Please complete the following two applied problems:
Problem 1:
William is the owner of a small pizza shop and is thinking of increasing products and lowering costs. William’s pizza shop owns four ovens and the cost of the four ovens is $1,000. Each worker is paid $500 per week.
Workers employeed Pizza Produced per week
0 0
1 75 2 180
3 360
4 600
5 900
6 1140
7 1260
8 1360
Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.
- Which inputs are fixed and which are variable in the production function of William’s pizza shop? Over what ranges do there appear to be increasing, constant, and/or diminishing returns to the number of workers employed?
- What number of workers appears to be most efficient in terms of pizza product per worker?
- What number of workers appears to minimize the marginal cost of pizza production assuming that each pizza worker is paid $500 per week?
- Why would marginal productivity decline when you hire more workers in the short run after a certain level?
- How would expanding the business affect the economies of scale? When would you have constant returns to scale or diseconomies of scale? Describe your answer.
Problem 2:
The Paradise Shoes Company has estimated its weekly TVC function from data collected over the past several months, as TVC = 3450 + 20Q + 0.008Q2 where TVC represents the total variable cost and Q represents pairs of shoes produced per week. And its demand equation is Q = 4100 – 25P. The company is currently producing 1,000 pairs of shoes weekly and is considering expanding its output to 1,200 pairs of shoes weekly. To do this, it will have to lease another shoe-making machine ($2,000 per week fixed payment until the lease period ends).
Show all of your calculations and processes. Describe your answer for each item below in complete sentences, whenever it is necessary.
- Describe and derive an expression for the marginal cost (MC) curve.
- Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).
- What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.
- Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications that underlie your recommendation.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
Total Possible Score: 7.00
1a. Describes Fixed Inputs and Variable Inputs
Total: 0.60
Distinguished – Provides a thorough description of fixed inputs and variable inputs.
Proficient – Provides a description of fixed inputs and variable inputs, but minor details are missing or inaccurate.
Basic – Provides a partial description of fixed inputs and variable inputs, but relevant details are missing or inaccurate.
Below Expectations – Provides a minimal description of fixed inputs and variable inputs, but significant details are missing or inaccurate.
Non-Performance – The description of fixed inputs and variable inputs is either nonexistent or lacks the components described in the assignment instructions.
1b. Provides a Description of What Number of Workers Appears to Be Most Efficient in Terms of Pizza Product Per Worker
Total: 0.70
Distinguished – Provides a thorough description of what number of workers appears to be most efficient in terms of pizza product per worker.
Proficient – Provides an adequate description of what number of workers appears to be most efficient in terms of pizza product per worker, but minor details are missing or inaccurate.
Basic – Provides a partial description of what number of workers appears to be most efficient in terms of pizza product per worker, but relevant details are missing or inaccurate.
Below Expectations – Attempts to provide a description of what number of workers appears to be most efficient in terms of pizza product per worker, but significant details are missing or inaccurate.
Non-Performance – The description of the most efficient production is either nonexistent or lacks the components described in the assignment instructions.
1c. Describes the Number of Workers that Minimizes the Marginal Cost (MC) of Pizza Production
Total: 0.70
Distinguished – Provides a thorough description of what number of workers appears to minimize the marginal cost (MC) of pizza production.
Proficient – Provides an adequate description of what number of workers appears to minimize the marginal cost of pizza production, but minor details are missing or inaccurate.
Basic – Provides a partial description of what number of workers appears to minimize the marginal cost (MC) of pizza production, but relevant details are missing or inaccurate.
Below Expectations – Attempts to provide a description of what number of workers appears to minimize the marginal cost of pizza production, but significant details are missing or inaccurate.
Non-Performance – The description of the number of workers that minimizes the marginal cost of pizza production is either nonexistent or lacks the components described in the assignment instructions.
1d. Describes Why Marginal Productivity Would Decline When You Hire More Workers In the Short Run After a Certain Level
Total: 0.70
Distinguished – Thoroughly describes why marginal productivity would decline when you hire more workers in the short run after a certain level.
Proficient – Describes why marginal productivity would decline when you hire more workers in the short run after a certain level, but minor details are missing.
Basic – Partially describes why marginal productivity would decline when you hire more workers in the short run after a certain level. Relevant details are missing.
Below Expectations – Attempts to describe why marginal productivity would decline when you hire more workers in the short run after a certain level; however, significant details are missing.
Non-Performance – The description of why marginal productivity would decline when you hire more workers in the short run after a certain level is either nonexistent or lacks the components described in the assignment instructions.
1e. Describes How Expanding the Business Would Affect the Economies of Scale and When There Would be Constant Returns to Scale or Diseconomies of Scale
Total: 0.70
Distinguished – Thoroughly describes how expanding the business would affect the economies of scale and when there would be constant returns to scale or diseconomies of scale.
Proficient – Describes how expanding the business would affect the economies of scale and when there would be constant returns to scale or diseconomies of scale, but minor details are missing.
Basic – Partially describes how expanding the business would affect the economies of scale and when there would be constant returns to scale or diseconomies of scale. Relevant details are missing.
Below Expectations – Attempts to describe how expanding the business would affect the economies of scale and when there would be constant returns to scale or diseconomies of scale; however, significant details are missing.
Non-Performance – The description of how expanding the business would affect the economies of scale and when you would have constant returns to scale or diseconomies of scale is either nonexistent or lacks the components described in the assignment instructions.
