Entry of new is the solution to any kind of price fixing. Like, if a subset of the market sets their price above the equilibrium price, then of course homes will get built because the inputs to housing construction have not changed. Price fixing literally only works if there are large barriers to entry, and for housing, the only actual barrier is zoning (you could build a code-compliant home entirely from stuff bought at big box store).

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Buts it not even that -- its that these firms are able to raise prices because they were underestimating people's willingness to pay. So that means that upzoning (ie legalizing housing more broadly) would be even more effective than we would expect because it means there is a larger gap between the cost of building and demand (in other words, the zoning tax/deadweight loss is bigger than we think).

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The city legalizes housing on the extremes, but little is done for starter size homes. By way of example, prices in my neighborhood have grown but the supply hasn't despite an abundance of lot space (approx 3x the space consumed by housing). And its not because its impossible to build 700sqft homes due to lack of supplies/labor. Its because the city fixed the quantity of housing.

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I just find it baffling that the "just legalize more housing" as a solution to a housing shortage is the most controversial take.