Define multiplier. What is the relation between marginal propensity to consume and multiplier?

Multiplier is the ratio between increase in income and increase in investment. It explains how many times is income increased by increasing the investment. Multiplier (k) = Change in income / change in investment. There exists a direct relationship between MPC and the value of multiplier. Higher the MPC, more will be the value of multiplier, and vice-versa. One person’s expenditure is another person’s income. So increase in consumption results into increase in income. People spend a part of this increased income on consumption which depends on the value of MPC. K = 1 / (1-MPC). Therefore, if K = 4, MPC = 3/4 or 0.75