# Math Help - marginal propencity to consume

1. ## marginal propencity to consume

The consumption function is given by $\displaystyle \Large C \ = \ \frac{6 \cdot (2 \cdot \sqrt{I^3}+5)}{I+10}$ where $I$ is the total national income and $C$ the total national consumption, both expressed in billions of dollars.
The marginal propensity to consume is defined as the rate of change of consumption with respect to income:

$\displaystyle \Large \mbox{Marginal propensity to consume }=\frac{dC}{dI}.$
The marginal propensity to consume for the consumption function C given above when $I=100$ equals??? (billions of dollars)/(one billion of dollars of change of the income).

2. Originally Posted by pourcarlos
The consumption function is given by $\displaystyle \Large C \ = \ \frac{6 \cdot (2 \cdot \sqrt{I^3}+5)}{I+10}$ where $I$ is the total national income and $C$ the total national consumption, both expressed in billions of dollars.
The marginal propensity to consume is defined as the rate of change of consumption with respect to income:

$\displaystyle \Large \mbox{Marginal propensity to consume }=\frac{dC}{dI}.$
The marginal propensity to consume for the consumption function C given above when $I=100$ equals??? (billions of dollars)/(one billion of dollars of change of the income).
$C = 6 \cdot \frac{2 \cdot I^{\frac{3}{2}} + 5}{I+10}$

$\frac{dC}{dI} = 6 \cdot \frac{(I+10)(3 \cdot I^{\frac{1}{2}}) - (2 \cdot I^{\frac{3}{2}} + 5)(1)}{(I+10)^2}$

sub in 100 for I and evaluate

3. so therefore

6 ( 16500 - 1000005 / 12100 )

which gives me -487.6884298

however, it is telling me that this answer is wrong.....

4. Originally Posted by pourcarlos
so therefore

6 ( 16500 - 1000005 / 12100 )

which gives me -487.6884298

however, it is telling me that this answer is wrong.....
"it" is telling you the truth ... you did not evaluate the value of the derivative correctly.

put away the calculator and try it by hand.

5. im sorry, but i still dont seem to understand.....

could you please help explain the correct way to plug in 100 for I to figure out the marginal propensity to consume

6. Originally Posted by pourcarlos
im sorry, but i still dont seem to understand.....

could you please help explain the correct way to plug in 100 for I to figure out the marginal propensity to consume
You have been told what to do. Your trouble is that you haven't done the basic arithmetic properly. Substitute I = 100. Do the calculation more carefully!!