Given  that total cost of a firm is  C(q)=60q-12q^2  + q^3.   At what level of output is average cost minimum ?

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The total cost of a firm is given in terms of the output q is C(q) = 60q - 12q^2 + q^3.

The average cost is the ratio of the total cost to the output. A = C(q)/q = (60q - 12q^2 + q^3)/q = 60 - 12q + q^2

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The total cost of a firm is given in terms of the output q is C(q) = 60q - 12q^2 + q^3.

The average cost is the ratio of the total cost to the output. A = C(q)/q = (60q - 12q^2 + q^3)/q = 60 - 12q + q^2

To determine the level of output at which the average cost is lowest solve A' = 0

A' = -12 + 2q

-12 + 2q = 0

=> q = 6

At an output of 6, the average cost is the minimum.

Approved by eNotes Editorial Team