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Income Determination Models



Y=C-H


Equilibrium condition


C=a-tf>y


Consumption function


Mo




Y=a-*y-H




Y-by=a-H




Y(l-b)=a-H




y,_a+IO
~l-b




Y=^(a-Ho)




If a=0




••' Y '=I^ I0 >





b= MPC ( Marginal Propensity Consume )
— — » The multiplier = k



Exp:- If you have

Y=C-H

C=340-K).8Y,l=lo=220
then find Y : (l)Equilibrium condition
(2) the reduced form

(l)Y=340-K).8y+220
y-0.8y=560

0.2Y' = 560 ->Y'=— =2800

0.2
a+IO 340+220



(2) y= ^^ = £^^ = 2800

1/7 l-b 1-0.8



The M ultiplier :■ J^^i ^i a^jH\ &\jJlL»i\ a^jl dtij (k) jiii oi 6^



Y=C-H




AY =


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AY '= K/

If l increasing to (240) the Increasing in y'= Ay = 5(240) = 1200

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Y=C-H

C=a-H>y d ^Y d =y-T
l=lo

Y=a-H)y d -H
=a-*(y-T)-H
=a-H>y-bT-H
y-by=a-bt+ 1
Y(l-b)=a-bt+l



- a+bT+10



EXP :- T=200 , l =160 , b=0.6 , a=400



Y=400-K).6y d +160
= 560-K).6(y-T)
= 560-K).6(Y-200)
= 560-K).6Y-120

0.4Y=440



Y=C-H-K3

C=a-*y

l=lo; G=Go

Y=a-fby+l -K3o Equilibrum conction

y-by=a+lo-K3o

Y(l-b)=a+l -K3o



EXP:- Go =120 ,l =300 , b=0.8 ,a=540

Y=540+0.8y+300+120
0.2y=960



.y=^=4800



Or



1-0.8 0.2



= « ±i o ± Go + _ LAGO

1—b 1—b



1-b 1-b



AY=—AG

1-b



i 1-b v



1-0.8 0.2



Y=C-H-KJ-KX-M) (1)

X=X ^Export(x)

M=a -*iy -* Import(m)

C=a-*y d

Y d =y-T

T=ty

l=lo; G =Go

Y=a-tf>y d + lo-K3o-KX -(a -H)iy))

Y=a-*(y-T) +l -K3o+Xo-a -biy

Y=a-tf>(y-ty) + l -tf3o+Xo-a -biy

Y=a-*y-bTy +l -K3o+Xo-a -biy

y-by-fbty-fbiy =a+l -K3o+Xo-a
y(l-b-H)t-H)i) =a+l -K3o+Xo-a

' _a+IO+GO+XO-aO
"" " 1-b+bt+bl

c=a-*y

_ ■ g+IO+GO+XO-aO
~ a 1-b+bt+bl



1-b+bt+bl



M=a -H)iY

kh , u a+IO+GO+XO-aO



•M =



aO-aOfc+aOM+aOM+aM+M/0+MGO+MXO-MaO



EXP:-
Find:-Y,M ,6

Y=C-H-KJ-KX-M)

C=20-K).75Y

lo=30

Go =50

X=35

M =5-K).2Y

Y= 20-K).75Y+30+50-K35-5-0.2Y)

Y=130-K).75Y-0.2Y

Y-0.75Y-K).2Y = 130



0.45Y = 130



Y=^ =288.9

0.45



M =5+0.2(288.9)
M =62.78

C=20-K).75(288.9)
C =236.675



Y=C-H-K3+X-M

C=40-K).7Y d

M=0.2Y d

T=0.4Y

lo=100 ,G =50 ,X=70

Find :- y , c , M , f

Y =40-K).7Y d +100 +50+70-0.2y d
Y=260-K).7(y-T)-0.2(Y-T)
Y=260-K).7(Y-0.4Y)-0.2(Y-0.4Y)
Y=260-K).7Y-0.28Y-0.2Y-K).08Y
Y-0.7Y +O.28Y-K).2Y-0.08Y = 260



Y(l-0.7-K).28-K).2-0.08)=260

0.62Y=260

,.Y=^ =419.4

0.62

f =0.4(419.4) =167.76
C=40-K).7(Y-T)

=40-K).7( 419.4 -167.76)

= 216.15
M =0.2(419.4-167.76)

=0.2(251.64)
M =50.33


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