
S:
saving (S = a + (1b) (YT), where a and b are parametric)
T: taxes (modeled as a lumpsum tax) I: investment spending (Shifts of the curve can swamp movements along it.) G: government spending (a policy tool used to offset shifts in investment spending) Mtrans transactions demand for money (in accordance with the equation of exchange) Mspec speculative demand for money (based on expected movements in the interest rate) i: the interest rate (monetary phenomenon for Keynes; real phenomenon for the classicals) Y: income (which moves in lockstep with labor income and is a measure of output) 
ISLM analysis builds upon the simple Keynesian IncomeExpenditure
relationships
by adding interestrate considerations. Using this analysis, we see
that
the multiplier effect is sometimes not as great as the simple
multipliers
imply, owing to a change in the rate of interest and hence a movement
along
the demand for investment funds.
In a number of applications, however, the simple
multipliers do apply. That is, DY = [1/(1
 b)] DI; DY = [1/(1
 b)] DG; or DY
=
[1/(1  b)] DE_{o},
where DE_{o} is the net change (DG
 DI) in autonomous expenditures.
Examples of conditions or instances in which the simple Keyneisan spending multiplier applies include:
1. An economy mired in the liquidity trap, in which case the
interest
rate does not change.
2. An economy with a perfectly inelastic demand for investment funds,
in
which case the changing interest rate has no effect on investment.
3. An instance where fiscal policy is fully accommodated by monetary
policy, in which case any movement in the rate of interest is arrested
by a suitable adjustment in the supply of money.
4. An instance where the initial round of spending is preadjusted
for the expected "crowding out" of investment. This is the application,
mentioned above, where the simple multiplier is applied to the net
change
in autonomous expenditures.
5. An instances where the issue is the extent of the shift of the IS
curve in response to a given shift in investment demand or increase in
government spending. Of course, the increase in income, DY,
may not be as great as the actual shift in IS, owing the interestrate
effect on investment.
6. An instance where an increase in the money supply lowers the
interest
rate and stimulates investment. Here, the DY
(associated with a movement along the unshifted IS curve) is related to
the DI (associated with a movement along
the
unshifted investment demand curve) by the simple Keynesian spending
multiplier.
A similar list could be compiled to identify the conditions or instances in which the simple Keynesian tax multiplier applies.
The question "Can I use the simple Keynesian multiplier to calculate the effect of X on income" resolves itself into a sequence of subsidiary questions:
1. Does X affect the interest rate?
If no, then use the simple Keynesian multiplier.
If yes, then go on to question 2.
2. Does the change in the interest rate affect investment?
If no, then use the simple Keynesian multiplier.
If yes, then go on to question 3.
3. Is the interestrateinduced change in investment taken into
account?
If yes, then use the simple Keynesian multiplier.