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 7 workers, who together produced an average of 70 carts per hour. Workers receive $15 per hour, and machine cost was $40 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $10 per hour while output increased by 4 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 2 decimal places.) Before _____ carts per worker per hourAfter ______carts per worker per hourb. Compute the multifactor productivity under each system. Use carts per dollar cost (labor plus equipment) as the measure. (Round your answers to 2 decimal places.)Before ______ carts/dollar costAfter _______ carts/dollar costc. Comment on the changes in productivity according to the two measures. (Round your intermediate calculations and final answers to 2 decimal places. Omit the "%" signs in your response.)Labor productivity by _____%Multifactor productivity by _____ %

Answer 1

Labor productivity increased from 10 to 12.33 carts per worker per hour after the new equipment purchase, showing a 23.33% increase. Multifactor productivity increased from 0.48 to 0.49 carts per dollar cost, a 2.08% increase. These calculations reflect the efficiency improvements due to the new equipment.

Step-by-step explanation:

The student is asking about labor productivity and multifactor productivity before and after the purchase of new equipment by a company that manufactures shopping carts. Productivity is calculated based on output per worker per hour and per dollar cost, reflecting the efficiency gains from the new equipment.

Labor Productivity:

Before the new equipment was purchased, labor productivity was 70 carts per 7 workers per hour, which is 10 carts per worker per hour. After the purchase, with one less worker, and an increase in output, the productivity became 74 carts per 6 workers per hour, which is approximately 12.33 carts per worker per hour.

Multifactor Productivity:

The total cost per hour before the equipment purchase was $145 ($105 for labor at $15 per hour and $40 for equipment), and the company produced 70 carts per hour, which results in a multifactor productivity of approximately 0.48 carts per dollar cost. After the purchase, the total cost per hour increased to $150 ($90 for labor and $50 for equipment) with an output of 74 carts per hour, resulting in a multifactor productivity of approximately 0.49 carts per dollar cost.

Productivity Changes:

Labor productivity increased by about 23.33%, and multifactor productivity increased by approximately 2.08%.

Answer 2

Before buying the new equipment:

Number of workers = 7

Production = 70 carts per hour

Worker wage = $15 per hour

Machine cost = $40 per hour

After buying the new equipment:

Number of workers = 6

Production = 74 carts per hour

Worker wage = $15 per hour

Machine cost = $50 per hour

(a) Labor productivity

Labor productivity = Number of carts produced per hour / Number of workers

Labor productivity (Before) = 70 / 7

Labor productivity (Before) = 10 carts per worker per hour

Labor productivity (After) = 74 / 6

Labor productivity (After) = 12.33 carts per worker per hour

(b) Multifactor productivity

Multifactor productivity = Carts produced / (Labor cost + Equipment cost)

Multifactor productivity = Carts produced / [(Number of workers x Worker wage) + Equipment cost)

Multifactor productivity (Before) = 70 / [(7*$15) + $40]

Multifactor productivity (Before) = 0.48 carts/dollar cost

Multifactor productivity (After) = 74 / [(6*$15) + $50]

Multifactor productivity (After) = 0.53 carts/dollar cost

(c) Increase in productivity

Increase in productivity = [(New productivity - Old productivity) / Old productivity] * 100

Increase in labor productivity = [(12.33 - 10) / 10] * 100

Increase in labor productivity = 0.233 * 100

Increase in labor productivity = 23.30%

Increase in multifactor productivity = [(0.53 - 0.48) / 0.48] * 100

Increase in multifactor productivity = 0.104167 * 100

Increase in multifactor productivity = 10.42%