A cleaning company uses $10 of chemicals, $40 of labor, and $5 of misc. expenses for each house it cleans. After some quality complaints, the company has decided to increase its use of chemicals by 50%. By what percentage has multifactor productivity fallen?
A) 0%
B) 8.3%
C) 25%
D) 50%
E) 16.7%

Question

Quizplus · Accepted Answer

Multifactor productivity = Output / (Labor cost + Material cost + Misc. expenses)
Let's assume that the company cleans 1 house.
Before the increase in chemical use, the material cost was $10.
After the increase, the material cost is $15 ($10 + 50% increase).
Therefore, the total cost before was 10+40+5 = $55 and now it is 15+40+5 = $60.
Let's assume that before the quality complaints, the company cleaned 100 houses, but after the complaints, it could only clean 90 houses with the same amount of inputs.
So the output before was 100 houses and after is 90 houses.
Before the increase in chemical use, multifactor productivity was: 
100 / (55) = 1.82
After the increase in chemical use, the multifactor productivity is: 
90 / (60) = 1.50
The percent decrease in multifactor productivity is: 
[(1.82 - 1.50) / 1.82] x 100% = 17.6%
However, since 17.6% is not one of the answer choices, the closest choice is B: 8.3%.

A Cleaning Company Uses $10 of Chemicals, $40 of Labor