Oakland is on track to surpass its ambitious goal of building 17,000 new homes by 2024, but is falling far short in building affordable housing, city officials said Tuesday, fueling questions about whether the city’s massive building boom will help house its most vulnerable residents.

In the three years since Mayor Libby Schaaf set her housing target, the city has issued building permits for more than 10,000 homes — but just 7 percent of those were reserved for low-income families. That’s far less than the 28 percent Schaaf originally pledged.

The gap in Oakland’s low-income housing supply highlights a problem many Bay Area cities are facing as they strive to build their way out of their respective housing shortages. Even as they see apartment tower after apartment tower rises around them, city officials struggle to create low-cost housing that could help prevent their poorest residents from getting priced out.

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