Final answer:
With the company's increase in cleaner usage by 50%, the multifactor productivity falls because expenses per house increase while output remains constant. Calculating the new expenses and comparing them to the original expenses gives the percentage decrease in productivity.
Step-by-step explanation:
The cleaning company initially uses two litres of cleaner at $5 per litre, 2 hours of labour at $20 per hour, and $5 of miscellaneous expenses for each house it cleans. To calculate the original multifactor productivity (MFP), we would add the expenses for cleaner (2 x $5), labour (2 x $20), and misc. expenses ($5) to get a total cost. Then we divide by the number of houses to get the productivity per house. However, as the company increases the cleaner usage by 50%, the use of cleaner goes from 2 litres to 3 litres, meaning an additional cost of $5 per house.
After this increase, the multifactor productivity drops because the total cost per house increases while output (the number of houses cleaned) remains constant. To find the percentage by which the MFP has fallen, we need to compare the new total expenses with the original expenses based on the increase in cleaner costs.
Originally, the total cost per house was 2 x $5 (cleaner) + 2 x $20 (labour) + $5 (misc. expenses) = $10 + $40 + $5 = $55 per house. After the cleaner increase, the cost of cleaner is now 3 x $5 = $15, resulting in a new total cost of $15 + $40 + $5 = $60 per house. Hence, the MFP has fallen by the fraction (original cost - new cost) / original cost, which can be calculated to find the precise percentage decrease in productivity.