Question

Show that Keynes’ multiplier is the reciprocal of MPS.

Answer 1

Keynes’ investment multiplier explains how an initial increase in investment leads to a multiplied increase in income. It is mathematically expressed as:

Multiplier (K) = `1/(1-"MPC")`

MPC + MPS = 1

K = `1/"MPS"`

This proves that Keynes’ multiplier is the reciprocal of the Marginal Propensity to Save (MPS). So, if MPS = 0.2, the multiplier will be:

K  = `1/0.2`

K  = 5

Thus, the smaller the MPS, the larger the multiplier, and vice versa.