land value tax discussion with jeremiah johnson
Jeremiah Johnson once commented to me that he felt land value tax (l.v.t.) has not just neutral but negative deadweight loss, in contradiction to this discussion i had with economist nicolaus tideman. jeremiah’s argument was essentially that being forced to pay the tax would make the property owner more productive with the land, because it would increase the marginal utility of his dollars, thus incentivizing him to develop the land — or sell it to someone who would.
i get that this seems intuitively true, but it’s based on a fundamental economic fallacy. time (or “leisure”) is a resource. you could even think of this more abstractly as the freedom — to not work on a project you don’t want to work on — is a “resource”. if the landowner converts his precious time (call it “leisure” if you like) into development activity that results in something he values less than the leisure, then that’s a decrease in productivity, not an increase — by definition.
i enlisted gemini to help construct the following simple example, with a minimal set of two resources: leisure and buildings.
Simplified Scenario (Buildings and Years):
- Utility function: U(L, B) = log₂(L + 1) + log₂(B + 1)
- Building one building takes one year.
- Initial situation: The person has 4 years of leisure (L=4) and 4 buildings (B=4).
Scenario 1: Initial Endowment
The person starts with 4 years of leisure (L=4) and 4 buildings (B=4). Their utility is U(4, 4) = log₂(5) + log₂(5) ≈ 2.32 + 2.32 = 4.64.
Scenario 2: Buildings Removed, Then Optimization, Then Buildings Returned
- Buildings Removed: Two buildings are taken away. The person now has L=4 and B=2. Their utility is U(4, 2) = log₂(5) + log₂(3) ≈ 2.32 + 1.58 = 3.9.
- Optimization: The person has 4 years of leisure. They can spend 0, 1, 2, 3, or 4 years building.
- Spend 0 years building: L=4, B=2. Utility remains at 3.9.
- Spend 1 year building: L=3, B=3. Utility becomes U(3, 3) = log₂(4) + log₂(4) = 2 + 2 = 4.
- Spend 2 years building: L=2, B=4. Utility becomes U(2, 4) = log₂(3) + log₂(5) ≈ 1.58 + 2.32 = 3.9
- Spend 3 years building: L=1, B=5. Utility becomes U(1,5) = log₂(2) + log₂(6) ≈ 1 + 2.58 = 3.58
- Spend 4 years building: L=0, B=6. Utility becomes U(0,6) = log₂(1) + log₂(7) ≈ 0 + 2.81 = 2.81
The optimal choice after the buildings are removed is to spend 1 year building, reaching a utility of 4.
- Buildings Returned: The two original buildings are given back. The person now has L=3 (because they spent a year building) and B=4. Their utility is U(3,4) = log₂(4) + log₂(5) ≈ 2 + 2.32 = 4.32
they end up with only 4.32 utils. whereas if they had not built the additional building, their utility would have remained at 4.64. this was a loss! sure, the ostensible value appears to be greater — 5 buildings versus 4. but hidden from that calculus is the value of the landowner’s time.
explanation:
- why do i take away buildings? because i want to simulate the effect of the tax revenue taken away as l.v.t. the cash payments you make are effectively like giving up consumption of other resources. the whole point is that when those are taken away, that increases the marginal utility of those resources relative to the marginal utility of leisure, and that’s the whole reason the landowner then wants to develop the land in the first place. but i don’t need to complicate the example with a third or fourth resource, when the buildings themselves can serve the purpose.
- why do I return the buildings? because! — the point of jeremiah’s argument wasn’t about equity effects, but about allocative efficiency effects. redistributing land rents as e.g. universal income already addresses equity.
- the landowner did choose to reallocate their leisure (spend one year building) to partially compensate for the loss, but they could not fully recover their original utility.
- therefore, there was no increase in “productivity.” The change in behavior (building) was a response to a loss, and even with that response, the person is worse off than they were originally. returning the buildings restores the original number of buildings, but not the original utility. this was a net loss in productivity because we converted leisure (or “freedom”) into buildings that had lower marginal utility.