Keynsian multipliers

In a closed economy, savings = investment; if someone has a marginal propensity to consume of 70%, that's a marginal propensity to save of 30%, so if you give them an exogenous windfall, 30% of that feeds back into GDP through investment, giving them that extra 30% in income, which then becomes another 9% of the original sum, so that you get a multiplier of 10/7. Of course, the multiplier effect is hampered by the fact that so much leaks out through the consumption channel instead; as marginal propensity to consume goes up, this only gets worse.