Editor's note: This story has been updated throughout.

BOULDER, Colo. — Ted Cruz unveiled a plan late Wednesday that calls for a "simple flat tax" of 10 percent and promises to grow the U.S. economy by nearly 14 percent a decade from now. 

The Republican U.S. senator from Texas rolled out the plan minutes before he took the stage at the third Republican presidential debate, where he touted his proposed flat tax as the “lowest personal rate any candidate up here has.”

In an op-ed published by The Wall Street Journal, Cruz wrote he had several goals when he set out to devise the plan with the help of Arthur Laffer, a tax adviser to President Ronald Reagan: "spur robust economic growth and job creation, while raising after-tax income for all Americans; be dramatically simpler, to allow working people to file their taxes with a postcard or phone app; and shrink Washington by getting rid of the rat’s nest of complex tax requirements, credits and loopholes.”

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In an analysis of Cruz’s plan released Thursday morning, the nonpartisan Tax Foundation said the senator's reforms would "represent a significant shift from the current tax code." The Washington, D.C.-based group estimated Cruz’s proposals would reduce taxes by $3.6 trillion over the next 10 years but scale back tax revenues by $768 billion at the same time. In the long run, Cruz's proposals could boost GDP by 13.9 percent, according to the foundation.

On Thursday morning, critics of the Cruz plan said it would disproportionately help the wealthiest 1 percent of the country's taxpayers. 

On the campaign trail, Cruz regularly calls for an overhaul of the tax code and the eventual abolishment of the Internal Revenue Service. With Cruz's plan in place, his campaign said the agency "will cease to exist as we know it, there will be zero targeting of individuals based on their faith or political beliefs, and there will be no way for thousands of agents to manipulate the system."

Under Cruz’s proposals, a family of four would not pay any taxes on their first $36,000 of income. As the family earns more, the plan would implement a flat tax, consolidating the current seven brackets into one with a rate of 10 percent. The flat tax would add more fairness to the tax code, ensuring that "no hedge fund manager pays less than his secretary," Cruz said at the debate.

Cruz wants to eliminate complex parts of the tax code such as the estate tax, the alternate minimum tax and any taxes related to the Affordable Care Act, commonly known as Obamacare. Cruz has made a repeal of that health care law central to his bid for the White House.

Cruz’s plan would also get rid of the payroll tax and corporate income taxes and replace them with a flat tax of 16 percent on businesses. "That applies universally to giant corporations that with lobbyists right now are not paying taxes and the small businesses,” Cruz said during the debate. 

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Cruz’s proposals would create Universal Savings Accounts into which adults could put $25,000 a year, with taxes deferred. Accountholders would be able to access those funds “at any time, for any purpose, Cruz said in the op-ed. "This will help create the next generation of capitalists by encouraging younger workers to save and invest,” the senator wrote.

Taken together, Cruz's ideas "would increase the incentives to work and invest and would greatly increase the U.S. economy’s size in the long run, leading to higher incomes for taxpayers at all income levels," the Tax Foundation concluded. 

Although everyone could see double-digit increases in their after-tax income under the senator's proposals, the "overwhelming benefit of Cruz’s tax cuts would flow to the richest Americans," the foundation said. At Wednesday's debate, Ohio Gov. John Kasich indirectly criticized Cruz's plan, saying candidates who were promising 10 percent flat taxes were being unrealistic.

Cruz's plan is similar to that of U.S. Sen. Rand Paul of Kentucky, said Alan Cole, an economist with the Center for Federal Tax Policy at the Tax Foundation. Paul, whose proposal Cruz complimented during the debate, is pitching a 14.5 percent rate for both the business and income taxes. 

"This plan is actually a narrower tax cut than the ones proposed by many of Cruz’s rivals. However, it is simultaneously a more radical transformation of the code," Cole wrote in an email, citing Cruz's proposed elimination of both the corporate income and payroll taxes.

In February, a Cruz campaign spokeswoman said that the senator's ultimate goal is to replace the federal income tax with a national sales tax, also known as a Fair Tax. “However, the most immediate, effective way to implement comprehensive tax reform is to pass a simple flat tax — so simple that Americans can file on a postcard," Cruz spokeswoman Catherine Frazier said. "This should be the starting point for reform, and once it's in place we should pursue a Fair Tax.”

In this week's op-ed, Cruz framed his flat tax plan in the vein of the tax cut that Reagan signed into law in 1981. In Cruz’s telling, Reagan’s plan only overcame Democratic opposition in Congress after the GOP president “took his case to the people." 

“Reagan did it in 1981, and we can do it again,” Cruz wrote. “I intend to take it to the people: a simple flat tax, to benefit every American."

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Aman Batheja contributed to this report.

 

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