The consumption function is given by
c=((14squar root of I^3)-35)/(I+9)
where I is the total national income and C the total national consumption, both expressed in billions of dollars.
A)The marginal propensity to consume is defined as the rate of change of consumption with respect to income:
Marginal propensity to consume = dC/dI
The marginal propensity to consume for the consumption function C given above when I=81 equals ______(billions of dollars)/(one billion of dollars of change of the income).
B)The total national savings is defined as the difference between income I and consumption C:
The marginal propensity to save is defined as the rate of change of savings with respect to income:
Marginal propensity to save =dS/dI=1-dC/dI
The marginal propensity to save for the consumption function C given above when I=81 equals ____(billions of dollars)/(one billion of dollars of change of the income).
For that, my first Calc teacher always started differentiating a quotient by exclaiming "bottoms up!" and pretending to take a swig of beer. "Bottoms up" means you begin by bringing the bottom of the fraction ( ) up to the top (without differentiating); then you multiply by the derivative of the other one ( ), and like the product rule, you then do the reverse only subtracting rather than adding. Then remember to square the original denominator.
That's the best I can do. If someone has a good mnemonic, I'd love to hear it.