The total revenue curve of a firm is R(q) = 40q − 12q2  and itsaverage cost A(q) = 1/30 q2 − 12.85q + 20 +400q i. Derive an expression C(q) for the firm's total cost function.ii. Derive an expression Π(q) for the firmᇱs profit function. iii. Is the rate of change of profit increasing or decreasing when theouput level of the firm is 10 units?

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
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 − 12qand its
average cost A(q) = 1/30 q2 − 12.85q + 20 +400q

i. Derive an expression C(q) for the firm's total cost function.
ii. Derive an expression Π(q) for the firmᇱs profit function.

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

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