A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment, installed on each existing machine, that speeds up each machine and as a result reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used four workers and two machines, who produced an average of 80 carts per hour. Workers receive $10 per hour per worker, and machine cost was $20 per hour per machine. With the new equipment, it was possible to transfer two of the workers to another department, and machine cost increased by fifty percent per hour per machine; while output increased by twenty five percent per hour. In both old and new systems, this process operates for 8 hours every day, 7 days a week, 52 weeks a year. Compute the multifactor productivity measure under the new system. Use carts per $ as the measure of productivity.

New average carts produced per hour = Old average carts produced per hour * (100% + Percentage increase in the old average carts produced per hour) = 80 * (100% + 25%) = 100

New number of workers = Old number of workers - Number of workers that can be transferred to another department = 4 - 2 = 2

Workers’ wages per hour = $10, or 10

New machine cost per hour for three machines = (Old machine cost per hour per machine * (100% + Percentage increase in the old machine cost per hour per manchine)) * Number of machines = ($20 * (100% + 50%)) * 3 = $90, or 90

Therefore, we have:

Multifactor productivity measure under the new system = New average carts produced per hour / ((New number of workers * Workers’ wages per hour) + New machine cost per hour for three machines) = 100 / ((2 * 10) + 90) = 0.91 carts