Mayor Eric Adams, chief among Democratic nominee Zohran Mamdani's detractors, quickly undercut Mamdani's ambitious policy agenda after the socialist declared victory in New York City's mayoral primary last Tuesday, arguing Mamdani does not have authority to deliver key campaign promises as mayor."Hes a snake-oil salesman," Adams said of Mamdani on "Fox & Friends." "He would say and do anything to get elected."The 33-year-old democratic socialist, who was born in Uganda and would be New York City's first Muslim mayor if elected this November, has a laundry list of radical campaign promises readily available on his website. Those promises include freezing the rent, city-owned grocery stores, free buses, free childcare, raising corporate taxes and increasing the minimum wage.CITY-RUN GROCERY STORES, DEFUNDING POLICE, SAFE INJECTION SITES: WHAT TO KNOW ABOUT NYC'S NEXT POTENTIAL MAYORMamdani triggered a political earthquake with his decisive Democratic primary win last week as Republicans and moderate Democrats criticized his socialist policies and accused him of being antisemitic. His opponents have claimed that Mamdani does not have the authority to deliver many of his campaign promises. The reality is a little more complicated.ERIC ADAMS WARNS ZOHRAN MAMDANI IS A 'SNAKE-OIL SALESMAN' AFTER DEM SOCIALIST'S NYC MAYORAL PRIMARY WIN"As Mayor, Zohran will immediately freeze the rent for all stabilized tenants, and use every available resource to build the housing New Yorkers need and bring down the rent," according to Mamdani's campaign website.Mamdani has accused Adams of appointing Rent Guidelines Board members to raise rents on stabilized apartments. While landlords and advocates argue the freeze would be illegal, Mamdani can accomplish this goal by appointing members to the board who wouldn't vote to increase the rent.Former Mayor Bill de Blasio's board voted to freeze the rent three times during his tenure.Former Gov. Andrew Cuomo, who lost the primary to Mamadani, called the socialist's plan to freeze rent "politically convenient posture," and said such a move would hurt landlords who would be "unable to maintain their buildings."Mamdani has committed to creating a "network of city-owned grocery stores focused on keeping prices low, not making a profit.""Without having to pay rent or property taxes, they will reduce overhead and pass on savings to shoppers. They will buy and sell at wholesale prices, centralize warehousing and distribution, and partner with local neighborhoods on products and sourcing," Mamdani has promised.The mayor of New York City has control over city-run programs, so he can accomplish this goal by securing New York City Council approval. Other cities have implemented similar programs.John Catsimatidis, Owner of Gristedes and DAgostinos, the largest independent supermarket chain in New York City, held a rally this week protesting Mamdani's proposal, calling it a "direct threat to the jobs, dignity, and livelihoods of the tens of thousands of hardworking New Yorkers who keep our city fed every single day."Mamdani has vowed to "permanently eliminate the fare on every city bus and make them faster by rapidly building priority lanes, expanding bus queue-jump signals, and dedicated loading zones to keep double parkers out of the way."This proposal would require coordination with the Metropolitan Transportation Authority (MTA). MTA is a state-run agency, which the mayor of New York City does not have direct control over.According to City & State New York, Mamdani's free bus fare promise would require an additional expense, possibly more than $700 million. It's unclear how Mamdani plans to pay for the additional fee."Zohran will implement free childcare for every New Yorker aged 6 weeks to 5 years, ensuring high quality programming for all families," according to Mamdani's campaign website.This would likely require a series of steps, including sign-off from state legislators in Albany, as reported by Bloomberg. Mamdani has floated a tax increase on the wealthiest New Yorkers and corporations to pay for the increased services, which would require state-level approval.New York Gov. Kathy Hochul has vocalized her opposition to tax hikes, which could create some hurdles for Mamdani. However, Hochul pushed for an increase in the state's child tax credit earlier this year, and she has nearly doubled funding for state-subsidized child care programs to about $2 million, according to The New York Times.Mamdani said he will fund his programs through a "revenue plan" that would "raise the corporate tax rate to match New Jerseys 11.5%, bringing in $5 billion. And he will tax the wealthiest 1% of New Yorkers those earning above $1 million annually a flat 2% tax."While Mamdani has certainly done the math, a plan like this requires approval from the state legislature and the signature of the governor.As Hochul doubles down on her opposition to tax hikes, Mamdani could face some roadblocks in delivering this marquee campaign promise, as reported in The New York Times."As Mayor, Zohran will champion a new local law bringing the NYC wage floor up to $30/hour by 2030. After that, the minimum wage will automatically increase based on the cost of living and productivity increases," Mamdani claims on his campaign website.It's unclear if the mayor has that power.By allowing the City Council to create its own minimum wage law, Mamdani has proposed a way to raise the minimum wage in New York City without the state's approval.But a state-level increase is unlikely, since a similar effort by the state legislature to raise the minimum wage statewide to $21.25 failed to garner much support, as reported by The New York Times.Bill Ackman, the billionaire founder of Pershing Square Capital Management, said on X, "His policies would be disastrous for NYC. Socialism has no place in the economic capital of our country."Mamdani did not immediately respond to Fox News Digital's request for comment.