RDP 2009-02: Competition Between Payment Systems Equation (11)

\begin{array}{l} Π_{i} = C D_{i}^{c} (f_{i}^{c} - g_{i}) + C M (D_{i, ~ j}^{c} + D_{i, j; i}^{c}) D_{i}^{m} (f_{i}^{m} - c_{i}) \\ + C M D_{i, j; j}^{c} D_{i, ~ j}^{m} (f_{i}^{m} - c_{i}) \\ = C D_{i}^{c} (f_{i}^{c} - g_{i}) + C M [D_{i}^{c} D_{i}^{m} - D_{i, j; j}^{c} D_{i, j}^{m}] (f_{i}^{m} - c_{i}) . \end{array}