Final answer:
Vaughn Hager's company, Hager Associates, which is run solely by himself, is best described as a sole proprietorship(option e), where the owner is liable for debts and entitled to profits.
Step-by-step explanation:
When Vaughn Hager started his consulting business under the name Hager Associates, the legal structure that best describes the company is a sole proprietorship. A sole proprietorship is defined as a business owned and operated by a single individual, which in this case is Vaughn Hager himself.
This business form is characterized by the owner being entirely responsible for all debts and liabilities and entitled to all profits. As Hager Associates is indicated to be a one-man consulting business, it does not meet the definitions of a trade alliance, partnership, or corporation.
Sole proprietorships are particularly common for private companies and small businesses due to their simplicity and ease of management.