a plant is going to buy a new machine. a productivity analysis is being done for the purchase. the current machine produces 20,000 parts per year. it needs 2500 labor hrs per year at a labor rate of s40 per hr and s80,000 capital cost per year. after automation, it is estimated to take 1500 labor hrs and $200,000 capital cost per year. it will then produce 30000 parts per year. labor rate increases to s45/hr consider only labor and capital inputs. ignore all other inputs. find the labor, capital and total factor productivity now and after automation. would you recommend the automation project? why and why not?
Analysis of Labor, Capital, and Total Factor Productivity for Automation Project
Current Labor Productivity:
The current machine produces 20,000 parts per year with 2500 labor hours at a rate of $40 per hour. Therefore, the current labor productivity is calculated as:
Labor \ Productivity = \frac{Output}{Input} = \frac{20000}{2500} = 8 \ parts/hr
New Labor Productivity after Automation:
After automation, the new machine is expected to produce 30,000 parts per year with 1500 labor hours at a rate of $45 per hour. The new labor productivity after automation is calculated as:
Labor \ Productivity = \frac{Output}{Input} = \frac{30000}{1500} = 20 \ parts/hr
Current Capital Productivity:
The current capital cost per year is $80,000, and the output is 20,000 parts. Therefore, the current capital productivity is calculated as:
Capital \ Productivity = \frac{Output}{Capital \ Cost} = \frac{20000}{80000} = 0.25 \ parts/dollar
New Capital Productivity after Automation:
After automation, the capital cost per year is $200,000, and the output is 30,000 parts. The new capital productivity after automation is calculated as:
Capital \ Productivity = \frac{Output}{Capital \ Cost} = \frac{30000}{200000} = 0.15 \ parts/dollar
Current Total Factor Productivity (TFP):
The current TFP can be calculated by dividing the total output by the total input costs. The total input cost now is $80,000 + ($40/hr * 2500 hr) = $180,000. Therefore, the current TFP is:
TFP = \frac{Output}{Labor \ Cost + Capital \ Cost} = \frac{20000}{180000} \approx 0.1111
New Total Factor Productivity after Automation:
The total input cost after automation is $200,000 + (45/hr * 1500 hr) = $272,500. Therefore, the new TFP after automation is:
TFP = \frac{Output}{Labor \ Cost + Capital \ Cost} = \frac{30000}{272500} \approx 0.1101
Recommendation for Automation:
The labor productivity increases significantly from 8 parts/hr to 20 parts/hr after automation, indicating a higher efficiency in production. However, the capital productivity decreases from 0.25 parts/dollar to 0.15 parts/dollar after automation, suggesting a less effective utilization of capital. The total factor productivity remains relatively similar before and after automation, with a slight decrease after automation.
Considering these factors, the automation project may still be recommended due to the substantial increase in labor productivity, which can lead to higher output with less labor input. However, the impact on capital productivity should be closely monitored to ensure the overall efficiency and profitability of the project. Regular evaluations and adjustments may be necessary to optimize the benefits of the automation investment.