Elon Musk is the poster child for the famous line “if you’re so rich, how come you’re not smart?” Mr. Musk is undeniably incredibly rich, but in his chainsaw crusade against the government he is not looking very smart.

He is botching almost everything he does in his supposed role as an efficiency warrior, laying off essential workers who then need to be rehired and making cuts at agencies where he doesn’t even know what they do. But part of Musk’s problem stems from the fact that he is dogmatically determined to see the private sector as more efficient than the government, even when the facts clearly show the opposite.

This is clearest with Social Security and Medicare, the country’s two biggest social programs. These programs are both hugely more efficient than their private sector counterparts, as can be easily seen with a quick look at the data.

The administrative costs of Social Security are less than 0.4 percent of the benefits paid out each year. By contrast, the administrative costs of 401(k) plans average at least 1.0 percent annually. That would make the administrative costs of private plans look two and a half times as large as the cost of Social Security, but that actually hugely understates the gap.

The 1.0 percent administrative costs refers to the stock of money in a 401(k). If a person has $100,000 in a 401(k) they would pay around $1,000 a year to the company that manages it. But they will make this payment every year that they have their 401(k), including in retirement.

The money in a 401(k) typically accumulates over a worker’s career, due to increased contributions and market returns, so they have much more money as they near retirement. But let’s say that an average dollar is in a retirement account for 20 years. This means a person will have paid the 1.0 percent fee on that dollar twenty times for a total of 20 percent. That compares to the 0.4 percent administrative costs of Social Security, a cost ratio of 50 to 1.

Where does all the extra money for 401(k) administrative cost go? Part of the additional cost is due to the fact that individual accounts are more costly to run than Social Security. People are needed to manage accounts, allow people to change holdings between funds and to provide information on assets and rates of return.

The Social Security system is far simpler. It collects and records our payments every month and then when we are ready to retire it pays back benefits based on a long-established formula. This can be called old-fashioned and simple, but when it comes to providing a core retirement income to people who have spent their lifetime working simplicity is a virtue. There is no reason to make this part of our lives complex.

But managing the accounts is only part of the picture. The financial sector also includes many of the highest paid people in the country, like billionaire privatization proponent Larry Fink, who also is the CEO of Blackrock. The people who manage funds, and executives who lead financial companies, make millions of dollars a year, or even tens of millions of dollars a year. Their incomes come out of our retirement savings.

Proponents of privatization often argue that the higher costs of private accounts are justified by the higher returns they offer. The issue of higher returns is questionable. It depends both on worker’s earning history and the specific performance of the market over a worker’s career.

However, if higher returns is really the issue, there is a simple answer. Just invest the Social Security funds directly. This means that instead of having 160 million workers have individual accounts, where returns will depend on their own choices and luck, just put whatever funds we would have designated for individual accounts directly into a stock index fund.

This would allow for Social Security beneficiaries to get higher returns relative to their contributions, without exposing them to risks from poor investment choices or bad timing. It would also save us tens of billions of dollars in administrative costs, you know, the money that would flow to people like billionaire Larry Finks in a privatized system.

In short, the current Social Security system is unambiguously more efficient than a privatized system. That’s probably why Elon Musk runs around spreading crazy lies about millions of dead people getting Social Security rather than trying to talk seriously about the program.

There is a similar story with Medicare and the system of private healthcare insurance. The administrative costs for the Medicare program last year were $11.5 billion, just 1.1 percent of the $1,037 billion the program paid out for care.

By comparison, we paid out $150.7 billion last year to cover the administrative costs of private insurers who paid out $1,314 billion to health care providers. This is an expense ratio of 11.5 percent, more than 10 times the cost of the public Medicare program.

As with Social Security, much of the additional money goes to cover all the paperwork done by insurers to file (and often deny) claims. And some of it goes to highly paid top executives of insurers, who can earn tens of millions of dollars a year.

Even this comparison understates the true cost of the inefficiency of the system of private health insurance. Insurers have varying rules and forms. As a result, hospitals, doctors’ offices and other providers must have large administrative staff to ensure that billings are handled properly, and they can get reimbursed for the services they provide. A universal Medicare-type system, like the one in Canada, avoids this problem.

In both the case of Social Security and Medicare, there is clear evidence and a compelling logical argument as to why a public system is more efficient than privatized alternatives. If Elon Musk was seriously interested in promoting efficiency, he would be touting the benefits of the public systems in the United States instead of running around like a jerk with his chainsaw and spewing nonsense about 250-year old zombies collecting Social Security benefits.