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.
To determine whether purchasing a textile machine would reduce the cost of assembling 5,400 units per day, we need to compare the costs of labor and machine usage.
a. To calculate the cost of labor, we multiply the number of laborers by their daily cost. Currently, the firm assembles 5,400 units per day, so they have (5,400 / 200) = 27 laborers. Therefore, the cost of labor is 27 * $50 = $1,350 per day.
If the company purchases a textile machine, the additional daily output would be 1,800 units. So, the total daily output with the machine would be 7,200 units (5,400 + 1,800). Since the laborers can produce 200 units each, the number of laborers required with the machine would be (7,200 / 200) = 36 laborers. So, the labor cost with the machine would be 36 * $50 = $1,800 per day.
Additionally, the price of the textile machine is $600 per day.
Comparing the costs, the current labor cost is $1,350 per day while the combined cost of labor and machine with the increased output is $1,800 + $600 = $2,400 per day. Therefore, purchasing a textile machine would not reduce the cost of assembling 5,400 units per day.
b. If the cost of labor increases to $100 per day due to a successful strike, the new cost of labor with 27 laborers would be 27 * $100 = $2,700 per day.
With the textile machine, the labor cost with 36 laborers would be 36 * $100 = $3,600 per day. Adding the cost of the machine ($600), the total cost would be $3,600 + $600 = $4,200 per day.
Comparing the costs, the increased labor cost due to the strike is $2,700 per day whereas the combined cost of labor and machine with the increased output is $4,200 per day. Therefore, the increased labor cost resulting from the strike makes purchasing a textile machine even less favorable as it would significantly increase the overall cost of production.