Adam Gray/Bloomberg via Getty Images This post originally appeared in the Business Insider Today newsletter. You can sign up for Business Insider's daily newsletter here . The city that never sleeps wants to put its high prices to rest. Addressing New York's affordability problems was a pillar of Zohran Mamdani's mayoral campaign. Now that he's in office, those promises are being tested. Three of his proposals — free buses, universal childcare, and a rent freeze — have been rolled out in other cities. BI's Juliana Kaplan broke down the previous successes (or failures) of the affordability plans to gauge what New Yorkers can expect. To fund these efforts, Mamdani is pushing to tax the city's richest residents ( or sometimes residents ). That's not entirely up to him, as those decisions are mostly handled at the state level, but he's made some progress. Gov. Kathy Hochul unveiled plans to tax property owners who primarily live outside NYC but have a local home worth over $5 million .…