Economics traditionally operates under the assumption of rationality, where individuals make optimal decisions based on complete information and perfect foresight. This assumption, while ideal, often falls short of real-world behavior. In reality, decision-making, from corporate strategies to household budgeting, tends to be adaptive, relying on iterative processes of planning, implementation, monitoring, and revision. This paper investigates the validity of both rational and adaptive decision-making principles in the context of household consumption/saving (investment) planning. The research question centers on whether adaptive strategies, represented by budget-controlled decision-making processes, can achieve outcomes comparable to those predicted by the optimal growth model, which assumes perfect rationality. The study's purpose is to demonstrate the practical applicability and stability of adaptive approaches in addressing intertemporal economic problems. The significance lies in offering a more realistic and manageable alternative to the often unstable and impractical dynamic optimization methods employed in conventional economic modeling. The framework will utilize the Ramsey-type optimal growth model to represent rational decision-making and a novel model incorporating replicator dynamics and the PDSA cycle to capture adaptive decision-making behaviors.

The paper draws upon existing literature on managerial accounting and budgetary control, highlighting the prevalence of adaptive decision-making in various organizations, including companies, households, and government agencies. Studies cited, such as those by Emmanuel et al. (1990), Otley (2006), and Deloitte (2014), underscore the common use of planning, budgeting, and forecasting procedures across organizations. Furthermore, the paper references research on household budgeting behavior, including surveys demonstrating the widespread practice of budgeting and savings planning among consumers (Hilgert et al., 2003; Board of Governors of the Federal Reserve System, 2019). The literature also incorporates behavioral economics, acknowledging the limitations of perfect rationality and the influence of factors such as self-control and context on individual decision-making (Hernandez et al., 2014; Jonker, 2016; Thaler and Shefrin, 1981). The paper highlights the Plan-Do-Study-Act (PDSA) cycle as a practical framework for adaptive decision-making, noting its applications in quality control and management (Deming, 2018; Ohnishi and Fukumoto, 2016). The role of adaptive learning in economics is also discussed, referencing works by Lucas (1986) and Day (1983), which emphasize the importance of trial-and-error processes and evolutionary perspectives. Finally, the paper introduces the replicator dynamics approach as a tool for modeling adaptive decision-making, referencing previous applications in various economic contexts (Safarzynska and van den Bergh, 2011; Sakaki, 2004; Cantner et al., 2019).

The paper employs a comparative approach, contrasting a rational decision-making model with an adaptive decision-making model. The rational decision-making model is represented by a Ramsey-type optimal growth model, which assumes perfect foresight and rational expectations. This model leads to a unique optimal growth path defined by the Keynes-Ramsey rule and the transversality condition. The adaptive decision-making model, on the other hand, is constructed using replicator dynamics and the PDSA cycle. The PDSA cycle serves as the operational procedure for sequential adaptive decision-making, wherein households and firms repeatedly contrast plans with actual results, adjusting their strategies accordingly. The replicator dynamics framework models the evolution of the adoption rates of different planning strategies over time, reflecting the adaptive learning process. A continuous-time system model is developed to represent the budget-controlled decision-making process, incorporating differential equations for the allocation ratio of production across periods (x), consumption (c), and capital accumulation (k). The steady-state behavior of these equations is analyzed through a phase diagram, providing insights into the dynamics of the adaptive growth paths. A Cobb-Douglas production function and a CES utility function are used in numerical simulations using Mathematica 12 to compare the social welfare levels achieved by the optimal and adaptive growth paths, considering factors such as the initial capital level, labor supply growth rate, subjective discount rate, and elasticity of marginal utility. The ratio of social welfare generated by adaptive paths to that of the optimal path serves as a key performance indicator to assess the efficiency of adaptive strategies.

The key findings demonstrate a significant divergence between the predictions of the optimal growth model and the behavior of the adaptive model. The optimal growth model, characterized by the Keynes-Ramsey rule, leads to a unique and highly sensitive saddle-point path. Any deviation from this path results in instability and failure to reach the optimal outcome. In contrast, the adaptive model exhibits a multitude of diverse and stable growth paths clustered around the optimal path. This redundancy provides stability and manageability in the planning process, allowing for multiple suboptimal but acceptable outcomes. Numerical simulations revealed that a wide range of initial consumption planning levels can lead to paths where social welfare levels are comparable to the optimal growth path, achieving over 90% of the optimal welfare level. This indicates a high degree of feasibility and robustness for the adaptive approach. Specifically, the simulations showed that approximately 58% of the feasible initial consumption levels result in paths reaching 90% or more of the optimal social welfare level. The adaptive model, therefore, offers a practically manageable alternative to the fragile optimal growth path, achieving comparable social welfare with considerable stability and reduced sensitivity to initial conditions. The paper also identifies different types of adaptive paths, including some that are dynamically inefficient due to capital overaccumulation, but others that effectively avoid this inefficiency and closely mirror the performance of the optimal growth path. The findings support the idea that the diverse and redundant paths generated by adaptive strategies contribute to the stability and manageability of the planning process.

The findings challenge the pervasive assumption of rational expectations and perfect foresight in economic modeling, offering a more realistic and practical approach to intertemporal decision-making. The superior stability and manageability of adaptive strategies, as revealed by the study, are critical for real-world applications where perfect information and foresight are unattainable. The high social welfare levels achieved by many of the adaptive paths, despite their inherent deviations from the optimal path, suggest that the cost of deviating from perfect rationality may be smaller than previously assumed. The study's insights are relevant to a wide range of fields, from household finance and corporate strategy to public policy, where intertemporal decision-making is crucial. The results imply that policymakers could potentially benefit from acknowledging and accommodating the inherent adaptability and bounded rationality of individual decision-makers rather than enforcing strict adherence to theoretically optimal but practically unstable plans. The study's findings also hold implications for the design of policies and interventions that could guide or support adaptive decision-making, promoting more efficient and sustainable outcomes.

This paper demonstrates the feasibility and practicality of adaptive decision-making as an alternative to the often-unstable optimal growth model. The findings highlight the importance of considering the inherent stability and manageability of alternative planning strategies in addressing real-world intertemporal economic problems. Future research could explore the integration of additional factors, such as technological progress and uncertainty, into the adaptive model. The potential of replicator dynamics coupled with advancements in computer science (such as Deep Learning and Big Data) for further improving the accuracy and effectiveness of adaptive decision-making also warrants further investigation. Overall, the study underscores the need for a paradigm shift towards more realistic and robust models of economic decision-making, recognizing the value of adaptive strategies and their potential to achieve social welfare levels comparable to those predicted by models based on the unrealistic assumption of perfect rationality.

The study's limitations primarily stem from the assumptions made in the model. The deterministic nature of the model may not fully capture the impact of uncertainty and stochasticity inherent in real-world situations. While the paper acknowledges the role of technological progress, it does not explicitly incorporate it into the adaptive model. The focus on household consumption/saving planning limits the generalizability of the findings to other types of intertemporal decision-making problems. Further research is needed to refine the model and account for these factors to ensure a more comprehensive understanding of adaptive decision-making in diverse contexts. Furthermore, the paper's applicability might be limited to contexts that readily allow for the application of the PDSA cycle; the suitability of this approach in certain sectors (like healthcare) is discussed but not fully investigated.