Π S � ˜γ2 1 m = γ2 α + γ � 2 − ˜γ2 q2m + γ2 ˜γ2m � � 1 − 1 (˜γ2 + q2) − cm = 0, (24) γ2 α respectively. We obtain the reaction function uS L (m, α) from Eq. (23), and mS L (u, α) from Eq. (24). The equilibrium is the intersection point of uS L (m, α) and mS L (u, α), and is denoted by (u S L , mS L ). 4 Housing Quality Because owner-owned housing internalizes all payoff functions, the equilibrium input levels, uO and mO, are efficient solutions. Therefore, we set q2(uO, mO) as benchmark quality, and compare this with the quality of tenant-owned housing and landlord-owned housing. 4.1 Tenant-Owned Housing First, we compare the first-order condition of owner-owned housing with that of tenant-owned housing to investigate the impact of the rental externality on housing quality. Comparing Eq. (7) with Eq. (10), we have uO(m) < uT (m) for all m, given ˇγ2 > γ ∗ 2 and λ > 0. The tenant over-utilizes the housing because he or she cannot capture its residual value. Second, comparing Eq. (7) with Eq. (18), we have uO(m) < u S T (u, α), given αˇγ2 > γ ∗ 2 and λ > 0. This comparison incorporates both the effects of the rental externality and tenure security on housing quality. We refer to this overall effect as the total effect. Third, we can determine the effect of tenure security by comparing Eq. (10) with Eq. (18). This shows that tenant utilization varies ambiguously in relation to tenure security. That is, the strengthening of tenure rights by tenancy rent control tends to increase over-utilization of the dwelling by the tenant. However, this behavior reduces compensation when the lease is terminated. Considering this, the tenant utilizes the dwelling responsibly. Consider the level of m. Comparing Eqs. (8) and (11) with Eq. (19), we have mO(u) > m S T (u, α) > mT (u) for all u, given ˆγ2 > γ ∗ 2 and λ > 0. This result is consistent with Kanemoto (1990). The inequality mO(u) > mT (u) implies that the tenant under-supplies m because the property rights are not perfectly protected. Because mO(u) > mS T (u, α), the 14

total effects reduce m. However, the effect of tenure security raises the marginal benefit of m, and consequently increases tenant investment. Therefore, m S T (u, α) > mT (u). ¿From the above analysis, we obtain the following propositions. Proposition 1 (i) In case I, uO < uT , uO < u S T , uT ⋚ u S T and mO > m S T > mT . In case S, uO < uT , uO < uS T , uT ⋚ uS T , mO > mT , mO > mS T , and mT ⋚ mS T . Thus, we have q2(uO, mO) > q2(uL, mL), q2(uO, mO) > q2(u S T , m S T ), q2(uT , mT ) ⋚ q2(u S T , m S T ) (25) in these cases. (ii) In case C, uO ⋚ uT , uO ⋚ u S T , uT ⋚ u S T , mO ⋚ mT , mO ⋚ m S T , mT ⋚ m S T . Thus, the ranking of quality is ambiguous in case C. Figures 1 and 2 illustrate cases I and S, respectively, where EO is the Nash equilibrium for owner-owned housing. Because uO(m) < uT (m) and mO(u) > mT (u), the Nash equilibrium for tenant-owned housing without tenure security is in the gray area, e.g., ET . We find that double moral hazard occurs in these cases. Figure 3 illustrates case C. In this case, the Nash equilibrium is in the gray area, e.g., ET . Because tenure security shifts the reaction curve for m between mT (u) and mO(u), the Nash equilibrium for tenant-owned housing with tenure security is in the gray area between mT (u) and mO(u). 4.2 Landlord-owned housing [Figs. 1–3 insert here] Consider next the quality of landlord-owned housing. First, compare Eq. (7) with Eq. (14). Because q2u < 0, the marginal benefit of u is larger in Eq. (14) than in Eq. (7) while the marginal costs are the same. Hence, uO(m) < uL(m) for all m. That is, the tenant ignores the rental externality and has an incentive to over-utilize the rental housing. This result is consistent with Henderson and Ioannides (1983). Second, comparing Eq. (14) and Eq. (23) indicates that uL(m) < u S L (m, α) for all m, given ˜γ2 > γ ∗ 2 and α > 1. That is, the marginal profit of u is increased by tenure security. This result is consistent with Seshimo (2003). Therefore, uO(m) < uL(m) < uS L (m, α). 15