Ramsey meets Thünen: the impact of land taxes on economic development and land conservation

Abstract

Land taxes can increase production in the manufacturing sector and enhance land conservation at the same time, which can lead to overall macroeconomic growth. Existing research emphasizes the non-distorting properties of land taxes (when fixed factors are taxed) as well as growth-enhancing impacts (when asset portfolios are shifted to reproducible capital). This paper furthers the neoclassical perspective on land taxes by endogenizing land allocation decisions in a multi-sector growth model. Based on von Thünen’s observation, agricultural land is created from wilderness through conversion and cultivation, both of which are associated with costs. In the steady state of our general equilibrium model, land taxes not only may reduce land consumption (associated with environmental benefits) but may also affect overall economic output, while leaving wages and interest rates unaffected. When labor productivity is higher in the manufacturing than in the agricultural sector and agricultural and manufactured goods are substitutes (or the economy is open to world trade), land taxes increase aggregate economic output. There is a complex interplay of conservation policy, technological change and land taxes, depending on consumer preferences, sectoral labor productivities and openness-to-trade. Our model introduces a new perspective on land taxes in current policy debates on development, tax reforms as well as forest conservation.

Appendix: Unit versus ad-valorem taxes on land

In this section we consider two forms of land value taxes. The first applies to the price of land p and the second to the price of land net of transportation cost. As we do not model spatial land price differentials explicitly, the latter land price net transportation costs would be more comparable to land prices observed on land markets.

1.1 Tax on land price

Considering an ad-valorem tax on land $\tau _A$, the profit function of the land owner (8) reads

$$\begin{aligned} \pi ^H&= p(1-\tau _A) A + q(A)H \end{aligned}$$

(44)

The equation of motion for the state variable (10) becomes

$$\begin{aligned} \dot{\lambda }= r \lambda - (p(1-\tau _A) + q'(A)H - \theta ) \end{aligned}$$

(45)

which leads to the modified steady-state equation for the land allocation (31)

$$\begin{aligned} p^A \phi ^A F_A - k'(A)&= \frac{-\rho q(A) + \theta }{1-\tau _A} \end{aligned}$$

(46)

Equivalence between the unit tax $\tau$ in (31) and the ad-valorem tax $\tau _A$ in (46) holds if

$$\begin{aligned} \tau&= \frac{\tau _A}{1-\tau _A} (-\rho q(A) + \theta ) \quad \text {or} \end{aligned}$$

(47)

$$\begin{aligned} \tau _A&= \frac{\tau }{-\rho q(A) + \tau + \theta } \end{aligned}$$

(48)

Hence, for each ad-valorem tax $\tau _A$, it is possible to calculate the equivalent unit tax $\tau$ which gives the same allocation in the steady state using (52). Contrary for each unit tax $\tau$, the equivalent ad-valorem tax $\tau _A$ can be calculated using (48). Although the transformation of unit taxes into ad-valorem taxes (and vice versa) is nonlinear, it is increasing and monotone as long as $\tau _A<1$ and $\tau , \tau _A>0$ (note that $q(A)<0$ by assumption). Hence, the comparative static analysis on the sign of the impact of land tax changes holds equally for unit and ad-valorem taxes.

1.2 Tax on land price net of transportation costs

Considering an ad-valorem tax on land $\tau _B$ net of transportation costs, the profit function of the land owner (8) reads

$$\begin{aligned} \pi ^H&= p(1-\tau _B) A + q(A)H + k(A)\tau _B \end{aligned}$$

(49)

The equation of motion for the state variable (10) becomes

$$\begin{aligned} \dot{\lambda }= r \lambda - \left( p(1-\tau _A) + k'(A)\tau _B + q'(A)H - \theta \right) \end{aligned}$$

(50)

which leads to the modified steady-state equation for the land allocation (31)

$$\begin{aligned} p^A \phi ^A F_A - k'(A)&= \frac{-\rho q(A) + \theta + k'(A)\tau _B}{1-\tau _B} \end{aligned}$$

(51)

Equivalence between the unit tax $\tau$ in (31) and the ad-valorem tax $\tau _A$ in (51) holds if

$$\begin{aligned} \tau&= \frac{\tau _A}{1-\tau _A} \left( -\rho q(A) + \theta + k'(A)\tau _B\right) \end{aligned}$$

(52)