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Case Study Calculations: Deep Creek Mining Company et. al.

See the attached file "Problem 1"

Problem 1:

A) Emco Company has an assembly line where total output is a function of the number of workers (crew size) as shown in the following schedule (see attached file).
Calculate the Marginal Product of Labor (MPL) and Average Product of Labor (APL) for each crew size from one-to-eight and put the result in the appropriate blank.

B) Use the data from the Deep Creek Mining Company. Assume that capital is fixed at one piece of capital equipment at a 500-bhp rating. Complete the following table:

Labor Input L (number of workers) Total Product of Labor TPL (=Q) Marginal Product of Labor MPL Average Product of Labor APL
1 __________ __________ __________
2 __________ __________ __________
3 __________ __________ __________
4 __________ __________ __________
5 __________ __________ __________
6 __________ __________ __________
7 __________ __________ __________
8 __________ __________ __________
9 __________ __________ __________
10 __________ __________ __________

C) Plot (graph) the Total Product, Marginal Product of Labor and Average Product of Labor curves using the data in Problem B.

D) Using the data in Problem B and the graph in Problem C, determine the boundaries of the three stages of production.
Stage 1: __________________ Stage 2: ________________ Stage 3: ______________

E) Use your knowledge of the relationships among various production functions to complete the blanks in the following table:

Variable Input L Total Product TPL (=Q) Average Product of Labor APL Marginal Product of Labor MPL
0 0 n/a n/a
1 __________ __________ 8
2 28 __________ __________
3 __________ 18 __________
4 __________ __________ 26
5 __________ 20 __________
6 108 __________ __________
7 __________ __________ -10

F) At present Able Corporation has (in relative terms):
Marginal Product of Labor = 30
Total Cost of Labor = 15
Marginal Product of Capital = 60
Total Cost of Capital = 20.

1. Is Able Corporation currently operating at its lowest possible cost? _____________
2. Why, or why not? _____________________________________________________
To achieve the Equimarginal Criterion, Able Corporation would have to:
3. Raise / Lower (delete one) the Relative Total Cost of Labor to: ________________
4. Raise / Lower (delete one) the Relative Total Cost of Capital to: _______________
5. Once done the MPL/CL would be: __________ and the MPK/CK would be: _____________

Attachments

Solution Preview

A.
See the attached file "MPL & APL" for the calculations and the graph.

Stages of production:
Stage 1: crew sizes 0-2 (MPL>APL)
Stage 2: crew sizes 3-7 (MPL<APL, MPL>0)
Stage 3: crew sizes 8 and up (MPL<0)

B, C.
See the attached file ...

Solution Summary

This solution shows how to use cost-benefit analysis to find the optimal course of action in several case studies. Topics covered include:

1. Marginal products of labor and capital
2. Graphing production data
3. Identifying the stages of production
4. Minimizing costs
4. The equimarginal criterion

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