Question

A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used 6 workers, who together produced an average of 70 carts per hour. Workers receive $15 per hour, and machine cost was $30 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $11 per hour, while output increased by 5 carts per hour.

a. Compute labor productivity under each system. Use carts per worker per hour as the measure of labor productivity. (Round your answers to 3 decimal places.)

b. Compute the multifactor productivity under each system. Use carts per dollar cost (labor plus equipment) as the measure. (Round your answers to 3 decimal places.)

c. Comment on the changes in productivity according to the two measures. (Round your intermediate calculations to 3 decimal places and final answers to 2 decimal places.)

Answer 1

Data provided
Before buying the new equipment:
Number of workers = 6
Production = 70 carts per hour
Worker wage = $15 per hour
Machine cost = $30 per hour
After buying the new equipment:
Number of workers = 5
Production = 70 + 5 = 75 carts per hour
Worker wage = $15 per hour
Machine cost = $30 + $11 = $41 per hour
a. The computation of labor productivity under each system is shown below:-
Labor productivity = Number of carts produced per hour / Number of workers
Labor productivity (Before) = 70 / 6
= $11.667  carts per worker per hour

Labor productivity (After) = 75 / 5
= 15.000  carts per worker per hour

b. The computation of the multifactor productivity under each system is shown below:-
Multifactor productivity = Carts produced / ((Number of workers * Worker wage) + Equipment cost)
Multifactor productivity (Before) = 70 / ((6 * $15) + $30)
= 70 / ($90 + $30)
= 70 / $120
= 0.583 carts per dollar cost

Multifactor productivity (After) = 75 / ((5 * $15) + $41)
= 75 / (75 + $41)
= $75 / 116
= 0.647 carts per dollar cost

c. The Comment on the changes in productivity according to the two measures is shown below:-
Increase in productivity = ((New productivity - Old productivity) / Old productivity) * 100
Increase in labor productivity = ((15.000 - 11.667) / 11.667) * 100
= (3.333 / 11.667) * 100
= 0.2857 * 100
= 28.27
Labor productivity increased by 28.57%

Increase in multifactor productivity = ((0.647 - 0.583) / 0.583) * 100
= (0.064 / 0.583) * 100
= 0.1098 * 100
= 10.98%

Multifactor productivity increased by 10.98%