MHB Cost Functions for a Firm: Marginal & Average Cost

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The cost function for a firm is defined as C(x) = 300x - 10x^2 - 1/3x^3. The marginal cost function can be derived by taking the first derivative of the cost function, resulting in MC(x) = 300 - 20x - x^2. The average cost function is obtained by dividing the total cost by the output, yielding AC(x) = (300x - 10x^2 - 1/3x^3) / x. To find the output level where marginal cost equals average cost, set MC(x) equal to AC(x) and solve for x. This analysis is crucial for understanding cost management in production.
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The cost function of a firm is given by C(x) = 300x - 10x^2 - 1/3x^3.

A) Find the Marginal Cost Function

B) Average cost function

C) The output at which marginal cost is equal to average cost.
 
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