By CARA BUCKLEY 
The mayor’s office is urging Gov. David A. Paterson to veto a bill that would offer greater rent relief to 11,000 New York City residents with H.I.V. or AIDS, saying the measure would tax the city’s strained budget.
The bill, which was passed by the State Senate on Tuesday and the Assembly in January, would mean that low-income people receiving housing assistance from the city’s H.I.V./AIDS Services Administration  would be required to spend no more than 30 percent of their income on rent. Despite the city’s current subsidy, many beneficiaries of the program still spend more than half of their income on rent.
The office of Mayor Michael R. Bloomberg, which sent a memo to senators in January opposing the bill, said that the city would spend $150 million on the program this fiscal year, and that the new measure would cost it an additional 10 percent.
Yet paying more toward low-income tenants’ rent would result in fewer evictions and fewer placements in emergency housing, both of which are expensive, according to Senator Tom Duane, the Democrat from Manhattan who sponsored the bill.
The state sets the policy for the H.I.V./AIDS housing assistance program, the city administers it, and they share funds for it. Under current regulations, people who are enrolled in the program and who receive income from Social Security, federal disability payments or wages must pay all but $344 of their income in rent.
Sean Barry, director of the NYC AIDS Housing Network,  a community organizing group that represents many of the program’s clients, said beneficiaries often pay upward of 60 percent of their income in rent. Among them is Wanda Hernandez, of the Bronx, who is on the board of Mr. Barry’s organization.
Ms. Hernandez, 48, learned she was H.I.V.-positive 15 years ago, and was later hobbled by chronic pain and carpal tunnel syndrome. She spends about $750, the bulk of her federal disability income, on her $1,085-a-month, one-bedroom apartment. Under the bill, the program would cover about $750 of her rent.
Living on the roughly $350 a month left over required scrimping on subway and bus travel, visiting food pantries and cutting out toiletries, she said. Sometimes, sympathetic neighbors leave bags of used clothing at her door. “I’ve been getting by on pennies,” she said.
Mr. Barry said the vast majority of the program’s housing assistance recipients live on some form of public assistance. But Jessica Scaperotti, a spokeswoman for the mayor, said the bill set an “expensive precedent” by basing the rental income contribution on medical diagnoses rather than solely on income.
“As sympathetic as we are to the people who this would help, this nevertheless is yet another unfunded mandate from Albany, and one that will have significant immediate and long-term costs,” she said in a statement.
Yet Ginny Shubert, of Shubert Botein Policy Associates, an analysis and advocacy group based in New York, calculated that the new law would cost the city and state an extra $19 million a year but result in $20 million in annual savings. Ms. Shubert, who supports the bill, said the savings would come from evicting fewer tenants, covering fewer rental arrears, and paying for less emergency housing. Keeping a subsidized tenant in an apartment costs $24 a day, she said, but paying for emergency housing costs about $55 daily.
Mr. Duane, who delivered an impassioned speech  on the Senate floor in support of the bill last summer, said those figures made supporting the bill a no-brainer.
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