# Please answer the following question about productivity. Road racing bikes have special seats that are flexible with minimum contact with cyclists. These seats are called toupe saddles. Roscoe...

Road racing bikes have special seats that are flexible with minimum contact with cyclists. These seats are called toupe saddles. Roscoe Specialty Equipment makes 100 of these seats per day with the following resources.

Labor: 40 hours per day @ \$15.00 per hour
Raw material: 20 kilograms per day @ \$1.00 per kg
Energy: \$200 per day
Capital costs: \$500 per day
What is the labor productivity per labor hour for these toupe saddles at Roscoe? What is the multifactor productivity for these toupe saddles at Roscoe? What is the % change in multifactor productivity if Roscoe can reduce the energy bill by \$150 per day without cutting production or changing any other inputs?

pohnpei397 | Certified Educator

In the first part of your question, our task is much like what we had to do in your previous question.  That is, we need to take the number of seats that are produced and divide it by the number of hours that are needed to produce the seats.  This is because productivity is generally defined as the amount produced divided by the amount of inputs.  Since this part of the question asks only about labor hours (and not the cost of labor or the cost of any of the other inputs), we only divide the number of seats produced by the number of hours worked.

Productivity =  100 seats/40 hours = 2.5 seats per hour.

Next, we have to calculate multifactor productivity.  To do this, we need to take the number of toupe saddles produced and divide it by the cost of all of the inputs that go into making them.  When it comes to labor and materials, we must be sure to multiply the cost per unit by the units used.

Labor costs = 40 hours per day x \$15.00 per hour = \$600 per day

Raw material costs = 20 kilograms per day x \$1.00 per kg = \$20 per day

Energy: \$200 per day

Capital costs: \$500 per day

When we add all of these costs, we find that it costs \$1320 to make 100 saddles in a day.  We then divide the number of saddles made (output) by the cost of making the saddles:

Multifactor productivity = 100 saddles/\$1320 = .076 saddles per dollar of inputs.

Next, we have to find the multifactor productivity if the energy costs are reduced to \$50 per day (they have been reduced by \$150 and \$200-\$150 = \$50).  This reduces the overall cost of making 100 saddles to \$1170 (\$1320-\$150 = \$1170).

We then divide the 100 saddles by the \$1170 that it cost to make them.

New multifactor productivity = 100 saddles/\$1170 = .085 saddles per dollar of inputs.

Finally, we calculate the percent change in productivity.  This is done by finding the difference between the new and old levels of productivity and dividing that by the original productivity.

Difference = .085 - .076 = .009

Percent change in multifactor productivity = .009/.076 = .118 = 11.8%