Answered: A firm's production function is…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A firm's production function is characterized by the following production function: Q=L^(1/2)K^(1/4) Suppose the input prices are w = 1 and r=4 and the firm wishes to produces 8 units of output. a.What kind of returns to scale is the firm experiencing? Briefly explain b.Find the cost-minimizing input bundle using the Lagrangian method.

Expert Solution

Step 1: Determine the given information:

Production function: $Q equals L to the power of 1 divided by 2 end exponent K to the power of 1 divided by 4 end exponent$

Input price: Wage rate = 1, rent = 4.

Return to scale: "Return to scale" refers to the rate at which output increases in response to a proportional increase in all inputs. If output increases in the same proportion as input increases, then the production function is said to be a constant return to scale.

When output increases in greater proportion as input increase, then the production function is said to be increasing return to scale. Output increases in less proportion than input increase, in this case, production function is said to be decreasing return to scale.

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