The Multiplier

In general algebraic terms, the formula for the solution is

7. Y = (a+I)

Notice how important it is that the marginal propensity to consume, b, is less than one -- that Keynes' "psychological law" holds true. If the marginal propensity to consume were greater than one, (1-MPC) would be negative, and the solution would then be a negative equilibrium income -- which doesn't make much sense!

The term

is called "the multiplier." In our numerical example, the multiplier is

1/0.3 = 3.333...

It will turn out that there are some other multipliers, although this is the most general one. When we need to be specific,

is also, more precisely, called "the autonomous expenditure multiplier," since (a+I) is called "autonomous expenditure,"

Multiplier: The "multiplier," also known as the "autonomous expenditure multiplier," is computed as one divided by one minus the marginal propensity to consume. In a simple Keynesian model, we may obtain the equilibrium income by multiplying the sum of all autonomous spending by "the multiplier."

(A reminder: since we have written the consumption function as C = a + bY, b is the marginal propensity to consume, and it is equally correct to write the multiplier as

in our context).