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A firm has a short-run cost curve C(Q) = 60 + 2Q + 0.05Q^2. At what value of Q is average cost minimized?

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Final answer:

There is no value of Q at which the average cost is minimized for this cost function.

Step-by-step explanation:

In order to find the value of Q at which average cost is minimized, we need to differentiate the cost function with respect to Q and set it equal to zero.

The average cost can be derived from the cost function by dividing C(Q) by Q. So, we have:

AC(Q) = (60 + 2Q + 0.05Q^2) / Q

To find the minimum, we differentiate AC(Q) with respect to Q:

d(AC(Q))/dQ = (2 + 0.1Q - 1) / Q^2 = 0

Setting the derivative equal to zero and solving for Q:

2 + 0.1Q - 1 = 0

0.1Q = -1

Q = -10

However, since we are dealing with quantities, a negative value for Q does not make sense in this context.

Therefore, there is no value of Q at which average cost is minimized for this cost function.

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