Question

1. A firm is the only producer of a particular good. The firm's marginal revenue function is MR = 9 - q, where q denotes the quantity of the good produced by the firm. The firm's fixed costs are 12 and its average variable cost function is 1 + q/2. Find an expression for the firm's profit function, ?(q). Find the value of the production, q, which maximises the firm's profit, and hence calculate the firm's maximum profit.

Name: 1. A firm is the only producer of a particular good. The firm's marginal revenue function is MR = 9 - q, where q denotes the quantity of the good produced by the firm. The firm's fixed costs are 12 and its average variable cost function is 1 + q/2. Find an expression for the firm's profit function, ?(q). Find the value of the production, q, which maximises the firm's profit, and hence calculate the firm's maximum profit.
Uploaded: 2022-06-28T16:10:56-08:00
Duration: 3 min 36 s
Channel: Madhur L

          1. A firm is the only producer of a particular good. The firm's marginal revenue function is MR = 9 - q, where q denotes the quantity of the good produced by the firm. The firm's fixed costs are 12 and its average variable cost function is 1 + q/2. Find an expression for the firm's profit function, ?(q). Find the value of the production, q, which maximises the firm's profit, and hence calculate the firm's maximum profit.

1. A firm is the only producer of a particular good. The firm's marginal revenue function is MR = 9 - q, where q denotes the quantity of the good produced by the firm. The firm's fixed costs are 12 and its average variable cost function is 1 + q/2. Find an expression for the firm's profit function, ?(q). Find the value of the production, q, which maximises the firm's profit, and hence calculate the firm's maximum profit.

Added by Denise J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/28/2022

Step 1

Step 1: Find the firm's profit function, \( \Pi(q) \): Given revenue function: \( R(q) = 9q - q^2/2 \) Cost function: \( C(q) = q + q^2/2 + 12 \) Profit function: \( \Pi(q) = R(q) - C(q) = (9q - q^2/2) - (q + q^2/2 + 12) = 8q - 2q^2/2 - 12 \) Show more…

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1. A firm is the only producer of a particular good. The firm's marginal revenue function is MR = 9 - q, where q denotes the quantity of the good produced by the firm. The firm's fixed costs are 12 and its average variable cost function is 1 + q/2. Find an expression for the firm's profit function, ̠(q). Find the value of the production, q, which maximises the firm's profit, and hence calculate the firm's maximum profit.