Chapter 15, Problem 28P

1 a.

To determine

Ascertain the productivity profile for 20x1 using actual inputs.

Explanation of Solution

Productivity measurement: The productivity measurement refers to the quantitative assessment of the changes in the productivity.

Profile measurement and analysis: The profile measurement and analysis refers to the computation of a set of operational partial productivity measures and their comparison to the corresponding set of base period, for the assessment of the nature of changes in productivity.

Compute the productivity profile for 20x1:

Compute the Material Productivity Profile for 20x1:

$\begin{array}{c}\text{Material Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Materials used}}\\ =\frac{55,000}{33,000}\\ \text{= }1.67\end{array}$

Compute the Labor Productivity Profile for 20x1:

$\begin{array}{c}\text{Labor Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Labor hours used}}\\ =\frac{55,000}{66,000}\\ \text{= }0.83\end{array}$

The Material Productivity Profile is 1.67 and Labor Productivity Profile is 0.83.

1 b.

To determine

Ascertain the productivity profile for 20x2 for the proposed process changes.

Explanation of Solution

Compute the productivity profile for 20x2 Change 1:

Compute the Material Productivity Profile for 20x2 Change 1:

$\begin{array}{c}\text{Material Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Materials used}}\\ =\frac{55,000}{38,500}\\ \text{= }1.43\end{array}$

Compute the Labor Productivity Profile for 20x2 Change 1:

$\begin{array}{c}\text{Labor Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Labor hours used}}\\ =\frac{55,000}{44,000}\\ \text{= }1.25\end{array}$

The Material Productivity Profile is 1.43 and Labor Productivity Profile is 1.25.

Compute the productivity profile for 20x2 Change 2:

Compute the Material Productivity Profile for 20x2 Change 2:

$\begin{array}{c}\text{Material Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Materials used}}\\ =\frac{55,000}{27,500}\\ \text{= }2.00\end{array}$

Compute the Labor Productivity Profile for 20x2 Change 2:

$\begin{array}{c}\text{Labor Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Labor hours used}}\\ =\frac{55,000}{55,000}\\ \text{= }1.00\end{array}$

The Material Productivity Profile is 2.00 and Labor Productivity Profile is 1.00.

There is an overall improvement in the output input ratio from 20x1 to 20x2.

1 c.

To determine

Ascertain the productivity profile for optimal input combination and recommend the most productive profile.

Explanation of Solution

Compute the productivity profile for optimal input combination:

Compute the Material Productivity Profile for optimal input combination:

$\begin{array}{c}\text{Material Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Materials used}}\\ =\frac{55,000}{22,000}\\ \text{= }2.50\end{array}$

Compute the Labor Productivity Profile for optimal input combination:

$\begin{array}{c}\text{Labor Productivity Profile = }\frac{\text{Number of Units produced}}{\text{Labor hours used}}\\ =\frac{55,000}{44,000}\\ \text{= }1.25\end{array}$

The Material Productivity Profile is 2.50 and Labor Productivity Profile is 1.25.

There is an overall improvement in the output input ratio from 20x1 to 20x2. The change 1 in 20x2 has the optimum labor productivity, however the material productivity is very low. In the Change 2 of 20x2, both material and labor productivity are good. Now for the decision regarding the implementation of the productivity profile, this depends on the productivity trade-offs of the inputs.

2.

To determine

Ascertain the productive inefficiency among the given combinations and compare the improvement along with the changes in the technical and allocative efficiency.

Explanation of Solution

Total productive efficiency: The total productive efficiency refers to the point where the maximum technical and allocative efficiency is achieved. This is the point where the production of a new product may compromise the production of another product, as the optimum quantity of inputs is being used to get the desired output.

The technical efficiency ensures no more units of input than the required number is used for any mix of inputs.

The allocative efficiency ensures the use of an inexpensive and most technically efficient mix.

