Different structures of lignite mines and power plants, that occure on the Polish market as a result of its transformation and the privatisation, were discussed. The attention is focused on the fact that the practice is overtaking the theory because there is a lack of models of functioning of such structures. A model of cooperation between the mine and the power plant was worked out for the established amount of coal, what reflects the situation of a particular ultimate pit choice (in a long run) or realization of supplies of the constant amount of lignite in frames of the long-term contract (in a short run e.g. one of year). It is proposed to treat a negotiation of the lignite price as a constant sum game and a lignite price as the determinant of the total profit division. The choice of lignite price between prices outlining breakeven points of the mine and the power plant determines the distribution of the profits to both sides. It is similar to the contract curve in the classical bilateral monopoly model. Ten different methods of the profit division are proposed. Argumentation for proposed solutions was presented favouring the proposal of equal profit margins calculated without the costs of fuel purchase.