Optimal taxation of a perfectly competitive firm with Cobb-Douglas production function as a bilevel programming problem

The paper formulates the problem of a government maximizing tax revenue in presence of profit maximizing perfectly competitive firm as a bilevel programming problem, where the output of the firm is described by the Cobb-Douglas production function and the per-unit tax is modeled as an amount per unit product. The government collects tax on output quantity of the firm. Government is the leader and decides about tax amount with the objective of maximizing its tax revenue. Perfectly competitive firm is the follower who, given the leader's tax decision, decides about input levels and thus output quantity with the objective of maximizing the profit. The first part of the paper considers the case of the Cobb-Douglas production function of two inputs, labor and capital, and derives the optimal decision of the leader and the follower, as well as the exact form of the tax revenue function. Also, it studies the properties of the tax revenue function. This case is illustrated by two numerical examples. The model is then generalized for the case of the Cobb-Douglas production function of any number of inputs.