Show that for a profit-maximizing firm producing at its optimal quantity, y∗, its average total costis minimized when marginal cost is equal to average total cost. Some tips to get you started: •Say the firm’s profit function is π=py∗−c(y∗). What is average total cost? •Find the first order condition that will show when average total cost is minimized. Use thefirst order condition to arrive at the desired conclusion.

Show that for a profit-maximizing firm producing at its optimal quantity, y∗, its average total costis minimized when marginal cost is equal to average total cost. Some tips to get you started: •Say the firm’s profit function is π=py∗−c(y∗). What is average total cost? •Find the first order condition that will show when average total cost is minimized. Use thefirst order condition to arrive at the desired conclusion.

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter21: Production And Costs

Section: Chapter Questions

Problem 9WNG

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Question

Show that for a profit-maximizing firm producing at its optimal quantity, y^∗, its average total costis minimized when marginal cost is equal to average total cost. Some tips to get you started:

•Say the firm’s profit function is π=py^∗−c(y^∗). What is average total cost?

•Find the first order condition that will show when average total cost is minimized. Use thefirst order condition to arrive at the desired conclusion.

Definition Definition Total cost of producing a certain quantity of a good, divided by the quantity produced. It is the sum of all costs (fixed and variable) required to produce one unit of output.

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