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:
S=I-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).
The quotient rule is The only tricky part is remembering which of the terms in the numerator comes first.
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.