Please provide DETAILED, CLEAR step by step EXPLANATION on how one find the answer. This is will intensely help me understand this problem. Please answer iv and v. (b) A firm has an average cost function125 q-4.16A(q) :where q is the firm's output.(i) Determine the level of output for average costs are minimum.(ii) Hence determine the range of values for which average costs are decreasing.(iii) What part of the decreasing range is practically feasible?(iv) Write an equation for the total cost function.(v) Hence calculate the level of output for which total costs are minimum.

Given: Average cost function is: Aq=125q+q216−4 Where q is firm's input For part iv: To find the…

Answered: Please answer iv and v

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please provide DETAILED, CLEAR step by step EXPLANATION on how one find the answer. This is will intensely help me understand this problem. Please answer iv and v.

(b) A firm has an average cost function
125 q-
4.
16
A(q) :
where q is the firm's output.
(i) Determine the level of output for average costs are minimum.
(ii) Hence determine the range of values for which average costs are decreasing.
(iii) What part of the decreasing range is practically feasible?
(iv) Write an equation for the total cost function.
(v) Hence calculate the level of output for which total costs are minimum.

Expert Solution

Step 1

Given:

Average cost function is:

$A (q) = \frac{125}{q} + \frac{q^{2}}{16} - 4$

Where q is firm's input

For part iv:

To find the total cost function.

Step 2

The total cost function, C(q), is find as:

$\begin{matrix} C (q) = q \times A (q) \\ = q (\frac{125}{q} + \frac{q^{2}}{16} - 4) \\ = 125 + \frac{q^{3}}{16} - 4 q \\ C (q) = 125 + \frac{q^{3}}{16} - 4 q \end{matrix}$

Thus, total cost function is:

$C (q) = 125 + \frac{q^{3}}{16} - 4 q$

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