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Stages of Production - Law of diminishing Returns

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Problem
2. A firm has following short-run production function:
Q=50L+6L^2-0.5L^3
Q=quality of output per week
L= number of worker
a. When dose the law of diminishing returns take effect?
b. Calculate the wage of the values for labor over which stage I, II, and III occurs.
C. Assume each worker is paid $10 per hour and works a 40-hours 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?

Problem
1. Indicate whether each of the following statement is true or false. Explain why.
a. when law of the diminishing returns takes effect, firm's average product will stats to decrease.
b. Decreasing returns to scale occurs when a firm has to increase all its input at an increasing rate to maintain constant rate of increase in its output.
c. A linear shot-run production function implies that the law of diminishing returns dose not take effect over the range of the output being considered.
d. Stage I of the production process ends at the point where the law of diminishing returns occurs.

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Solution Summary

Solution explains the stages of Production for a given algebric non-linear production function. Marginal Product, Average Product and their optimum values are worked out by the use of calculus.
In second part short discussion type questions are explained about Marginal Product, Average Product, Stages of Production.

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Please refer enclosed document for complete solution. As formulas and tables may not print here.

Solution

A) When dose the law of diminishing returns take effect?
Given that

Marginal Product =
For Law of diminishing returns to take Place, Marginal Product should attain maximum value i.e.

(Please refer attached file for formula and tables.)

For the Value L>4, law of diminishing return takes place.

b. Calculate the range of the values for labor over which stage I, II, and III occurs.

Average Product Function AP is given by

Stage I ends at the point at which Average Product assumes maximum value i.e.

Stage I will be for

Stage II will end at the point when Marginal Product =0

Negative value of L does not ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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