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:
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.
(d). What is the maximum profit.
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