When considering such economic phenomenon as an export, the producers of the exported goods, the participants in production within the country, consumers within the country and abroad, the state with its customs and tax services and other economic agents may come into the view. This paper considers one (generalized) producer of the good, households as consumers within the country and the government that sets the export duty and manages the export income. The price outside the country is considered to be constant, i. e. does not depend on the volume of exports. Since the interests of these participants in the production, distribution and consumption of this good are very different and often uncertain, the standard way would be to build a Pareto-optimality region and allocate some strategy in it as a solution. We made an attempt to estimate the boundary of the Pareto-optimality domain but managed to construct only some of its inner part, and the function, the largest value of which indicates an acceptable equilibrium, was too complex for analytical solutions. This prevented the use of such a well-known approach as the Nash arbitration solution. As a result, we proposed a method that gives the best export duty from the point of view of the government, which uses the income to expand production, which will give a profit to both producers and households in the form of a decrease in domestic prices. We specifically did not consider any particular product because the restrictions defined by Customs laws are very diverse both in countries and in products. The paper presents one example with illustrative data and one - with real volumes of production and export of wheat from the Russian Federation.