The nonpartisan Congressional Budget Office is out with a new report on President Obama's proposal to raise the minimum wage from $7.25 to $10.10 an hour by 2016, and its most important finding is this:

The increase in the minimum wage would have two principal effects on low-wage workers: The large majority would have higher wages and family income, but a much smaller group would be jobless and have much lower family income.

More specifically, the CBO found that raising the minimum wage to $10.10 an hour (and then indexing it to inflation) would reduce employment by between a very small amount and 1 million workers, with the agency's best guess being about 500,000 workers. Republicans are seizing on that finding, with a spokesman for House Speaker John Boehner (R-Ohio) saying: "This report confirms what we’ve long known: While helping some, mandating higher wages has real costs, including fewer people working."

At the same time, the report finds that about 16.5 million low-wage Americans would see an increase in their earnings as a result of the hike in the minimum wage. A much smaller number of higher-wage earners would also see a jump in income, the CBO said. The agency explained the impact on employment this way:

According to conventional economic analysis, increasing the minimum wage reduces employment in two ways. First, higher wages increase the cost to employers of producing goods and services. The employers pass some of those increased costs on to consumers in the form of higher prices, and those higher prices, in turn, lead the consumers to purchase fewer of the goods and services. The employers consequently produce fewer goods and services, so they hire fewer workers. That is known as a scale effect, and it reduces employment among both low-wage workers and higher-wage workers. Second, a minimum-wage increase raises the cost of low-wage workers relative to other inputs that employers use to produce goods and services, such as machines, technology, and more productive higher-wage workers. Some employers respond by reducing their use of low-wage workers and shifting toward those other inputs. That is known as a substitution effect, and it reduces employment among low-wage workers but increases it among higher-wage workers.

The CBO summarizes the effects in this helpful chart. (The agency also analyzed a $9-an-hour minimum wage option that is not indexed to inflation.)