Maximizing Tax Revenue for Profit Maximizing Monopolist with the Cobb-Douglas Production Function and Linear Demand as a Bilevel Programming Problem

Optimal taxation and profit maximization are two very important problems, naturally related to one another since companies operate under a given tax system. However, in the literature, these two problems are usually considered separately, either by studying optimal taxation or by studying profit maximization. This paper tries to link the two problems together by formulating a bilevel model in which the government acts as a leader and a profit maximizing follower acts as a follower. The exact form of the tax revenue function, as well as optimal tax amount and optimal input levels, are derived in cases when returns to scale take on values 0.5 and 1. Several illustrative numerical examples and accompanying graphical representations are given for decreasing, constant, and increasing returns to scale values.