The pursuit of eloquence and mastery in the art of public speaking is an endeavor that can vastly enhance personal and professional lives. It can mean the difference between fading into the background and standing out, between a missed opportunity and a successful launch. The process of honing this skill can be accelerated significantly with the guidance of a public speaking coach. However, this guidance comes at a price. How then does one navigate the financial aspect of this venture? The task of creating a budget for hiring a public speaking coach requires a comprehensive understanding of various factors.

The first step towards creating a budget is to understand the pricing structure of public speaking coaches. They can charge per hour, per session, or offer package deals. An hourly rate can range from $50 to $500 or more, depending on the coach's experience, reputation, and level of expertise. This broad spectrum underscores the necessity of having a clear budgetary framework when embarking on this journey.

The creation of any budget, including for public speaking coaching, is based largely on two variables: income and expenses. This is not dissimilar to the principles elucidated by economist John Maynard Keynes in his income-expenditure model. He proposed that an individual's (or an entity's) income ultimately determines their expenditure and vice versa. Thus, evaluate your monthly income, be it a salary, business income, or other sources. After accounting for fixed expenses like mortgage, bills, food, and other essentials, the remainder can be considered for variable expenses, such as hiring a public speaking coach.

But before you allocate a significant chunk of your income to this cause, consider the value proposition. This is a concept in microeconomic theory that correlates the price of a good or a service to the benefits it offers, leading to an individual's decision to purchase. In this case, determine the value that public speaking coaching would provide. Are you an entrepreneur looking to secure venture capital, or an executive aiming for a higher leadership role, or perhaps a student seeking to boost your academic career? Each scenario warrants a different level of investment.

The next factor to consider is the opportunity cost, another fundamental tenet of economics. This is the loss of potential gain from other alternatives when one alternative is chosen. By investing in a public speaking coach, what other pursuits or opportunities are you potentially sidelining? It might be a trade-off between hiring a coach and subscribing to an online course, attending a workshop, or buying public speaking books. These alternatives might be cheaper, but the personalized feedback and tailored approach of a private coach often provide a higher return on investment.

The 'where' in the equation is also significant. Hiring a local coach vs. an international one, or opting for face-to-face sessions vs. online coaching can substantially impact the cost. Thanks to technology, you can now have access to international coaches via platforms like Skype, Zoom, or Facetime, which can offer a wider selection of coaches but at a potentially higher cost due to factors like exchange rates.

The temporal aspect, or the 'when', plays a role too. It's worth considering whether you need a coach for a one-off event, such as a keynote speech at a conference, or for ongoing development. The former might require an intensive short-term coaching plan, often more expensive, while the latter allows for a more spread-out cost.

Lastly, always remember that while the price is an important component, the selection of a coach should not solely rest on it. The coach's approach, methodology, and rapport with you are equally important. As the renowned statistician George E. P. Box stated, "All models are wrong, but some are useful." Similarly, all coaches have their strengths and weaknesses, but the right one for you is the most useful one that aligns with your needs, goals, and yes, your budget.

To wrap up, creating a budget for hiring a public speaking coach is not a task to be taken lightly. It requires a careful assessment of one's financial status, a clear understanding of the value proposition, an evaluation of the opportunity cost, and a deep consideration of the possible trade-offs. However, with a well-thought-out budget, the journey towards public speaking mastery need not break the bank.