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[0 ¯γ2], where 0 < ¯γ2. 10
In each period, the landowner offers the homeowner a rent γt, and the homeowner offers
the user of the land a dwelling rt. At the beginning of period 1, the owner and the user make
a one-period lease contract. The tenancy terminates at the end of period 1. In the second
period, rent is offered by the owner, and the initial user decides to either continue to rent
or to move at the beginning of period 2. Before examining this, we consider the relationship
between q2 and v2.
If the utilization rate is 0, or in other words, if the initial user does not add any investment
during period 1, it is plausible that the second-period user’s utility from the housing equals
the social evaluation q2. However, since q2u < 0 (u only benefits the initial user), if u > 0,
the second-period user’s utility v2 from the housing exceeds the social evaluation. Thus,
Furthermore, assume that
∀m v2(u, m) ≥ q2(u, m) if u ≥ 0.
∃γ ′ 2 ∈ (0 ¯γ2] v2(u, m) < q2(u, m) + γ ′ 2.
This implies that the second period user’s utility can be less than the second period value of
the land with a dwelling, if we consider the random variable γ2.
We also assume that
∀u, m v2m = q2m. (1)
This assumption implies that the marginal utility of m for the initial tenant is equivalent to
the marginal social evaluation of m for all u and m.
In our model, the sign of the cross-partial derivatives of v2(u, m) and q2(u, m) are of
critical importance, because these signs determine the type of strategic interaction between
the inputs of owners and users. From the assumption Eq. (1), v2um must equal q2um; i.e.,
v2um = q2um. Therefore, if v2um is 0, then q2um is also 0(positive), then q2um is negative
10 The effects of the rental externality on housing quality do not depend on the functional form of the pdf.
The effects of tenure security on housing quality, however, do depend on this simplifying assumption.
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