The advent of the information age has necessitated organizations to engage in continual adaptation to stay competitive. This dynamic environment has birthed the concept of Fractional Executive Services, a business model that offers organizations the expertise of seasoned executives at a fraction of the cost. It is an innovative solution to address the challenges faced by businesses, particularly small-to-medium enterprises (SMEs) and start-ups, in cost-effectively acquiring top-tier executive talent.

Fractional Executive Services entail hiring experienced executives on a part-time basis. These individuals are well versed in their respective fields and provide their expertise to more than one company concurrently. Given this model, these executives are often referred to as 'Fractional Executives'.

The first step in budgeting effectively for Fractional Executive Services is understanding the principle of 'Economies of Scale', which postulates that the cost per unit decreases as the volume of production increases. Similarly, Fractional Executives offer their expertise to multiple organizations, thereby allowing these costs to be distributed among these entities.

Secondly, organizations should understand the concept of 'Opportunity Cost', defined as the cost of forgoing the next best alternative. The cost of hiring a full-time, top-tier executive can be exorbitant, especially for SMEs and start-ups. However, the opportunity cost of not having such expertise could be much higher. The Fractional Executive Services model presents an optimal solution to this dilemma - providing the needed expertise without the accompanying financial burden of a full-time executive.

The third step is to comprehend the 'Law of Diminishing Marginal Returns', a principle that states that as more of one input is added while holding other inputs constant, the additional output gained from the extra input will eventually decline. In the context of Fractional Executive Services, this means that there might be a point beyond which investing in more executive hours does not yield proportional benefits.

Having understood these three economic principles, setting a budget for Fractional Executive Services requires a careful examination of the organization's needs and capabilities. This begins with defining clear objectives and desired outcomes from the engagement, such as setting up a marketing strategy, improving financial performance, or turning around a failing project.

Next, organizations should assess their financial capabilities and constraints. A return on investment (ROI) analysis could be insightful at this juncture, projecting the potential returns against the cost of the Fractional Executive.

Another significant consideration is the selection of the right Fractional Executive, which necessitates a detailed analysis of the candidate’s expertise and experience. Here, the principle of 'Pareto Efficiency' comes into play. It states that resources should be allocated in a way that no one can be made better off without making someone else worse off. The chosen executive should be the one who maximizes the benefits to the organization without causing any undue strain on its resources.

Lastly, a flexible budget should be employed due to the variable nature of the services required from a Fractional Executive. This allows for adjustments based on actual performance and needs, rather than being rigidly tied to forecasted numbers.

In conclusion, budgeting for Fractional Executive Services involves a careful understanding of several economic principles, clear articulation of objectives, and proper financial analysis. It offers an optimal solution for organizations seeking experienced executive talent without the heavy financial burden. While there may be initial challenges in implementation, the potential benefits far outweigh these. Therefore, an intelligent, thoughtful approach to budgeting for such services can bring about significant positive transformations in organizational performance.