Profit
Profit is given by:
where: C(X) = Total Cost, R(X) = Revenue, p = Price
Profit maximization is:
Maximizing the Profit of Stackelberg and Cournot Power Systems
Both models are used to analyze two supply/demand outputs two power system firms. In those models the companies influence each others supply/demand and price.
Thus the price of firm 1 is influenced by supply/demand of firm 2:
where: a and b are constants
The cost functions equal to:
where: F = Fixed cost, c is a constant
Then the profit of firm 1 will equal to:
In Stackelberg model it is assumed that firm 2 follows firm 1 according to reaction function:
Then maximized profit will equal to:
From equation above:
From reaction function:
In Cournot model the supply/demand of firm 1 is equal to supply/demand of firm 2. Therefore:
References
Operation of Market-oriented Power Systems, Yong-Hua Song, Xi-Fan Wang, 2003.