# incentive compatibility

**Funding and TLAC under MPOE.**

- 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.
- 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.
- 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.
- The subsidiaries are separated during resolution so that each subsidiary bears an effective redundancy or separation cost of |$\min [ \widetilde{F}-F,(1-p_{1}+\gamma )(1-\lambda )\overline{p}_{2}V]$|.