Chapter 2, Problem 7P

a)

Summary Introduction

To compute: The labor productivity and multifactor productivity for each unit.

Introduction: Labor productivity is the measure of productivity of a worker during a period of time. It the ratio of total output to the total productivity hours.

Answer to Problem 7P

Multifactor productivity has dropped from 0.020 to 0.015.

Explanation of Solution

Given information:

Unit	Employees	Customer processed/day
A	4	36
B	5	40
C	8	60
D	3	20

$\begin{array}{c}\text{Hourly}\text{wage}=\text{\$25}\\ \text{Overhead}=\text{1}\text{.0}\times \text{Labor}\text{cost}\\ \text{Material}\text{cost}=\text{\$5}\text{per}\text{customer}\end{array}$

Formula:

$\begin{array}{c}\text{Multifactor}\text{Productivity}=\frac{\text{Output}}{\text{Total}\text{cost}}\\ \text{Labor}\text{Productivity}=\frac{\text{Customers}\text{}\text{per}\text{day}}{\text{Employees}}\\ \text{Total}\text{cost}=\text{Labor}\text{cost}+\text{Overhead}\text{cost}+\text{Material}\text{cost}\end{array}$

$\begin{array}{l}\text{Laborcost}=\text{Number}\text{of}\text{workers}\times \text{8}\text{hours}\times \text{\$25/hour}\\ \text{Overhead}\text{cost}=\text{Labor}\text{cost}\times \text{1}\text{.00}\\ \text{Material}\text{cost}=\text{Customers}\times \text{\$5/customer}\end{array}$

Calculation of multifactor productivity:

Unit	Employees	Customer processed/day	Labor cost	Overhead cost	Material cost	Total cost	Labor productivity	MFP (2decimal)	MFP (3decimal)
A	4	36	800	800	180	1780	9	0.02	0.020
B	5	40	1000	1000	200	2200	8	0.02	0.018
C	8	60	1600	1600	300	3500	7.5	0.02	0.017
D	3	20	600	600	100	1300	6.6666667	0.02	0.015

Table 1

Excel Worksheet:

Calculation of multifactor productivity:

Unit A:

Labor cost is calculated by multiplying number of workers (4) with 8working hours and 25 hourly wages which gives 800.

Overhead cost is calculated by multiplying Labor cost of 800 with 1.0 which gives 800.

Material cost is calculated by multiplying 36 with 5 which gives 180.

Total cost is calculated by adding labor cost of 800, overhead cost of 800 and material cost of 180 which yields 1780.

Labor productivity is calculated by dividing 36 with 4 which yields 9.

Multifactor productivity is calculated by dividing 36 with the total cost of 1,780 which yields 0.02 (2-decimal) and 0.020 (3 decimal).

Same procedure is followed for unit B, C and D the result is shown in table 1.

Hence, multifactor productivity has dropped from 0.020 to 0.015.

b)

Summary Introduction

To compute: The labor productivity and multifactor productivity for each unit.

Introduction: Multifactor productivity is also referred as total factor productivity. It is the measure of economic performance by comparing the amount of goods and services produced to the total input used to produce the output.

Answer to Problem 7P

Multifactor productivity has dropped from 0.022to 0.017.

Explanation of Solution

Given information:

Every employee process on additional customers.

Unit	Employees	Customer processed/day
A	4	40
B	5	45
C	8	68
D	3	23

$\begin{array}{c}\text{Hourly}\text{wage}=\text{\$25}\\ \text{Overhead}=\text{1}\text{.0}\times \text{Labor}\text{cost}\\ \text{Material}\text{cost}=\text{\$5}\text{per}\text{customer}\end{array}$

Formula:

$\begin{array}{c}\text{Multifactor}\text{Productivity}=\frac{\text{Output}}{\text{Total}\text{cost}}\\ \text{Labor}\text{Productivity}=\frac{\text{Customers}\text{}\text{per}\text{day}}{\text{Employees}}\\ \text{Total}\text{cost}=\text{Labor}\text{cost}+\text{Overhead}\text{cost}+\text{Material}\text{cost}\end{array}$

$\begin{array}{l}\text{Laborcost}=\text{Number}\text{of}\text{workers}\times \text{8}\text{hours}\times \text{\$25/hour}\\ \text{Overhead}\text{cost}=\text{Labor}\text{cost}\times \text{1}\text{.00}\\ \text{Material}\text{cost}=\text{Customers}\times \text{\$5/customer}\end{array}$

Calculation of multifactor productivity:

Unit	Employees	Customer processed/day	Labor cost	Overhead cost	Material cost	Total cost	Labor productivity	MFP (2decimal)	MFP (3decimal)
A	4	40	800	800	200	1800	10	0.02	0.022
B	5	45	1000	1000	225	2225	9	0.02	0.020
C	8	68	1600	1600	340	3540	8.5	0.02	0.019
D	3	23	600	600	115	1315	7.6666667	0.02	0.017

Table 2

Excel Worksheet:

Calculation of multifactor productivity:

Unit A:

Labor cost is calculated by multiplying number of workers (4) with 8 working hours and 25 hourly wages which gives 800.

Overhead cost is calculated by multiplying Labor cost of 800 with 1.0 which gives 800.

Material cost is calculated by multiplying 40 with 5 which gives 200.

Total cost is calculated by adding labor cost of 800, overhead cost of 800 and material cost of 200 which yields 1800.

Labor productivity is calculated by dividing 40 with 4 which yields 10.

Multifactor productivity is calculated by dividing 40 with the total cost of 1,800 which yields 0.02 (2-decimal) and 0.022 (3 decimal).

Same procedure is followed for unit B, C and D the result is shown in table 2.

Hence, multifactor productivity has dropped from 0.022to 0.017.