Theoretical Aspects Regarding the Optimal Taxation of Effort With More Conditions

In this article, the authors propose to conduct a pertinent analysis of the use of mathematical models in relation to optimal effort taxation. The effort taxation must be a balance between allocative efficiency and distribution. It is a question of determining the optimal tax level for three conditions. The theory is that the shift to a fixed amount, a single share, is not feasible for wage compensation, being important to note that this condition is one that must be considered. The mathematical model proposed by the authors regarding optimal taxation of multi-condition effort is relevant and suggestive for the analysis. It is well known that, in order to increase tax revenue, they must inevitably be based on the unobservable variant, which is the potential gain or, most importantly, on the individual productivity of labor. Solving a problem of this sensibility, such as the optimal taxation of multi-state effort, needs to be analyzed and conditioned by the establishment of a mathematical-econometric model that highlights both the aspects of a minimum expectation threshold or a situation that depends on the economic outcome. The authors consider the existing variants and establish variants based on a mathematical model that is analyzed to best answer the problem of the adverse selection ie the balance between allocation efficiency and distribution. We analyze the optimization problem from Lagrange’s function and associated multiplier, highlighting the mathematical functions that can be used. Further, the authors consider the case of adverse selection based on asymmetric information. For the objective function and budget constraint, the authors consider that they need to add incentive restrictions, especially when they are taxed on income. By analyzing this hypothesis in depth, the authors propose and demonstrate a mathematical function that best suits these adjustment needs and solve the adverse selection. The way in which the authors suggest and demonstrate the implementation condition that is equivalent to the assertion that the plurality of admissible solutions is unclear gives a solution perspective applicable in most cases. The authors propose, by synthesizing, conditions (sentences) that demonstrate that the model used is one that must be considered and can be successfully used in optimal taxation of the multi-state effort. In the explanatory approach, it is also appreciated that the combination of the Kuhn-Tucker multipliers of the two constructions can determine the Lagrange function. This feature built by all Kuhn-Tucker multipliers is strictly positive and the level of effort is optimal given by a series of equalities that imply a final aspect of its use.