An elementary approach to solving the optimal taxation of a perfectly competitive firm with CES production function as a bilevel programming problem

This note presents an elementary approach to solving the problem of optimal taxation for a perfectly competitive firm with the CES production function, treated as a bilevel programming problem, using only elementary inequalities. Lukač (Cent Eur J Oper Res 31:891–909, 2023) previously formulated and solved a similar problem for a firm with the Cobb-Douglas production function using multivariable calculus. Our approach does not require any knowledge of calculus, nor does it involve the nontrivial checking necessary and sufficient optimality conditions. Moreover, we demonstrate that Lukač’s results are a special case of ours.