If the current tax system were extended beyond the scheduled expiration of income tax cuts in 2012, the family would pay $248,025 in federal income taxes. That includes taxes on the investment income of high earners included in the 2010 health-care law that are scheduled to take effect in 2013.

Top Tax Rate

The extent of the Republican candidates' tax cuts for the wealthy family depends on how they may adjust the top income tax rate and especially on how they tax investment income.

"Whatever you do to dividends and capital gains, they benefit or get hurt in spades," said Roberton Williams, senior fellow at the Tax Policy Center, a nonpartisan research group in Washington. "The ones that exempt investment income all benefit the rich enormously."

Among the Republican presidential candidates, former Massachusetts Governor Romney's plan provides the smallest tax cut of $16,400 to this family, because he would repeal taxes from the health-care law while keeping the top rate at 35 percent and the capital gains rate at 15 percent for high earners.

Texas Governor Perry's 20 percent flat tax would exempt capital gains and dividends. The wealthy family would lose its deductions, though it would receive a 39.8 percent tax cut and pay $149,300. Businessman Cain's 9 percent income tax would offer a deeper cut, dropping the family's income tax to $63,810.

Huntsman's Plan

Under former Utah Governor Huntsman's plan, the decline in the top rate to 23 percent would more than outweigh the loss of all deductions and credits, and the family would pay $144,525.

The tax plan of former House Speaker Newt Gingrich, which features a 15 percent top rate, would provide a benefit for this family similar to the one proposed by Perry.

The upper-income family in the study has a small business, which means that the company's profits are reported on the family's tax return. In this case, the total adjusted gross income is $200,000 a year, and the family earns $30,000 in capital gains and dividends subject to preferential rates.

In this income range, tax breaks such as the mortgage interest deduction tend to matter more, meaning that the results can vary widely across family structures, Williams said.