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# incentive compatibility

Funding and TLAC under MPOE.

1. When |$\widetilde{F} – F \geq (1-p_1+ \gamma)(1-\lambda) \overline{p}_2 V$|⁠, it is not efficient for subsidiaries to set up redundant systems. Each subsidiary issues safe short-term debt with face value |$R_1^{\text{MPOE}} = C_1^L + \lambda \overline{p}_2 V$|⁠. Required TLAC per subsidiary is given by |$F- (1+\gamma) R_1^{\text{MPOE}} = F- (1+\gamma) (C_1^L + \lambda \overline{p}_2 V)$| and is raised by the national holding company via a combination of equity and subordinated long-term debt.
2. When |$\widetilde{F} – F < (1-p_1+ \gamma)(1-\lambda) \overline{p}_2 V$|⁠, it is efficient for subsidiaries to set up redundant systems. Each subsidiary issues safe short-term debt with face value |$R_1^{\text{MPOE}} = C_1^L + \overline{p}_2 V$|⁠. Required TLAC per subsidiary is given by |$\widetilde{F}- (1+\gamma) {R}_1^{\text{MPOE}} = \widetilde{F}- (1+\gamma) (C_1^L + \overline{p}_2 V)$| and is raised by the national holding company via a combination of equity and subordinated long-term debt.
3. In both cases, each subsidiary finds it privately optimal to raise at least |$\hat{R}_{LT}^{\text{MPOE}} = C_1^H + \Delta – R_1^{\text{ MPOE}}$| of the required TLAC as subordinated long-term debt so that all fairly priced cash flows are sold to investors.
4. The subsidiaries are separated during resolution so that each subsidiary bears an effective redundancy or separation cost of |$\min [ \widetilde{F}-F,(1-p_{1}+\gamma )(1-\lambda )\overline{p}_{2}V]$|⁠.