1. Modern Lumber, Inc., Art Binley, president and producer of apple crates sold to growers, has been able, with his current equipment, to produce 240 crates per 100 logs. He currently purchases 100 logs per day, and each log requires 3 labor- hours to process. He believes that he can hire a professional buyer who can buy a better-quality log at the same cost. If this is the case, he can increase his production to 260 crates per 100 logs. His labor-hours will increase by 8 hours per day. What will be the impact on productivity (measured in crates per labor- hour) if the buyer is hired?
Answer:
To determine the impact on productivity when the professional buyer is hired, you need to calculate the productivity before and after the hiring. Productivity is typically measured as output per unit of input, so in this case, it would
be measured as crates per labor-hour.
Before the professional buyer is hired:
- Crates produced per 100 logs = 240 crates
- Labor-hours per 100 logs = 100 logs * 3 labor-hours/log
= 300 labor-hours
So, before the buyer is hired, the productivity is:
Productivity (before hiring) = 240 crates / 300 labor-hours
= 0.8 crates per labor-hour
After the professional buyer is hired:
- Crates produced per 100 logs = 260 crates
- Labor-hours per 100 logs = 100 logs * 3 labor-hours/log
= 300 labor-hours
However, it's important to note that the hiring of the professional buyer will increase the labor-hours by 8 hours per day.
So, the new total labor-hours per day will be:
300 labor-hours (as before) + 8 labor-hours (additional labor) = 308 labor-hours.
Now, calculate the productivity after hiring the professional buyer:
2. Art Binley has decided to look at his productivity from a multifactor (total factor productivity) perspective (refer to Solved Problem Mini Case 1). To do so, he has determined his labor, capital, energy, and material usage and decided to use dollars as the common denominator. His total labor-hours are now 300 per day and will increase to 308 per day. His capital and energy costs will remain constant at $350 and $150 per day, respectively. Material costs for the 100 logs per day are $1,000 and will remain the same. Because he pays an average of $10 per hour (with fringes), Help Binley determines his productivity increase
Answer:
To determine the total factor productivity increase, you can use the following formula:
Total Factor Productivity (TFP) = (Output After / Input After) / (Output Before / Input Before)
In this case, you've already calculated the productivity (output per labor-hour) before and after hiring the professional buyer, which are 0.8 crates per labor-hour before and 0.844 crates per labor-hour after.
The inputs involved are labor, capital, energy, and material costs. The labor input has increased from 300 labor-hours per day to 308 labor-hours per day, and the capital and energy costs remain constant at $350 and $150 per day, respectively. Material costs for the 100 logs per day are $1,000 and will remain the same.
Calculate the inputs before and after hiring the professional buyer:
- Total input before = Labor cost + Capital cost + Energy cost + Material cost Total input before = (300 labor-hours * $10/hour) + $350 + $150 + $1,000 Total input before = $3,000 + $350 + $150 + $1,000
Total input before = $4,500
- Total input after = Labor cost + Capital cost + Energy cost + Material cost Total input after = (308 labor-hours * $10/hour) + $350 + $150 + $1,000 Total input after = $3,080 + $350 + $150 + $1,000
Total input after = $4,580
Now, plug these values into the TFP formula:
Total factor productivity measure = Total Output/Total Input
= 260 Crates/$4,580
= 0,057 Crates/Dollar
Conclusion: After Art Binley hired a professional buyer, his productivity are increase 0,003 Crates/Dollar from 0,054 Crates/Dollar to 0,057 Crates/Dollar