Initiating a well-orchestrated plan for budgeting mobile device management (MDM) software is no small feat. It requires a calculated blend of various disciplines - from corporate finance, to technical analysis and operational management. The aim of this discourse is to elucidate the intricacies involved in budgeting for MDM software, shedding light on the economic, technological and strategic aspects of such an undertaking.

As our starting point, we need to have a comprehensive insight into what exactly MDM software is. In simple terms, MDM software provides a centralized platform to manage, secure, monitor, and enforce policies on smartphones, tablets and other end-point devices. The relevance of this software arises from the increasing reliance of businesses on mobile technologies. As per the law of requisite variety, an organization must possess internal complexity commensurate with the external complexity it faces, which in this case, would be managing mobile devices. Therefore, MDM software has become an integral part of businesses, especially those for whom mobile connectivity is a critical operational aspect.

Budgeting for MDM software, however, is a strategic exercise, which demands an understanding of the software's potential benefits and the cost associated with its implementation and maintenance. Here, the principles of cost-benefit analysis come into play, and the law of diminishing marginal utility is also relevant. As the number of mobile devices in an organization increases, the utility derived from each additional unit of MDM software decreases, thus making it crucial to find the optimal budget allocation for MDM software.

To kickstart the budgeting process, the first step should be recognizing and quantifying the need for MDM software. Investigating the current state of mobile device administration and the potential threats and opportunities that might arise from improved management would be the starting point. This stage aligns closely with the principles of Pareto efficiency, balancing cost and benefits to achieve an optimal outcome.

The next step, determining the financial allocation for MDM software, can be guided by modern portfolio theory (MPT). MPT, usually applied to the field of finance and investment, can also be relevant for budgeting in information technology (IT). In essence, MPT suggests that it's not enough to look at the expected risk and return of one particular investment (in this case, MDM software). Instead, the investment should be evaluated based on how it impacts the overall portfolio risk and return (the complete IT infrastructure). Therefore, the allocated budget for MDM software should not only be guided by its individual cost and expected benefits, but also by its effect on the overall IT expenditure and the organization's strategic objectives.

Moreover, the adoption of MDM software will involve a trade-off between the degree of control and user privacy. The more the control exerted by the software, the greater the potential intrusion into user privacy. Therefore, it is crucial to find a balance where the software fulfills its purpose without flouting privacy norms. This is where the social science theory of rational legal authority can be applied, which mandates that any form of authority should be bound by established rules and laws. In this case, the MDM software must adhere to data privacy laws and regulations.

Finally, the budgeting process should also incorporate the costs of continuous maintenance and upgrading of the MDM software, reflecting the principles of the product lifecycle theory. Like any other software product, MDM software will go through different stages of the lifecycle - introduction, growth, maturity, and decline, each with its associated costs.

In conclusion, budgeting for MDM software is a sophisticated process that requires a strategic alignment of various academic theories and principles, ranging from economics, finance, technology, and social sciences. A deep understanding of these various elements will not only ensure effective budget allocation but also optimize the strategic benefits derived from the MDM software.