The total cost of producing a certain good is given by TC=300ln(q+30)+150. Find the marginal cost (MC) and the avarage cost (AC) functions.
Question
Solution 1
The marginal cost (MC) is the derivative of the total cost (TC) with respect to quantity (q).
First, let's find the derivative of the total cost function:
TC = 300ln(q+30) + 150
MC = d(TC)/dq = d(300ln(q+30) + 150)/dq = 300/(q+30)
So, the marginal cost function is MC = 300/(q+30).
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