What is the relationship between the marginal propensity to consume and the marginal propensity to save, and how do they affect GDP?
Marginal propensity to consume (MPC) is the fraction of the extra income that if earned by a person is likely to be consumed. The marginal propensity to save is the fraction of the extra income earned that is likely to be saved.
As an example, if a person who normally earns $10,000 per month gets an extra bonus of $2000 in January. And $1600 out of the $2000 is consumed, the MPC is equal to 1600/2000 = 0.8. The marginal propensity to save (MPS) is equal to 1 – MPC or 1 - 0.8 = 0.2 in this case.
Now GDP in its standard use in economics is the sum of private consumption (C), gross investment (I), government spending (G) and net exports (X). If any of these terms increases we see an increase in GDP equal to the initial GDP multiplied by 1/ (1-MPC) or 1/MPS. So a larger propensity to consume increases GDP to a larger extent for the same change in either of C, I, G or X.