Find the marginal average cost function.?
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I do not arrive at either of your posted candidates for the definition of the Marginal Average Cost function.
(Warning: I have not taken any financial-math courses.)
I believe that the word "marginal" can be replaced with the phrase "derivative of the".
For example, "marginal cost function" means "the derivative of the cost function".
Likewise, "marginal average cost function" means "the derivative of the average cost function."
The Average Cost function is the total cost of producing some number of units divided by the very number of units produced.
In other words, if the variable C(x) represents the Total Cost, then the Average Cost is defined by C(x) divided by x.
I'll name this function AC (as in "Average Cost").
AC(x) = C(x)/x
Then, the Marginal Average Cost function is the first derivative of AC(x).
I'll name this function MAC (as in "Marginal Average Cost").
MAC(x) = AC '(x)
So, to find the algebraic definition of function MAC(x), try first dividing the definition of C(x) by x, followed by taking the derivative of your result.
I hope that I explained all of this properly; if not, we can be confident that Denis will soon correct me.
Tell me what you get for MAC(x), and I'll compare it to my result.
As an aside, that's some pretty pricey perfume!
I can't be sure what the units are on the variable C(x), but, if it's US dollars, then the cost to produce 1,000 bottles of this smelly stuff exceeds $72 million.
That's enough to make even Elizabeth Taylor's dry 'ol mouth water.
(Warning: I have not taken any financial-math courses.)
I believe that the word "marginal" can be replaced with the phrase "derivative of the".
For example, "marginal cost function" means "the derivative of the cost function".
Likewise, "marginal average cost function" means "the derivative of the average cost function."
The Average Cost function is the total cost of producing some number of units divided by the very number of units produced.
In other words, if the variable C(x) represents the Total Cost, then the Average Cost is defined by C(x) divided by x.
I'll name this function AC (as in "Average Cost").
AC(x) = C(x)/x
Then, the Marginal Average Cost function is the first derivative of AC(x).
I'll name this function MAC (as in "Marginal Average Cost").
MAC(x) = AC '(x)
So, to find the algebraic definition of function MAC(x), try first dividing the definition of C(x) by x, followed by taking the derivative of your result.
I hope that I explained all of this properly; if not, we can be confident that Denis will soon correct me.
Tell me what you get for MAC(x), and I'll compare it to my result.
As an aside, that's some pretty pricey perfume!
I can't be sure what the units are on the variable C(x), but, if it's US dollars, then the cost to produce 1,000 bottles of this smelly stuff exceeds $72 million.
That's enough to make even Elizabeth Taylor's dry 'ol mouth water.