo