The excellent July 24 front-page article “Health law’s unintended impact on part-timers” showed how President Obama’s health-care law is cutting part-time workers’ pay by forcing employers to limit these employees’ hours in order to avoid penalties. Yet the reality is even worse.

Obamacare does not authorize those penalties in states that leave the task of establishing a health insurance exchange to the federal government. That means most of the employers the article cited — the commonwealth of Virginia, various Texas employers, the Ohio-based White Castle burger chain, the city of Dearborn, Mich., and Utah’s Granite School District — don’t need to cut part-timers’ hours, because the federal government has no authority to penalize them.

Yet the Obama administration has decreed it will do so anyway, contrary to the clear language of federal law, proving that taxation without representation is not confined to the District.

Two lawsuits have been filed to stop this illegal action — one by the state of Oklahoma, another by employers and individual taxpayers in Kansas, Missouri, Tennessee, Texas, Virginia and West Virginia.

Even so, thousands of part-time workers are already losing wages because of a tax Congress did not authorize. As underemployed music professor Kevin Pace told The Post, “This isn’t right on any level.”

Michael F. Cannon, Washington

The writer is director of health policy studies at the Cato Institute.