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# Full text (PDF) - AsRES

Full text (PDF) - AsRES

## (positive). 11 We refer

(positive). 11 We refer to this substitutes (complements) case as case S (C). We normalize the reservation utility level at 0 when the initial user lives in another dwelling in period 2. Then the maximum rent that he or she pays for the dwelling while enjoying a utility level of at least 0 can be written as v2(u, m). Suppose that the owner has no bargaining power. 12 Then, at the beginning of the second period, the owner of the housing offers q2(u, m) and the owner of the land offers γ2; i.e., the offered rent is R2 = q2(u, m) + γ2. The initial user renews the contract if the maximum rent is greater than or equal to the offered rent. Otherwise, he or she moves to other housing and obtains the reservation utility level. Hence, the efficient renewal-move condition is as follows: � F (γ ∗ 2 ) = Pr[v2(u, m) ≥ q2(u, m) + γ2] ⇒ renewal, 1 − F (γ ∗ 2 ) = Pr[v2(u, m) < q2(u, m) + γ2] ⇒ move, where F (γ2) is the cumulative distribution function (cdf) of γ2. Equation (2) implies that the tenant renews the contract if γ2 is less than or equal to γ∗ 2 , or otherwise moves to other housing in period 2. We refer to γ ∗ 2 as the critical value. From Eq. (2), we have γ ∗ 2 = γ ∗ 2(u, m) = v2(u, m) − q2(u, m). The critical value thus depends on both u and m. 2.1 Payoffs to the Owner and the User Assume that the owner and the user are both risk neutral and have the same discount factor, set at unity. Then, from Eq. (2), the utility of the user of the housing and the land is v1(u) − R1 − g(u) + � γ ∗ 2 0 (2) [v2(u, m) − q2(u, m) − γ2]f(γ2)dγ2, (3) where g(u) is the cost of utilization during period 1, in which gu > 0 and guu > 0 for all u. Consider the owner of the housing. When property rights are perfectly protected, the owner obtains q2(u, m) whether or not the initial user renews the contract in period 2. How- 11 For example, suppose that the tenant spills sauce on the carpet and the landlord cleans it up. The more sauce that is spilt, the more difficult it is for the landlord to clean it up. In this case, q2um is negative. Next, suppose that the tenant papers the walls. As Seshimo (2003) has stated, the tenant cannot enjoy the wallpaper without the wall (which is maintained well). In this case, q2um is positive. 12 See Kanemoto (1990) and Seshimo (2003) for the effect of the bargaining power of lessors and lessees on housing investment. 8

ever, property rights are not perfectly protected in tenant-owned housing. This is because the landowner and the homeowner are separated. Thus, when the lease is terminated, the landowner must compensate the homeowner for the value of the housing on the rented site. This compensation is determined by the court. We assume that it is difficult for the court to know the true value of the housing, as has been argued by Kanemoto (1990). Noting that the net rent for the homeowner in each period is rt = Rt − γt, the homeowner’s profit can be written as � γ∗ 2 r1 − c(m) + q2(u, m)f(γ2)dγ2 + 0 1 � γ2 λ γ∗ q2(u, m)f(γ2)dγ2, (4) 2 where c(m) is the cost of maintenance in period 1, in which cm > 0 and cmm > 0 for all m. The degree of property security has no effect on either owner-owned housing or landlord-owned housing because the landowner and the homeowner are the same individual. Therefore, λ = 1 in these cases. Due to imperfect delineation of property rights, however, λ > 1 in tenant- owned housing. 13 Next, we examine the profit of the owner of the land. The landowner obtains γ2 whether or not the initial user renews the contract in period 2. Therefore, the profit for the landowner is � � γ2 γ1 + γ2f(γ2)dγ2 + 1 − 0 1 � � γ2 λ γ∗ q2(u, m)f(γ2)dγ2. (5) 2 The third term is eliminated in both owner-owned housing and landlord-owned housing be- cause λ = 1. In the following sections, we consider the payoffs in each tenure mode. 2.1.1 Owner-owned housing The payoff for owner-owned housing is the sum of the user’s payoff (Eq. (3)), the homeowner’s payoff (Eq. (4)), and the landowner’s payoff (Eq. (5)). From the assumption that f(γ2) is uniform, the utility (V ) of the owner can be rewritten as max u, m VO = v1(u) − g(u) − c(m) + γ∗ 2 γ2 v2(u, m) + γ 2 − γ ∗ 2 γ 2 � q2(u, m) + γ2 + γ∗ � 2 . (6) 2 13 In 1992, a fixed-term land lease system was introduced. Under a lease with a term of 50 years or more, no request can be made to the landowner to purchase the asset on the rented site. In this case, λ = ∞. 9

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