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In today's complex economic environment, individuals and households alike grapple with the challenge of financial planning. This paper introduces novel methodologies for both individual and cooperative (household) financial budgeting. We firstly propose an optimization framework for individual budget allocation, aiming to maximize savings by efficiently distributing monthly income among various expense categories. We then extend this model to households, wherein the complexity of handling multiple incomes and shared expenses is addressed. The cooperative model prioritizes not only maximized savings but also the preferences and needs of each member, fostering a harmonious financial environment, whether they are short-term needs or long-term aspirations. A notable innovation in our approach is the integration of recommendations from a large language model (LLM). Given its vast training data and potent inferential capabilities, the LLM provides initial feasible solutions to our optimization problems, acting as a guiding beacon for individuals and households unfamiliar with the nuances of financial planning. Our preliminary results indicate that the LLM-recommended solutions result in budget plans that are both economically sound, meaning that they are consistent with established financial management principles and promote fiscal resilience and stability, and aligned with the financial goals and preferences of the concerned parties. This integration of AI-driven recommendations with econometric models, as an instantiation of an extended coevolutionary (EC) theory, paves the way for a new era in financial planning, making it more accessible and effective for a wider audience, as we propose an example of a new theory in economics where human behavior can be greatly influenced by AI agents. [ABSTRACT FROM AUTHOR]