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Given that the total cost of a firm is C(q)= 60q- 12q^2+ q^3Derive an expression for marginal cost Derive an expression for average cost At what level of output is average cost minimum? Verify that at the same level of output at which average cost is minimum, average cost is equal to marginal cost.  

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The total cost of a firm is C(q)= 60q - 12q^2 + q^3

The marginal cost is C'(q) = 60 - 24q + 3q^2

The average cost is C(q)/q = (60q - 12q^2 + q^3)/q = 60 - 12q + q^2

The derivative of 60 - 12q + q^2 is -12 + 2q

The average cost is minimum when -12 + 2q = 0

=> q = 6

At q = 6, the average cost is 60 - 12*6 + 6^2 = 24 and the marginal cost is equal to 60 - 24*6 + 3*6^2 = 24.

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