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> How does prop 13 cause a housing crisis?

Because it heavily discourages people from selling their houses, reducing turnover and with it the potential for redevelopment.

Without prop 13, houses would be re-assessed every few years. The owners' taxes would increase (or decrease) as the value of their home changed. If property values increased enough, the taxes would encourage them to sell the property for a tidy sum and move someplace cheaper. A new buyer is much more likely to demolish and redevelop than the existing owner.