costs are irrelevant here, imagine there was no tax hike, but just landlords decided to be greedy.

if they hike rents, whoever is more inelastic will eat the rent increase to the degree of her inelasticity.

the cost increase is shared between renters/landlords in the ratio of their elasticities. Whoever is more inelastic, will eat the cost.

Inealstic renters will pay up increased rent (like techbros in SF are eating up all rent increases).

Elastic renters will get up and move to Texas, if renter swill hike rent.

Elastic landlords will lever down and decrease number of low margin properties like rent-controlled properties, or unprofitable properties.

Inelastic landlords will eat the taxes and take a hit to profitability.