Question

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%

Answer 1

B) 8.3%

Step-by-step explanation:

The multifactor productivity is given the ratio between output (amount charged per each house cleaned) and input (chemical, labor and misc. expenses)

Let x be the amount charged per housed cleaned, the original and new productivities are:

`P_(old)=(x)/(10+40+5)=0.018182x \\P_(new)=(x)/(1.5*10+40+5)=0.016667x`

The rate by which the multifactor productivity has fallen is:

`R = (P_(new)-P_(old))/(P_(old))\\R=(0.0166667-0.018182)/(0.018182) \\R=-0.083=-8.3\%`

The multifactor productivity has fallen by 8.3%.