Design a study of a production function for a steel mill and another one for a call center, which variables would you use, and what statistical method would you select for each function?

Part 1-Analytical Report

Write a short analytical report (3 – 4 pages) on two topics: shortages / scarcity and point elasticity / arc elasticity and specifically address the following points:

1. Design a study of a production function for a steel mill and another one for a call center, which variables would you use, and what statistical method would you select for each function? In general, compare and contrast the production function for a product and one for a service center.
2. Comment briefly on the following methods of cost estimation:
   1. Engineering cost
   2. Survivorship principle

Part2 – Quantitative Analysis Case

Write a Quantitative Analysis report on the following problems:

1. The owner of a car wash is trying to decide on the number of people to employ based on the following short-run production function:   Q = 6L – 0.5L2
         Where Q = Number of car washers per hour L = Number of workers
   1. Generate a schedule showing total product, average product, and marginal product, Plot this schedule on a graph.
   2. Suppose the price of basic car wash (no undercoating, no waxing treatment, etc) in his area of business is $5. How many people should he hire if he pays each worker $6/hour?
   3. Suppose he considers hiring students on a part-time base for $4/hour. Do you think he should hire more workers at this lower rate? Explain.
2. You are given the following cost functions:
         TC = 100 + 60Q – 3Q2 + .1Q3
         TC = 100 +60Q + 3Q2
         TC = 100 + 60Q
   1. Compute the average variable cost, average cost, and marginal cost for each function. Plot them on a graph.
   2. In each case, indicate the point at which diminishing returns occur. Also indicate the point of maximum cost efficiency (i.e. the point of minimum average cost). Is this company operating in stage II?
   3. For each function, discuss the relationship between marginal cost and average variable cost and between marginal cost and average cost. Also discuss the relationship between average variable cost and average cost.

Below is a recommended outline.

1. Cover page (See APA Sample paper)
2. Introduction
   1. Purpose of paper
   2. Thesis sentence
3. Body (Cite sources using in-text citations.)
   1. Main point 1
      1. Example or evidence
      2. Evidence (support from the literature)
      3. Student’s original thoughts and ideas about the section’s content and a concluding thought
   2. Main point 2
      1. Example or evidence
      2. Evidence (support from the literature)
      3. Student’s original thoughts and ideas about the section’s content and a concluding thought
   3. Main point 3
      1. Example or evidence
      2. Evidence (support from the literature)
      3. Student’s original thoughts and ideas about the section’s content and a concluding thought
4. Conclusion – Summary of main points
   1. Lessons Learned and Recommendations as needed

 

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