For a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and Average Total Cost (ATC) are given as follows: Marginal Cost (MC) = C'(0) Average Total Cost (ATC) = C(Q)/Q Prove that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at its minimum value. (Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization. Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
For a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and Average Total Cost (ATC) are given as follows: Marginal Cost (MC) = C'(0) Average Total Cost (ATC) = C(Q)/Q Prove that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at its minimum value. (Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization. Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
Chapter6: Proudction Costs
Section: Chapter Questions
Problem 8SQ
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For a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and
Total Cost
Marginal Cost (MC) = C'(0)
Average Total Cost (ATC) = C(Q)/Q
Prove that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at its
minimum value.
(Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization.
Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
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