Optimal tax policy for single homogeneous commodity on n markets with export costs as a Stackelberg game

Taxation is one of the most powerful instruments of fiscal policy, affecting economic growth and investments, as well as competitiveness of companies. Therefore, designing the optimal tax policy is of crucial importance for any government. This study formulates the problem of determining optimal tax policy for single homogeneous commodity produced by n competing companies located in n different countries with export costs as a Stackelberg game with multiple followers. Companies produce the commodity in their country of origin and sell it on all n markets. Countries have different tax systems. If a company is selling the product in a foreign country, it has to pay export costs consisting of transportation costs and duty costs. Government of country i is the leader and makes the tax amount decision with the objective of maximizing its tax revenue. Companies are the followers. They make decisions about production and export quantities in order to maximize their profit functions. The study derives the optimal tax policy, i.e. the optimal tax amount and the optimal value of tax revenue function as well as companies' optimal production and export quantities. It discusses the properties of the tax revenue function and analyzes the effect of unit increase of taxes on optimal production and export quantities as well as on companies' revenue and profit functions. Finally, the study shows how the tax burden is divided between producers and consumers.