Consider a firm operating in a perfectly competitive market with the following production function:\[ f(x_1, x_2) = \frac{1}{2} x_1^{\frac{1}{2}} x_2^{\frac{1}{2}} \]In the short run, $ x_2 $ is fixed at 1 - the firm cannot increase or decrease its amount of this input, and must pay for this 1 unit of $ x_2 $ regardless of what production decision it makes.(a) Suppose that $ p $, the price of the firm’s output, is 1, and the input prices are $ w_1 = 1 $ and $ w_2 = 10 $. Calculate the firm’s profit maximizing choice of $ x_1 $ and output.(b) Calculate the firm’s profit-maximizing level of profit using your answers in part (a). You should see that the firm is making losses at its optimal choice of input and output. Explain in one sentence why the firm chooses to produce a positive output despite making losses.

perfectly competitive market can be defined where all firms sell an identical product, all firms are…

(b) Calculate the firm's profit-maximising level o profit using your answers in part (a). You should see that the firm is making losses at its optimal choice of input and output. Explain in one sentence why the firm chooses to produce a positive output despite making losses.

(b) Calculate the firm's profit-maximising level o profit using your answers in part (a). You should see that the firm is making losses at its optimal choice of input and output. Explain in one sentence why the firm chooses to produce a positive output despite making losses.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider a firm operating in a perfectly competitive market with the following production function:

\[ f(x_1, x_2) = \frac{1}{2} x_1^{\frac{1}{2}} x_2^{\frac{1}{2}} \]

In the short run, $ x_2 $ is fixed at 1 - the firm cannot increase or decrease its amount of this input, and must pay for this 1 unit of $ x_2 $ regardless of what production decision it makes.

(a) Suppose that $ p $, the price of the firm’s output, is 1, and the input prices are $ w_1 = 1 $ and $ w_2 = 10 $. Calculate the firm’s profit maximizing choice of $ x_1 $ and output.

(b) Calculate the firm’s profit-maximizing level of profit using your answers in part (a). You should see that the firm is making losses at its optimal choice of input and output. Explain in one sentence why the firm chooses to produce a positive output despite making losses.

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