1. ## Business calc/applications. Marginal costs and such.

alright problem #1

If a question gives you the MC (marginal cost) function c'(q), and asks you to find the cost to increase production from a to b units, then is it simply c'(b) - c' (a)? or do we need to know the TC (Total cost) function for this?

problem #2

If and investment increases by 500% over a 15 year period under a constant periodic interest rate of r% monthly, the annual interest rate is approximately...

a) 10.78 %
b) 11.32 %
c) 12.69 %
d) 12.00 %

Um, so here i am not sure whether this question is pertaining to interest compounded continuously or compound interest. I tried using the compound interest formula for this, it should start off like this i think:

5P = P(1+r/180)^180
5 = (1+r/180)^180
180 sqrt 5 = 1 + r/180
(180 sqrt 5 - 1) x 180 = r

Cant seem to get the right answer though...

2. ## Business calc/applications. Marginal costs and such.

1. I think you need to integrate the MC function to determine the total cost (TC) function. Then your answer should be TC(b) - TC(a). The marginal costs are per-unit costs; you seemed like you wanted the total cost change.

2. If the amount increases by 500%, it means you're going to end up with 600% of what you started with. So I think the formula you want is:
(1+r/12)^180 = 6, which, if I did the math right, works out to about 12.0% for r. (You want to divide r by 12, not 180, because it's an annual interest rate compounded monthly.)

- Steve J

3. Originally Posted by Steve_J
1. I think you need to integrate the MC function to determine the total cost (TC) function. Then your answer should be TC(b) - TC(a). The marginal costs are per-unit costs; you seemed like you wanted the total cost change.

2. If the amount increases by 500%, it means you're going to end up with 600% of what you started with. So I think the formula you want is:
(1+r/12)^180 = 6, which, if I did the math right, works out to about 12.0% for r. (You want to divide r by 12, not 180, because it's an annual interest rate compounded monthly.)

- Steve J
Thx for that

But just wondering, why does a 500% increase yield a 6x increase?

4. ## Business calc/applications. Marginal costs and such.

It doesn't. If you start (for example) with $100, and you increase it by 500%, you're adding$500, which leaves you with a total of \$600. Hence the 6 instead of the 5. You're working with the total sum of money available, not the incremental increase.

- Steve J