8.3 The long-run total cost function for a firm producing skateboards is TC=q^3-30q^2+350q, where q is the number of skateboards per week. a. What is the general shape of this total cost function? b. Calculate the average cost function for skateboards. What shape does the graph of this function have? At what level of skateboard output does average cost reach a minimum? What is the average cost at this level of output? c. The marginal cost function for skateboards is given by MC=3q^2-60q+350. Show that this marginal cost curve intersects average cost at its minimum value.

8.3 The long-run total cost function for a firm producing skateboards is TC=q^3-30q^2+350q, where q is the number of skateboards per week. a. What is the general shape of this total cost function? b. Calculate the average cost function for skateboards. What shape does the graph of this function have? At what level of skateboard output does average cost reach a minimum? What is the average cost at this level of output? c. The marginal cost function for skateboards is given by MC=3q^2-60q+350. Show that this marginal cost curve intersects average cost at its minimum value.

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter12: The Cost Of Production

Section: Chapter Questions

Problem 3CQQ

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Question

8.3 The long-run total cost function for a firm producing skateboards is

TC=q^3-30q^2+350q,

where q is the number of skateboards per week.

a. What is the general shape of this total cost function?

b. Calculate the average cost function for skateboards. What shape does the graph of this function have? At what level of skateboard output does average cost reach a minimum? What is the average cost at this level of output?

c. The marginal cost function for skateboards is given by

MC=3q^2-60q+350.

Show that this marginal cost curve intersects average cost at its minimum value.

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