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

  • Derive 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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    Expert Answers

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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...

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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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