What is a Keynesian multiplier?
The Keynesian multiplier derives from the observation that all spending is also income, and therefore in theory, all spending generates additional income beyond the initial spending.
The multiplier effect applies to both government spending and government tax cuts. Both of these government actions effectively increase disposable income for consumers and firms.
In the case of an increase in government spending, the multiplier is:
where MPC is the marginal propensity to consume (referring to how much of each additional dollar the average consumer will spend vs. save).
You can see from the expression for the multiplier, that as the MPC increases, the multiplier increases as well. In fact, the multiplier is theoretically infinite if the MPC = 1. This would mean that every household immediately spends every dollar of income. Even though this possibility seems entirely theoretical, I like to imagine just how fast we would spend money if every single household spent every single dollar of income, immediately upon receiving it. We would indeed have an economy with infinitely high velocity of money.
In practice, observed multipliers are much, much lower than infinity and in fact often lower than we might expect with a typical MPC based on observed national savings rates of around 10% or less. This would imply a spending multiplier of about 10 (1/.1), and I don't think we often (if ever) observe multiplier effects that high.
In the case of tax cuts, the multiplier is:
which you should be able to see will always be lower than the spending multiplier, unless MPC=1, which would again make it infinite.
You should also note that some political ideologies won't like the conclusion that the stimulus impact of a tax cut is lower than the stimulus impact of a spending increase. Within the field of economics, we can also find plenty of economists who think that Keynes and his disciples have not completely considered the impact that spending increases have on expectations of future government spending, as well as the positive impact that tax cuts might have on expectations of future government spending.