SOLUTION: Marginal cost is the additional cost imposed by the production of one additional item. Marginal benefit is the additional benefit of producing one additional item. For a certain c
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Question 1046357: Marginal cost is the additional cost imposed by the production of one additional item. Marginal benefit is the additional benefit of producing one additional item. For a certain company, the marginal cost C, in dollars, if you are currently producing n items, is given by C(n)= 8+n, and the marginal benefit B, in dollars, is given by B(n)= 40*0.5^n. Economic efficiency occurs at the production level where marginal cost and marginal benefit are the same. What production level n gives economic efficiency for this company?
C(n)= 8 + n
B(n)= 40 * 0.5^n
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need to set the two functions equal to each other and then solve for 
. The problem with that idea is that you end up with:
\right)\ -\ 8\ln(2)}{\ln(2)})
Where \right))
is a Lambert W-Function that requires a mighty ugly Taylor Series expansion to evaluate.
On the other hand, if you graph the two functions, it looks like they intersect at the point )
.
.jpg)
And lo and behold:
And
^2\ =\ 40\left(\frac{1}{4}\right)\ =\ 10)
John
My calculator said it, I believe it, that settles it
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