**Production Function and Labor Employment Decision**A firm produces output via the function: $ Q = L - \left(\frac{L^2}{800}\right) $, where $ Q $ is the output per week and $ L $ is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $25 per hour (wage plus fringe benefits). The firm faces the fixed selling price, $ P = $40 $.*Question: How much labor should the firm employ?*This text describes a firm's production function and provides the context needed to determine the optimal labor hours by weighing the marginal cost of labor against the fixed selling price of the output. The goal is to maximize profit. An explanation of solving such problems generally involves setting marginal revenue equal to marginal cost (i.e., using calculus to find the derivative of the production function and setting it equal to 25, the labor cost, and solving for $ L $).

Answered: A firm produces output via the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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**Production Function and Labor Employment Decision**

A firm produces output via the function: $ Q = L - \left(\frac{L^2}{800}\right) $, where $ Q $ is the output per week and $ L $ is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $25 per hour (wage plus fringe benefits). The firm faces the fixed selling price, $ P = $40 $.

*Question: How much labor should the firm employ?*

This text describes a firm's production function and provides the context needed to determine the optimal labor hours by weighing the marginal cost of labor against the fixed selling price of the output. The goal is to maximize profit. An explanation of solving such problems generally involves setting marginal revenue equal to marginal cost (i.e., using calculus to find the derivative of the production function and setting it equal to 25, the labor cost, and solving for $ L $).

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Step 1

Input cost minimization:-

According to the conception of a firm, a firm will strive to maximize profit while lowering input costs. In the near run, an organization will continue to use a variable input to reduce input costs until the input's marginal revenues product equals the input price.

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