Absentee ownership, land taxation and surcharge

Abstract

This paper studies the efficiency of land taxation in a system of jurisdictions with absentee ownership of land. The government of a jurisdiction exploits absentee owners and overtaxes land. Hence, even if land taxation does not distort the use of land, it distorts the allocation of resources between the private and public goods, creating an efficiency loss. If individuals choose their land ownership by trading it in the asset market, they do not necessarily choose an efficient ownership. The government of a jurisdiction also imposes an absentee owner surcharge, reducing the return to absentee ownership and eliminating absentee ownership. Surcharges thus improve the efficiency of land taxation in the long run.

Appendix

1.1 Proof of $\theta _{ii}^* = 1$ and $\theta _{ji}^* = 0$ in Proposition 4

The inequality constraints for a resident of jurisdiction i are $\theta _{ii} \in [0, 1]$ and $\theta _{ij} \in [0, 1],$ so the maximization problem in (22) and (23) becomes

$$\begin{aligned} V_i(c_i) + U_i(x_i, z_i) + \gamma _{ii} \theta _{ii} + \delta _{ii} (1 - \theta _{ii}) + \gamma _{ij} \theta _{ij} + \delta _{ij} (1 - \theta _{ij}). \end{aligned}$$

(37)

$\gamma _{ii}$ is the nonnegative multiplier associated with the constraint $\theta _{ii} \ge 0$, and $\delta _{ii}$ is the nonnegative multiplier associated with the constraint $\theta _{ii} \le 1$, and similarly for $\gamma _{ij}$ and $\delta _{ij}.$ The FOCs with respect to $\theta _{ii}$ and $\theta _{ij}$ are

$$\begin{aligned} \frac{\mathrm{d}W_{i}}{\mathrm{d}\theta _{ii}}= & {} U_{i}^{x}[(f_{i}' - \tau _{i})m_{i} - r p_{i}m_{i}] + \gamma _{ii} - \delta _{ii} = 0, \end{aligned}$$

(38)

$$\begin{aligned} \frac{\mathrm{d}W_{i}}{\mathrm{d}\theta _{ij}}= & {} U_{i}^{x}[(f_{j}' - \tau _{j} - \tilde{s}_{j})m_{j} - r p_{j}m_{j}] + \gamma _{ij} - \delta _{ij} = 0, \end{aligned}$$

(39)

and the complementary slackness conditions are

$$\begin{aligned} \gamma _{ii}\theta _{ii} = 0,\;\; \delta _{ii}(1 - \theta _{ii}) = 0,\;\;\gamma _{ij}\theta _{ij} = 0,\;\; \delta _{ij}(1 - \theta _{ij}) = 0. \end{aligned}$$

(40)

For a resident of jurisdiction j, the maximization problem becomes

$$\begin{aligned} V_j(c_j) + U_j(x_j, z_j) + \gamma _{ji} \theta _{ji} + \delta _{ji} (1 - \theta _{ji}) + \gamma _{jj} \theta _{jj} + \delta _{jj} (1 - \theta _{jj}), \end{aligned}$$

(41)

and the FOCs and the complementary slackness conditions are

$$\begin{aligned} \frac{\mathrm{d}W_{j}(x_{j},z_{j})}{\mathrm{d}\theta _{ji}}= & {} U_{j}^{x}[(f_{i}' - \tau _{i} - \tilde{s}_i)m_{i} - r p_{i}m_{i}] + \gamma _{ji} - \delta _{ji}= 0 \end{aligned}$$

(42)

$$\begin{aligned} \frac{\mathrm{d}W_{j}(x_{j},z_{j})}{\mathrm{d}\theta _{jj}}= & {} U_{j}^{x}[(f_{j}' - \tau _{j})m_{j} - r p_{j}m_{j}] + \gamma _{jj} - \delta _{jj} = 0, \end{aligned}$$

(43)

$$\begin{aligned} \gamma _{ji}\theta _{ji}= & {} 0,\;\; \delta _{ji}(1 - \theta _{ji}) = 0,\;\;\gamma _{jj}\theta _{jj} = 0,\;\; \delta _{jj}(1 - \theta _{jj}) = 0. \end{aligned}$$

(44)

To show that $\theta _{ii}^* = 1.$ Suppose to the contrary that $\theta _{ii} < 1.$ Then, $\delta _{ii} = 0$ by (40). Since $\theta _{ii} + \theta _{ji} = 1,$$\theta _{ji} > 0$ and hence $\gamma _{ji} = 0$ by (44). Since $\gamma _{ii} \ge 0,$ (38) with $\delta _{ii} = 0$ implies $f_{i}' - \tau _{i} \le rp_i.$ Since $\delta _{ji} \ge 0,$ (42) with $\gamma _{ji} = 0$ implies $f_{i}' - \tau _{i} - \tilde{s}_i \ge rp_i$, so $f_{i}' - \tau _{i} > rp_i$, a contradiction to the earlier inequality $f_{i}' - \tau _{i} \le rp_i.$ Thus, $\theta _{ii}^* = 1,$ and hence $\theta _{ji}^* = 0.$