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A generation firm in an electricity market may own multiple generators located at multiple locations. This paper generalizes the concept of transmission-constrained residual demand from a single generator's perspective to that of a generation firm. We calculate the derivative of a generation firm's inverse residual demand function, i.e., the Jacobian matrix, based on a multi-parameter sensitivity analysis of the optimal power flow solution, and characterize some of its properties. This Jacobian matrix provides valuable information, such as in characterizing a generation firm's profit maximizing strategy. We apply the bundle-Newton method utilizing the Jacobian matrix to find a generation firm's maximum profit. The effectiveness and performance of the algorithm is demonstrated with the IEEE 118-bus system example. The Jacobian matrix and the profit maximizing algorithm are helpful for market participants to bid into electricity markets, and for market monitors to analyze firm-based strategic behaviors.