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Delivering an important boost to a campaign by the city of Los Angeles to hike its minimum wage, Los Angeles County supervisors voted 5-0 Tuesday to study what would happen if they also raised the base pay for not just for county workers but also for employees of county contractors and wage earners in unincorporated areas.

The county’s step comes as Los Angeles city leaders are poised to gradually raise the minimum wage for everyone working within city limits from $9 — the current state minimum — to $13.25 or $15.25 an hour.

Many local business leaders have argued that an increase would lead to job losses at a time when the city is trying to improve its image for business development. But with a City Council heavily backed by labor, the debate has mostly been over not whether to raise the rate, but how much and how fast.

While several neighboring cities — including Santa Monica and West Hollywood — are considering following suit, the political drumbeat would intensify if wages also went up for the least-paid of the county’s roughly 100,000 workers, who form the largest local government in the United States and for workers at thousands of businesses in unincorporated areas of the county.

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