One of the principles Charles Hooper and I state in our book, “Making Great Decisions in Business and Life,” is that in solving a problem, any alternatives you consider must be feasible.

There is no point in considering “solutions” that are impossible. For example, take Mitchell, a young boy who wanted to have two things: all his friends at his birthday party and the party on his actual birthday, which fell on a Monday. Even though many of Mitchell’s friends could come only on a Saturday, that didn’t stop him from wanting the infeasible: a party on Monday with all of his friends present.

The principle that choices should be feasible seems so obvious that we wondered whether even to put it in the book. But the recent discussion about immigration law reinforces our view that the principle is worth stating.

Many people in the debate, especially on the right, talk about the importance of controlling our borders and make it sound as though doing that is straightforward. It’s not. At least in the way they seem to mean, closing our borders is close to impossible without making America into a kind of reverse pre-1989 East Berlin.

Consider one of most commonly advocated solutions — a wall between Mexico and America. For the wall to be useful, it has to deter a large percentage of the people who would otherwise be here illegally. Would it? No. There are two reasons why.

First, the most commonly used estimate of the number of illegal aliens in America, which comes from the Pew Hispanic Center, is 12 million, 4% of the total U.S. population. Let’s assume that this estimate is correct.

According to the same source, about 78% of the illegal residents came from Latin America, leaving 22% who came from other countries. And between 25% and 40% of all illegal residents arrived here legally but overstayed their visas. Presumably some of the overstayers were from Latin America. This means that more than 25% of the people here illegally, and possibly more than 40%, would not have been kept out by a perfectly effective wall.

Now, you might think that deterring even half of illegal immigrants would make a wall worth building. But that brings us to the second reason a wall would fail — it would not be a completely effective deterrent, even for the illegal aliens who would otherwise cross illegally into America from Mexico.

Comedians Penn and Teller, on the April 26 episode of their HBO TV show, “Bulls–t!,” showed a wall that they had built to U.S.-government specifications and had three pairs of people compete to get to the other side quickly. One pair was to go over it, one under it, and one through it. The result? The pair that went through the wall did so in a few minutes.

Even if the wall had been made impregnable, one of the other pairs would have won — i.e., someone would have gotten past the wall. As the saying goes, build a wall that is 30-feet high and industrious people will find ladders that are 32-feet high.

Because a wall on its own won’t make much of a difference, for it to work, America would have to man the wall East-German style, with a few troops every few hundred feet. Otherwise, a wall between our country and Mexico would just be one more government boondoggle.

This piece led off by saying that any solution must be feasible rather than impossible. Is an East German-style wall, with U.S. enforcers shooting those who come through, over, or under, feasible? In a literal sense, yes. What would it cost?

If two enforcers were placed every 500 feet, that would take 10 enforcers per mile. With a 2,000-mile border with Mexico, that means 20,000 enforcers. But given that the typical work week is 40 hours, and a week has 168 hours, we would need a full-time staff not of 20,000, but of 80,000. At a labor cost of about $100,000 per employee, based on wages plus benefits plus other employer costs, the annual cost of all this would be $8 billion.

That is just the cost of labor: we haven’t even considered the cost of capital and other resources. And the enforcers would have to be prepared to shoot violators. Otherwise, one set of illegal aliens could create a diversion that causes the enforcers to chase them, while another set gets to the American side of the wall. This is “feasible” too. But then the question becomes, are those who want to control our borders willing to have violators shot?

Mr. Henderson is a research fellow with the Hoover Institution and an associate professor of economics with the Naval Postgraduate School. He is co-author of “Making Great Decisions in Business and Life.”