The MorTex Company assembles garments entirely by hand even though a textile ma-chine 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 the 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.
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 costs of the two options: assembling by hand and using the machine.
Currently, the cost of labor for assembling 5,400 units per day is:
Labor cost = Number of workers * Cost per worker
= 5,400 units / 200 units per worker * $50 per day
= 270 workers * $50 per day
= $13,500 per day
If the company purchases a textile machine, the output will increase by 1,800 units daily, giving a total output of 7,200 units per day.
The cost of the textile machine is $600 per day. So the cost of using the machine is:
Machine cost = $600 per day
Comparing the costs, we see that:
Cost of assembling by hand = $13,500 per day
Cost of using the machine = $600 per day
Since the cost of using the machine is significantly lower than the cost of assembling by hand, 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 re-evaluate the decision to purchase a textile machine.
Currently, the cost of labor for assembling 5,400 units per day is:
Labor cost = Number of workers * Cost per worker
= 5,400 units / 200 units per worker * $50 per day
= 270 workers * $50 per day
= $13,500 per day
If labor costs increase to $100 per day, the cost of assembling 5,400 units per day would be:
Labor cost = Number of workers * Cost per worker
= 5,400 units / 200 units per worker * $100 per day
= 270 workers * $100 per day
= $27,000 per day
Now, let's compare the costs of using the machine and the cost of assembling by hand with increased labor costs:
Cost of assembling by hand (with increased labor costs) = $27,000 per day
Cost of using the machine = $600 per day
In this case, the cost of using the machine is still significantly lower than the cost of assembling by hand with increased labor costs. Therefore, even with higher labor costs due to a strike, management can still reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor.