The total revenue curve of a firm is R(x) = 32·5x – 12x2 and its average cost A(x) = x² – 13x + 20 + 200; where x is the firm’s output. 30 x (a). Derive an expression, Π (x), for the firm’s profit function. [Hint: Average Cost = Total Cost quantity (Average cost)(quantity) = Total Cost Or Total Cost = (Average cost)(quantity); where, in this case, quantity is output level, x]. (b). Is the rate of change of profit increasing or decreasing when the output level of the firm is x = 10 and x = 30? (c). Determine the level of output for which profit is maximized.

The total revenue curve of a firm is R(x) = 32·5x – 12x2 and its average cost A(x) = x² – 13x + 20 + 200; where x is the firm’s output. 30 x (a). Derive an expression, Π (x), for the firm’s profit function. [Hint: Average Cost = Total Cost quantity (Average cost)(quantity) = Total Cost Or Total Cost = (Average cost)(quantity); where, in this case, quantity is output level, x]. (b). Is the rate of change of profit increasing or decreasing when the output level of the firm is x = 10 and x = 30? (c). Determine the level of output for which profit is maximized.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

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