A firm uses a single input to produce its output, which is sold in a competitive market.It gets quantity discounts on purchases of its input.If it buys x units of the input, the price it must pay per unit of input is 25/x + 4.If it buys no inputs, it doesn't have to pay anything.The firm's production function is f(x)= 60x - x².If the price of the firm's output is 1, the profit-maximizing amount of input to buy is

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Quizplus · Accepted Answer

To find the profit-maximizing amount of input, we need to maximize the profit function, which is revenue minus cost. The revenue is given by the production function f(x) = 60x - x^2, and the cost is the input price times the quantity, which is (25/x + 4)x = 25 + 4x. The profit function is then (60x - x^2) - (25 + 4x). Simplifying and taking the derivative to find the maximum, we get the optimal input x = 28.

A Firm Uses a Single Input to Produce Its Output