Technical Appendix for “ Willpower and Personal Rules ”

Pooling: q1 = 1. Then ρ2 = ρ1, while ρ − 2 can be any ρ 0 ≤ ρ. Optimality in (3) then requires ρ1 ≥ ρ∗2 > ρ0, otherwise the right-hand side would be zero. Let therefore ρ1 > ρ∗2 (leaving aside the measure-zero case where ρ1 = ρ ∗ 2). Given that c/βL < C(λ), this is indeed an equilibrium. Semi-separation: q1 ∈ (0, 1). This implies ρ2 ∈ (ρ1, 1) and ρ2 = 0. Furthermore, (3) must now hold with equality, c/βL = B − b+ δλ £ V L 2 (ρ + 2 )− a ¤ . This can only occur if