The MorTex Company assembles garments entirely by hand even though a textile machine exists that can assemble garments faster than a human can. Workers cost $50 per day, and each additional laborer can produce 200 more units per day (i.e., marginal product is constant and equal to 200). Installation of the first textile machine on the assembly line will increase output by 1,800 units daily. Currently the firm assembles 5,400 units per day.
a. The financial analysis department at MorTex estimates that he price of a textile machine is $600 per day. can management reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor? Why or why not?
b. The Textile Workers of America is planning to strike for higher wages. Management predicts that if the strike is successful, the cost of labor will increase to $100 per day. If the strike is successful, how would this affect the decision in part a to purchase a textile machine? Explain.
Take a shot. What do you think.
a)additional worker costs (50/200 = 1/4) dollar per unit
additional machine costs (600/1800 = 1/3) dollar per unit
So it would not pay to buy the machine
b) If the hourly wage doubles, the labor would cost (1/2) dollar per unit, which is now greater than the (1/3) dollar per unit for the machine. Now the union caused layoffs :(
By the way, I can sometimes help with math based questions. However I am a physicist and do not know management speak.
a. To determine if purchasing a textile machine can reduce the cost of assembling 5,400 units per day, we need to compare the cost of labor with the cost of using the machine.
Currently, the cost of labor is $50 per worker per day, and each additional worker produces 200 units per day. So, currently, the cost of labor for assembling 5,400 units would be:
(5,400 / 200) * $50 = $1,350
If they purchase a textile machine, the output would increase by 1,800 units per day. To calculate the cost of using the machine, we need to consider the cost of the machine itself, which is $600 per day.
Using the machine, the cost of labor for assembling 5,400 units would be:
(5,400 / 200) * $50 = $1,350
In this case, the cost of using the machine is the same as the cost of labor. Therefore, management cannot reduce the cost of assembling 5,400 units per day by purchasing a machine.
b. If the strike is successful and the cost of labor increases to $100 per day, we need to reevaluate the decision to purchase a textile machine.
The cost of labor for assembling 5,400 units per day, with the increased cost of $100 per day, would be:
(5,400 / 200) * $100 = $2,700
Now, let's compare this with the cost of using the machine. The cost of the machine remains the same at $600 per day.
Using the machine, the cost of labor for assembling 5,400 units would still be:
(5,400 / 200) * $50 = $1,350
In this case, the cost of using the machine is much lower than the cost of labor. Therefore, if the strike is successful, it would be more cost-effective to purchase a textile machine to reduce labor costs and assemble the 5,400 units per day.
a. To determine if management can reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor, we need to compare the cost of labor with the cost of the machine.
Currently, the firm is assembling 5,400 units per day using labor. Each additional laborer can produce 200 more units per day, so the firm is currently using 5,400 / 200 = 27 laborers. The total cost of labor per day is 27 * $50 = $1,350.
If the firm purchases a textile machine, it will be able to increase its output by 1,800 units per day. This means the firm will be able to produce 5,400 + 1,800 = 7,200 units per day.
The price of the textile machine is $600 per day. Let's compare the cost of using labor and the cost of using the machine:
Cost of labor: 27 laborers * $50 per day = $1,350 per day.
Cost of machine: $600 per day.
Since the cost of using the machine is lower than the cost of using labor ($600 < $1,350), management can reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor.
b. If the strike is successful and the cost of labor increases to $100 per day, we need to reassess whether it is still cost-effective to purchase a textile machine.
Currently, the firm is assembling 5,400 units per day using labor. With a labor cost of $100 per day, the total cost of labor per day would be 27 laborers * $100 = $2,700.
Comparing the cost of labor with the cost of the machine:
Cost of labor: $2,700 per day.
Cost of machine: $600 per day.
In this scenario, the cost of labor is still higher than the cost of using the machine ($2,700 > $600). Therefore, even if the strike is successful and labor costs increase, management can still reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor.