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Given a total cost function of TC = 120 + 2Q^2 determine the marginal cost function...

Given a total cost function of TC = 120 + 2Q^2 determine the marginal cost function which is obtained by differentiating the total cost function. What will be the total cost and marginal cost at an output of 10 units?

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Answer #1

The total cost function is as follows -

TC = 120 + 2Q2

Determine the marginal cost function -

MC = dTC/dQ

MC = d(120 + 2Q2)/dQ

MC = 4Q

The marginal cost function is 4Q.

Calculate the total cost when output is 10 units -

Total cost = 120 + 2Q2 = 120 + [2 * (10)2] = 120 + 200 = 320

Thus,

The total cost when output is 10 units is $320.

Calculate the marginal cost when 10 units are produced -

MC = 4Q = 4 * 10 = 40

Thus,

The marginal cost when 10 units are produced is $40.

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