Final answer:
Francis Cabot Lowell built the first integrated textile mill in New England, which is true. For a firm with different production technologies, the most cost-effective one is typically chosen. The statement that short staple cotton was preferred before the invention of the cotton gin is false. The efficiency of a simple machine is always less than 100 percent due to friction, which is true.
Step-by-step explanation:
The statement regarding Francis Cabot Lowell is true. He is known for establishing the first integrated textile mill in America, which was in New England. This was an innovation that incorporated the necessary steps to transform cotton into cloth all under one roof.
In the context of economics and production technology, when given different technologies with varying numbers of workers and machines, a firm typically selects the one with the lowest total cost. This often leads to a scenario where machine hours become cheaper, and consequently, firms may opt for technology that utilizes more machines and less labor. Therefore, if production technology 3 has the lowest total cost, then it would be the rational choice for the firm.
Regarding the preference of cotton types before the invention of the cotton gin, the statement that short staple cotton was preferred to long staple is false. It was actually the other way around; long staple cotton was preferred because it was easier to process by hand than short staple cotton. The invention of the cotton gin by Eli Whitney made processing short staple cotton much easier, altering the industry preference afterwards.
The statement about the efficiency of a simple machine is true. Due to inevitable energy losses primarily in the form of heat due to friction, no machine can have an efficiency of 100 percent. This is a basic principle of physics concerning work, energy, and efficiency.