2a. Describes and Derives an Expression for the Marginal Cost (MC) Curve
Total: 0.75
Distinguished – Thoroughly describes and accurately derives an expression for the marginal cost (MC) curve.
Proficient – Adequately describes and derives an expression for the marginal cost (MC) curve. The calculations are mostly accurate, but minor details are missing.
Basic – Partially describes and derives an expression of the marginal cost (MC) curve. The calculations are mostly inaccurate and/or relevant details are missing.
Below Expectations – Attempts to describe and derive an expression of the marginal cost (MC) curve; however, the calculations are inaccurate and/or significant details are missing.
Non-Performance – The description and derivation of an expression of the marginal cost (MC) curve are either nonexistent or lack the components described in the assignment instructions.
2b. Describes and Estimates the Incremental Costs of the Extra 200 Pairs of Shoes Per Week
Total: 0.75
Distinguished – Thoroughly describes and accurately estimates the incremental costs of the extra 200 pairs of shoes per week (from 1,000 pairs to 1,200 pairs of shoes).
Proficient – Adequately describes and estimates the incremental costs of the extra 200 pairs of shoes per week (from 1,000 pairs to 1,200 pairs of shoes), but a few inaccuracies or minor details are missing.
Basic – Partially describes and estimate the incremental costs of the extra 200 pairs of shoes per week (from 1,000 pairs to 1,200 pairs of shoes). Several inaccuracies and/or relevant details are missing.
Below Expectations – Attempts to describe and estimate the incremental costs of the extra 200 pairs of shoes per week (from 1,000 pairs to 1,200 pairs of shoes), but numerous inaccuracies and significant details are missing.
Non-Performance – The description and estimation of the incremental costs are either nonexistent or lack the components described in the assignment instructions.
2c. Describes and Calculates the Profit-Maximizing Price and Output Levels
Total: 0.75
Distinguished – Thoroughly describes and accurately calculates the profit-maximizing price and output levels.
Proficient – Adequately describes and calculates the profit-maximizing price and output levels. A few inaccuracies in calculations or minor details are missing.
Basic – Partially describes and calculates the profit-maximizing price and output levels. Several inaccuracies in calculations and/or relevant details are missing.
Below Expectations – Attempts to describe and calculate the profit-maximizing price and output levels; however, the calculations are inaccurate and significant details are missing.
Non-Performance – The description and calculation of the profit-maximizing price and output levels are either nonexistent or lack the components described in the assignment instructions.
2d. Discusses Whether or Not Paradise Shoes Should Expand its Output Further Beyond 1,200 Pairs Per Week
Total: 0.75
Distinguished – Thoroughly discusses whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week.
Proficient – Adequately discusses whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week, but minor details are missing.
Basic – Partially discusses whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. Relevant details are missing or unclear.
Below Expectations – Attempts to discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. Significant details are missing.
Non-Performance – The discussion of Paradise Shoes’ output expansion is either nonexistent or lacks the components described in the assignment instructions.
Critical Thinking: Explanation of Issues
Total: 0.20
Distinguished – Clearly and comprehensively explains in detail the issue to be considered, delivering all relevant information necessary for a full understanding.
Proficient – Clearly explains in detail the issue to be considered, delivering enough relevant information for an adequate understanding.
Basic – Briefly recognizes the issue to be considered, delivering minimal information for a basic understanding.
Below Expectations – Briefly recognizes the issue to be considered, but may not deliver additional information necessary for a basic understanding.
Non-Performance – The assignment is either nonexistent or lacks the components described in the instructions.
Written Communication: Content Development
Total: 0.10
Distinguished – Uses appropriate, pertinent, and persuasive content to discover and develop sophisticated ideas within the context of the discipline, shaping the work as a whole.
Proficient – Uses appropriate and pertinent content to discover ideas within the context of the discipline, shaping the work as a whole.
Basic – Uses appropriate and pertinent content, but does not apply it toward discovering or developing ideas. Overall, content assists in shaping the written work.
Below Expectations – Uses content, though it may be unrelated or inappropriate to the topic. Content does not contribute toward the development of the written work, and may distract the reader from its purpose.
Non-Performance – The assignment is either nonexistent or lacks the components described in the instructions.
Written Communication: Control of Syntax and Mechanics
Total: 0.10
Distinguished – Displays meticulous comprehension and organization of syntax and mechanics, such as spelling and grammar. Written work contains no errors, and is very easy to understand.
Proficient – Displays comprehension and organization of syntax and mechanics, such as spelling and grammar. Written work contains only a few minor errors, and is mostly easy to understand.
Basic – Displays basic comprehension of syntax and mechanics, such as spelling and grammar. Written work contains a few errors, which may slightly distract the reader.
Below Expectations – Fails to display basic comprehension of syntax or mechanics, such as spelling and grammar. Written work contains major errors, which distract the reader.
Non-Performance – The assignment is either nonexistent or lacks the components described in the instructions.
Written Communication: APA Formatting
Total: 0.20
Distinguished – Accurately uses APA formatting consistently throughout the paper, title page, and reference page.
Proficient – Exhibits APA formatting throughout the paper. However, layout contains a few minor errors.
Basic – Exhibits basic knowledge of APA formatting throughout the paper. However, layout does not meet all APA requirements.
Below Expectations – Fails to exhibit basic knowledge of APA formatting. There are frequent errors, making the layout difficult to distinguish as APA.
Non-Performance – The assignment is either nonexistent or lacks the components described in the instructions.
