Investment multiplier refers to the number of time by which the increase in output or income exceeds the increase in investment. It is measured as the ratio between change in income and change in investment and it is denoted as 'k'.
Marginal Propensity to consume refers to the percentage change in consumption for every one rupee of change in the income. It is the ratio between the change in income and corresponding change in consumption.
Multiplier(K) = 1/ (1- MPC) = 1 / (1 - Change in consumption/ change in income)
= change in income/ change in income- change in consumption
= change in income/ change in savings
= change in income/ change in investment
For example, If MPC= 0.8 then
Multiplier(K) = 1/ (1- 0.8) = 1 / (1 - 8/ 10)
= 10/ 10- 8
= 10/ 2 = change in income/ change in investment
= 5 times
Therefore, Change in income = 10 and change in investment = 2