RI tax for the mod gods. Again /u/JustTaxLandLol is just the one that happens to have finally pushed me over the edge to write this, but my response is because this is a common sentiment. u/onetrillionamericans might also be interested.

My excel art wasn't met with as great reviews as I hoped so it is back to MSPaint we go. Although I will borrow the first two plat layouts of 50' front lots and 100' front lots from my previous post on the relationship between density and infrastructure.

The third image above illustrates a linear rent gradient in a linear city 1 mile wide with 100' lots that will stretch 24 miles in two directions from the city center in order to contain 100,000 households. The equilibrium condition in a city like this is that total land commute cost must be equivalent at every point on the gradient. With ag land at $1,000/acre (~0 for our lots), average wages of $30/hour and a federally funded freeway designed to provide free flow 60mph speeds during the peak hour the annual travel cost at the agricultural fringe = 24 miles * 2 back and forth * $30/hour / 60 miles/hour=$24/day. At a 5% discount $24/day for 40 years has a present value of $151.486.01 ~ $150k. When faced with an amenity/job that is worth locating in the city the a consumer should be indifferent between locating at the urban fringe on a $250 lot or paying $150k to be located just outside downtown. The fourth image above adds the same rent gradient if instead of 100' lots the lots were 50'. The same calculation gets us a peak land value of $75k.

RESTRICTIONS ON DENSITY ARE RESTRICTIONS ON PROXIMITY AND THE REASON LAND IS VALUABLE IN CITIES IS BECAUSE THERE IS SOMETHING PEOPLE WANT TO BE CLOSE TO. IF YOU ALLOW MORE PEOPLE TO BE CLOSE TO IT THE VALUE OF PROXIMITY FALLS

But don't we find that upzoning a parcel increases the value of that parcel?

For example, its been a while since I read the paper but, if memory serves Yonah Freemark essentially found that spot upzoning was perfectly capitalized in land prices. If that applied in my example we would expect to see all land values double instead of fall by half. What's the difference?

The spot upzoning. The fifth image above illustrates the impact of a spot upzoning of a single 100' parcel 6 miles from the city center two two 50' parcels 6 miles from the city center. The city extent (the ~24 miles) would shrink by 24/100000 to 23.99976. Due to the shorter maximum commute distance all remaining 100' parcels would fall in price by $1.50 but now this lucky land owner has two parcels where there used to be one. The previous value of the single 100' lot was $113,614.51 and now they have two lots. So far we've abstracted away the value of land, all that is needed by our consumers is a lot/location, which is essentially what literature following Glaeser and Gyuorko's zoning tax utilizes to measure the real impacts of zoning. So, under my model, this spot upzoning would exactly match Yonah's findings, the two lots should be able to be sold for exactly twice (the original price minus $1.50), in reality it will be even slightly more lower because there is some extra value in having a 10,000 square foot lot but as the zoning tax literature shows there is a significant spread between average and marginal land values under zoning. Even in the real world, two lots will be significantly more valuable than 1/2 the original price of the one lot. But, that is precisely because the rest of the lots remained zoned at 100'.

IF WE HAD A WIDESPREAD REMOVAL OF ALL RESIDENTIAL DENSITY REGULATIONS (AND THE IMPLICIT RULES BACKED INTO THE REST OF OUR URBAN PLANNING REGULATIONS) WE WOULD SEE PRICE FALL FOR ALL LAND AND ALL HOUSING TYPES THROUGHOUT THE WHOLE EXTENT OF THE CITY.

What if instead we accidently made some of our cities better places to live?

The sixth graph at the imgur link above illustrates the equilibrium condition for city population, with the C1 an C2 illustrating increased costs due to zoning, from an older RI. As we lower the artificially high sum of land and travel costs this will induce more people to move to the city allowing the capture and creation of continuing increases in agglomeration benefits that we find in larger cities. It may end up that a city that allows itself to grow eventually reaches a point where its future land prices are higher than artificially lower land prices under constraints when the city was smaller. But, that would only be because we are also significantly higher on that upward sloping benefits curve too.