The total revenue curve of a firm is R(q) = 40q-12q2 and its average cost A(q) = 1/30 q2 – 12.85q+20+400/q, where q is the firm’s output. Derive an expression C(q) for the firm’s total cost function.Derive an expression (q) for the firm’s profit function.Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units?Determine the level of output for which the firm’s profit is maximized.What is the firm’s maximum profit?

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Description: The total revenue curve of a firm is R(q) = 40q-12q2 and its average cost A(q) = 1/30 q2 – 12.85q+20+400/q, where q is the firm’s output. Derive an expression C(q) for the firm’s total cost function.Derive an expression (q) for the firm’s p

The total revenue curve of a firm is R(q) = 40q – 12q2 Average cost A(q) = (1/30) q2 -12.85q + 20…

Answered: The total revenue curve of a firm is…

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Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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The total revenue curve of a firm is R(q) = 40q-12q² and its average cost A(q) = 1/30 q² – 12.85q+20+400/q, where q is the firm’s output.

Derive an expression C(q) for the firm’s total cost function.

Derive an expression (q) for the firm’s profit function.

Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units?

Determine the level of output for which the firm’s profit is maximized.
What is the firm’s maximum profit?

Expert Solution

Step 1

The total revenue curve of a firm is R(q) = 40q – 12q²

Average cost A(q) = (1/30) q² -12.85q + 20 + 400/q, q is the firms output.

Firm’s total cost function:

Step 2

Part (i):

Firm’s profit function:

Step 3

The rate change of the profit increasing or decreasing at q =10

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