Suppose a firm\'s Total Cost Function is: TC = 4Q^2 + 12Q +30. Identify: 1.) Fix

Question

Suppose a firm's Total Cost Function is: TC = 4Q^2 + 12Q +30. Identify: 1.) Fixed Cost 2.) Variable Cost 3.) Marginal Cost 4.) Average Fixed Cost 5.) Average Total Cost 6.) The quantity where AVC is at its minimum 7.) The Quantity where ATC is at its minimum
I'm having a lot of trouble calculating number 6 and 7. Any help would be greatly appreciated!! Suppose a firm's Total Cost Function is: TC = 4Q^2 + 12Q +30. Identify: 1.) Fixed Cost 2.) Variable Cost 3.) Marginal Cost 4.) Average Fixed Cost 5.) Average Total Cost 6.) The quantity where AVC is at its minimum 7.) The Quantity where ATC is at its minimum
I'm having a lot of trouble calculating number 6 and 7. Any help would be greatly appreciated!! TC = 4Q^2 + 12Q +30. Identify: 1.) Fixed Cost 2.) Variable Cost 3.) Marginal Cost 4.) Average Fixed Cost 5.) Average Total Cost 6.) The quantity where AVC is at its minimum 7.) The Quantity where ATC is at its minimum Identify: 1.) Fixed Cost 2.) Variable Cost 3.) Marginal Cost 4.) Average Fixed Cost 5.) Average Total Cost 6.) The quantity where AVC is at its minimum 7.) The Quantity where ATC is at its minimum
I'm having a lot of trouble calculating number 6 and 7. Any help would be greatly appreciated!!

Explanation / Answer

TC = 4Q^2 + 12Q+30

1) Fixed cost = 30 which is the constant number.

2) variable cost = 4Q^2 + 12Q as cost increases with the quanity

3) Marginal cost = 8Q + 12 WHICH IS NOTHING BUT DERIVATIVE OF THE TOTAL COSTS

4) AVERAGE FIXED COST = 30/Q (which is fixed cost divided by the Q)

5) AVERAGE TOTAL COST = (4Q^2 + 12Q + 30) / Q (WHICH IS TOTAL COST DIVIDED BY Q)

6) AVC cost will be minimzed at quanity 0.

7) MC cuts ATC at the minimum

so MC=ATC

8Q + 12 = (4Q^2 + 12Q + 30)/Q

8Q^2 + 12Q = 4Q^2 + 12Q + 30

4Q^2 =30

Q^2 = 7.5

Q = 2.74 units

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