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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

The total cost of producing a certain good is given by

TC=300ln⁡(q+30)+150. TC = 300 \ln(q + 30) + 150.

Find the marginal cost (MC)
and the average cost (AC) functions.

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Solution

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).

Next, let's find the average cost (AC). The average cost is the total cost (TC) divided by the quantity (q):

AC = TC/q = (300ln(q+30) + 150)/q

So, the average cost function is AC = (300ln(q+30) + 150)/q.

This problem has been solved

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