# Thread: At a loss - finding the formula

1. ## At a loss - finding the formula

There are two parts to this one. I actually plotted and created my own a table to organize the data to find the slope of the linear function. They call this function marginal propensity to consume.
from the book the table looks like this
year 1990 1997
total consumption(C) 3839 5494
National income(I) 6650 4215

my table is
year I C
1990 6650 3839
1997 4215 5494
I plotted I on the X axis and C on the Y.
I saw the line went from right to left meaning I should find a negative slope
I subtracted the change in both categories to come up with m= 1655/-2435 or -.67967.
That is the long answer to part b I believe.

Part a I am totally at a loss.
Find the formula for C as a function of I.
c(i) = i -c ? how does year get input into the formula? Been looking at this for days and still stuck.

2. You have a point and the slope. You can make an equation as long as it is linear:

$\displaystyle \text{Point 0} = (6650, 3839)$

$\displaystyle \text{Slope} = -\frac{1655}{2435}$

Where the point is of the form:

$\displaystyle (I, C(I))$

And:

$\displaystyle y = C(I)$

Now, we use point slope form:

$\displaystyle (y - y_0) = m(I - I_0)$

Now, we plug in what we know:

$\displaystyle (y - 3839) = -\frac{1655}{2435}(I - 6650)$

$\displaystyle C(I) - 3839 = -\frac{1655}{2435}I + 4520$

$\displaystyle C(I) = -\frac{1655}{2435}I + 8359$

Now, we just try to generate the NEXT point that you have given:

$\displaystyle C(4215) = -\frac{1655}{2435}(4215) + 8359$

$\displaystyle C(4215) = -2864.8152 + 8359$

$\displaystyle C(4215) = 5494.18 \approx 5494$

Therefore the formula stands.

There you go.

3. ## still shakey

OK I see I should have pulled up using the point-slope formula.
I am having trouble seeing (I must be blind).
where did you come up with 4520?
I am racking my pea brain to find it. I think I am too old for this stuff.
Thanks

4. I got the 4520 from:

$\displaystyle -\frac{1655}{2435}*-6650$

It actually yields 4519 point something, but rounding up doesn't change it's validity by much.