Compute the total cost of productive efficiency:

Particulars	Number of Units (A)	Cost per Unit (B)	$\text{(c}\text{=}\text{A}\times \text{B)}$Amount
20x1
Cost of materials	33,000	$ 60	$ 1,980,000
Cost of labor	66,000	$ 15	$ 990,000
Total Cost			$ 2,970,000
20x2 Change 1
Cost of materials	38,500	$ 60	$ 2,310,000
Cost of labor	44,000	$ 15	$ 660,000
Total Cost			$ 2,970,000
20x2 Change 2
Cost of materials	27,500	$ 60	$ 1,650,000
Cost of labor	55,000	$ 15	$ 825,000
Total Cost			$ 2,475,000
Optimal Input
Cost of materials	22,000	$ 60	$ 1,320,000
Cost of labor	44,000	$ 15	$ 660,000
Total Cost			$ 1,980,000

Table (1)

Compute the total cost of productive inefficiency:

Compute the cost of productive inefficiency for 20x1:

$\begin{array}{c}\begin{array}{l}\text{Cost of Productive}\\ \text{Inefficiency}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of productive efficiency for profile 20x1 }-\\ \text{Cost of productive efficiency for optimal inputs }\end{array}\right)\\ =\$2,970,000-\$1,980,000\\ \text{= }\$990,000\end{array}$

Compute the cost of productive inefficiency for 20x2 Change 1:

$\begin{array}{c}\begin{array}{l}\text{Cost of Productive}\\ \text{Inefficiency}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of productive efficiency for profile 20x1 }-\\ \text{Cost of productive efficiency for optimal inputs }\end{array}\right)\\ =\$2,970,000-\$1,980,000\\ \text{= }\$990,000\end{array}$

Compute the cost of productive inefficiency for 20x2 Change 2:

$\begin{array}{c}\begin{array}{l}\text{Cost of Productive}\\ \text{Inefficiency}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of productive efficiency for profile 20x1 }-\\ \text{Cost of productive efficiency for optimal inputs }\end{array}\right)\\ =\$2,475,000-\$1,980,000\\ \text{= }\$495,000\end{array}$

Compute the potential improvement:

Compute the potential improvement for 20x2 Change 1:

$\begin{array}{c}\begin{array}{l}\text{Potential}\\ \text{Improvement}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of productive efficiency for profile 20x1 }-\\ \text{Cost of productive efficiency for 20x2 Change 1}\end{array}\right)\\ =\$2,970,000-\$2,970,000\\ \text{= }\$0\end{array}$

Compute the potential improvement for 20x2 Change 2:

$\begin{array}{c}\begin{array}{l}\text{Potential}\\ \text{Improvement}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of productive efficiency for profile 20x1 }-\\ \text{Cost of productive efficiency for 20x2 Change 2}\end{array}\right)\\ =\$2,970,000-\$2,475,000\\ \text{= }\$495,000\end{array}$

The Change 1 has greater technical efficiency but the allocative efficiency is reduced, on the other hand Change 2 is able to attain both technical and allocative efficiency.

3.

To determine

Compute and describe the price recovery component.

Explanation of Solution

Profit-linked productivity measurement and analysis: The profit-linked productivity measurement and analysis is the ascertainment of the amount of change in profit, from the base period to the current period, due to the various changes in the productivity.

Compute the profit-linked productivity measurement:

Compute the profit-linked productivity measurement for 20x2 Change 1:

$\begin{array}{c}\begin{array}{l}\text{Potential}\\ \text{Improvement}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of productive efficiency for profile 20x1 }-\\ \text{Cost of productive efficiency for 20x2 Change 1}\end{array}\right)\\ =\$2,970,000-\$2,970,000\\ \text{= }\$0\end{array}$

Compute the profit-linked productivity measurement for 20x2 Change 2:

$\begin{array}{c}\begin{array}{l}\text{Potential}\\ \text{Improvement}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of productive efficiency for profile 20x1 }-\\ \text{Cost of productive efficiency for 20x2 Change 2}\end{array}\right)\\ =\$2,970,000-\$2,475,000\\ \text{= }\$495,000\end{array}$

The profit-linked productivity measurement takes into consideration only the changes in the input with no regards to the base or optimal combination.