Question

If a competitive firm's cost function is $C(q)=a+b q+c q^2+d q^3$, where $a, b, c$, and $d$ are constants, what is the firm's marginal cost function? What is the firm's profit-maximizing condition? (Hint: See Solved Problem 8.3.) M

Name: Problem 11, Chapter 8: Microeconomics : theory and applications with calculus
Uploaded: 2021-08-07T20:57:27-08:00
Duration: 1 min 54 s
Channel: Kaylee Mcclellan
Description: If a competitive firm's cost function is C(q)=a+b q+c q^2+d q^3, where a, b, c, and d are constants, what is the firm's marginal cost function? What is the firm's profit-maximizing condition? (Hint: See Solved Problem 8.3.) M

    If a competitive firm's cost function is $C(q)=a+b q+c q^2+d q^3$, where $a, b, c$, and $d$ are constants, what is the firm's marginal cost function? What is the firm's profit-maximizing condition? (Hint: See Solved Problem 8.3.) M

Microeconomics : theory and applications with calculus

Jeffrey M. Perloff 5th Edition

Chapter 8, Problem 11

Instant Answer

Solved by Expert Kaylee Mcclellan

08/07/2021

Step 1

The cost function is $ C(q) = a + bq + cq^2 + dq^3 $, where $ a, b, c, $ and $ d $ are constants, and $ q $ is the quantity of output produced. Show more…

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If a competitive firm's cost function is $C(q)=a+b q+c q^2+d q^3$, where $a, b, c$, and $d$ are constants, what is the firm's marginal cost function? What is the firm's profit-maximizing condition? (Hint: See Solved Problem 8.3.) M

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Key Concepts

Profit Maximization in Competitive Markets

In a perfectly competitive market, firms maximize their profit where marginal revenue equals marginal cost. Since the marginal revenue for a competitive firm is equal to the market price, the profit-maximizing condition is achieved by setting the market price equal to the marginal cost. This condition ensures that the firm is not missing out on profitable opportunities nor incurring unnecessary costs by overproducing.

Marginal Cost

Marginal cost is the additional cost incurred when an additional unit of output is produced. It is calculated by taking the derivative of the total cost function with respect to quantity. For a polynomial cost function, this means differentiating each term of the function, which gives you an expression that shows how cost changes as output increases.

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