A firm has the following short-run production function: Q = 50L+6L2 -0.5L3 where Q = Quantity of output per week L = Labor (number of workers) a. When does the law of diminishing returns take effect?
A firm has the following short-run production function: Q = 50L+6L2 -0.5L3 where Q = Quantity of output per week L = Labor (number of workers) a. When does the law of diminishing returns take effect?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![A firm has the following short-run production function:
\[ Q = 50L + 6L^2 - 0.5L^3 \]
where
- \( Q = \) Quantity of output per week
- \( L = \) Labor (number of workers)
**a.** When does the law of diminishing returns take effect?
**b.** Calculate the range of values for labor over which Stages I, II, and III occur.
**c.** Assume each worker is paid $10 per hour and works a 40-hour week. How many workers should the firm hire if the price of the output is $10? Suppose the price of the output falls to $7.50. What do you think would be the short-run impact on the firm’s production? The long-run impact?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62273c70-b248-4b75-84ee-5ee5c83ce6ef%2F48e2bcec-63bc-4d8e-af1c-3e60c9e8bbd3%2F4qtpbah_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A firm has the following short-run production function:
\[ Q = 50L + 6L^2 - 0.5L^3 \]
where
- \( Q = \) Quantity of output per week
- \( L = \) Labor (number of workers)
**a.** When does the law of diminishing returns take effect?
**b.** Calculate the range of values for labor over which Stages I, II, and III occur.
**c.** Assume each worker is paid $10 per hour and works a 40-hour week. How many workers should the firm hire if the price of the output is $10? Suppose the price of the output falls to $7.50. What do you think would be the short-run impact on the firm’s production? The long-run impact?
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