The data is here: https://fred.stlouisfed.org/series/AUST448BPPRIVSA.
Assume austin is only half as bad as LA, a 25% rent decrease would be incredible
Gruber's paper: https://evansoltas.com/papers/Permitting_SoltasGruber2026.pd...
That is not what Gruber shows. The 50% figure is that there's a permit adds a 50% premium on the value of raw land. In other words, the permit cost is "only" 33% of the cost of the permitted raw land. That's significant and a big problem, but very very far from "50% of on LA home's price."
But yeah structurally the solution is indeed to reduce the cost of production. Which if your 50% figure was correct, would be huge. But it's not correct.