A cleaning company uses $10 of chemicals, $40 of labour, 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 % has multifactor productivity fallen?
A) 0%
B) 8.3%
C) 25%
D) 50%
E) 0.83%

Question

Quizplus · Accepted Answer

Multifactor productivity = Output / (Labor + Material + Misc. expenses)
Let's say the company charges $100 for cleaning one house. So, the initial output is:
Output = $100
The initial cost of cleaning one house is:
Cost = $10 (chemicals) + $40 (labor) + $5 (misc. expenses) = $55
Now, the company increases the use of chemicals by 50%, so the new cost of chemicals is $15.
The new cost of cleaning one house is:
New cost = $15 (chemicals) + $40 (labor) + $5 (misc. expenses) = $60
As the output is still $100, the new multifactor productivity is:
New multifactor productivity = $100 / ($40 + $15 + $5) = 1.54
The initial multifactor productivity was:
Initial multifactor productivity = $100 / ($40 + $10 + $5) = 1.54
So, there is no change in the multifactor productivity. However, the cost of cleaning one house has increased by (60-55)/55 = 9.09%, which means the multifactor productivity per dollar has fallen by 8.3%. Therefore, the answer is B.

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