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 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 labor and machine usage.
Currently, the company is assembling garments entirely by hand with workers costing $50 per day. The additional laborers can produce 200 more units per day at a constant marginal product.
Installing the first textile machine on the assembly line will increase output by 1,800 units daily. The price of the machine is estimated to be $600 per day.
Let's calculate the cost under the current manual labor scenario:
Labor cost = Number of workers * Cost per worker per day
Labor cost = 1 * $50 per day = $50 per day
Now, let's calculate the cost if the company purchases the textile machine:
Labor cost = Number of workers * Cost per worker per day
Labor cost = 1 * (5,400 units / 200 units per worker) * $50 per day = $1,350 per day
Machine cost = Price of machine per day
Machine cost = $600 per day
Total cost = Labor cost + Machine cost
Total cost (without the strike) = $1,350 + $600 = $1,950 per day
Since the total cost of using labor and the machine is higher than the cost of using only labor, management cannot 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 will need to recalculate the costs with the new labor cost.
Labor cost with higher wages = Number of workers * Cost per worker per day
Labor cost = 1 * (5,400 units / 200 units per worker) * $100 per day = $2,700 per day
Total cost (with the strike) = Labor cost + Machine cost
Total cost (with the strike) = $2,700 + $600 = $3,300 per day
With the increase in labor cost, the total cost of using labor and the machine becomes even higher. Therefore, even with a higher wage for workers, management still cannot reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor.
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 labor and machine usage.
Currently, the cost of labor is $50 per day per worker, and each additional laborer can produce 200 more units per day. We can calculate the additional labor cost as 200 units / 5,400 units * $50 per day = $1.85.
The installation of the first textile machine will increase output by 1,800 units per day. So, if the daily cost of the machine is $600, the additional cost per unit is $600 / 1,800 units = $0.33.
Comparing the additional labor cost of $1.85 with the additional machine cost of $0.33, it is more cost-effective to purchase a textile machine and use less labor. By doing so, the cost of assembling 5,400 units per day can be reduced.
b. If the strike is successful, and the cost of labor increases to $100 per day, we need to reevaluate the decision from part a.
With the increased labor cost, the additional labor cost for each worker would be 200 units / 5,400 units * $100 per day = $3.70. By considering this higher labor cost, we can compare it to the additional machine cost.
Considering the higher labor cost of $3.70 and the additional machine cost of $0.33, it is still more cost-effective to purchase a textile machine and use less labor. Therefore, even with the increased labor cost due to the strike, management should still consider purchasing the textile machine to reduce the cost of assembling 5,400 units per day.