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'.
Multiplier(k) => Change in income / change in investment = 1/ {1-MPC(c)} where c is the marginal propensity to consume.
If MPC = 1, then
Multiplier(k)= 1/(1-1)= 1/0 = Infinity.
Therefore, the value of the multiplier is infinity.