Given logical proof that the accountants have misled us and as a
simple logical matter the government budget must always
be in balance (see below), let's start at the other end!
Simply assume that G=T.
So since Y=C+I+G, we must conclude that
Y-T = C + I
Introduce (and why not?!) the behavioral assumption C = b(Y-T) and we
can conclude that
(1-b)(Y-T) = I
Now for the coup de grace.
Introduce (and why not?!) the behavioral assumption I = (1-b)(Y-T) and we have
(1-b)(Y-T) = (1-b)(Y-T)
or
0=0.
Even among the most stubborn and misguided Keynesians,
who will dare deny *this*?!  (Of course because they admit to being
Keynesians, we suspect they might try, but the force (of the argument)
is with us!)

Evidently, from simple economic foundations we have deduced
irrefutable eternal truths!  And should one of our Keynesian colleagues
try to object, we can now just say, "look at the algebra my friend".

Alan Isaac

On 8/31/2018 1:04 PM, Fred Foldvary wrote:

Steve Kates <[log in to unmask]> seeks a rebuttal to the Keynesian multiplier.



The Keynesian multiplier is 1/(1-b).

As I see it, the derivation is:

T is taxes that pay for G, government spending.
b is the portion of income Y that is spent for consumption C.
I is economic investment.

Y = C + I + G[
C = b(Y-T)
Y = bY -bT + I + G
Y-bY = I + G - bT
Y(1-b) = I + G -bT
Y=(I+G-bT)/(1-b)

That assumes constant I.
If investment I is a function of savings, then
I = (1-b)(Y-T)
Substitute into the third equation:
Y = bY -bT + (1-b)(Y-T) + G
Which concludes with
G=T

The multiplier disappears, and there is no determination of Y from 1/(1-b)

Fred Foldvary