This week’s “Daily Journal” guest columnist is Mitch Kokai, John Locke Foundation Director of Communications.

RALEIGH — Defenders of free markets like to use analogies involving pie. Perhaps they believe the way to a man’s brain is through his stomach. Perhaps they hope to appeal to iconic American traditions. (You know the song: “Baseball, hot dogs, apple pie, and Chevro. …” Well, never mind.)

Or perhaps the pie example seems to offer a simple means for expressing a not-so-simple economic concept. While left-leaning pundits and politicians focus on slicing an economic pie in different ways to meet their definition of fairness, those who tout market-based solutions focus instead on creating a larger economic pie for everyone.

It’s pretty clear that when you slice a small pie and an extra-large pie in the same way, one slice of the extra-large pie is larger than one slice of the small pie. In other words, a larger pie gives you more to eat, even if your “share” of the pie hasn’t budged.

Market advocates believe you create the conditions for larger pies by promoting economic freedom. Limit the size of government. Reduce burdensome regulations. Secure property rights. Promote the rule of law. Ensure access to sound money. Promote free trade.

Nowhere in that recipe will you find higher taxes, increased government spending, or more regulation. You’ll find no other policy prescriptions tied to reconfiguring the size of the existing pie’s slices. This set of policy prescriptions leads to less economic freedom.

Offer this argument, and some critics of market-based thinking will skip the debate, grab a piece of pie, and go home. Others will complain that Big Pie has bought and paid for this analysis (much as Big Oil, Big Pharma, and Big Bird have polluted discussion of other public policy issues). But the intellectually honest skeptic might be willing to play along.

“I understand that a bigger pie will lead to more pie for everyone,” he says. “But that doesn’t mean we can’t even up the size of the slices within that larger pie. The last few years notwithstanding, the American economic pie always has grown bigger over time. Distributing the larger pie a little more evenly seems like a worthwhile solution.”

That’s the point in the discussion when a chart might come in handy. Not a pie chart, mind you, but a bar graph. Specifically, a bar graph from the Fraser Institute’s Economic Freedom of the World 2011 Annual Report, as developed by economists James Gwartney (Florida State University), Robert Lawson (Southern Methodist University), and Joshua Hall (Beloit College). (Lawson recently discussed key findings from the report for a Campbell University audience.)

If market critics are correct, their policies — those that lead to less economic freedom — should allow the poorest members of our society to earn a larger share of the nation’s income. But the chart above tells a different story.

Split nations into four groups based on economic freedom, and calculate the share of income earned by the poorest 10 percent. In the most economically free countries, the “bottom 10 percenters” earn 2.6 percent of the nation’s income. That sounds bad? In the least free countries, the “bottom 10 percenters” collect 2.4 percent of the nation’s income.

Maybe there’s a sweet spot between the most free and least free countries. We don’t want to be North Korea, but too much freedom is bound to lead to too much income inequality. Like Goldilocks, we should pursue the level of freedom that’s neither too hot nor too cold, but just right. Except that the “bottom 10 percenters” earn about the same amount in the middle quartiles as well: 2.2 percent and 2.3 percent.

In other words, the poorest members of society earn about the same percentage of a nation’s income regardless of economic freedom. Free or unfree, they’re unlikely to get much more than an average of 2.5 percent of that income. In other words, they can expect to get about 2.5 percent of the economic pie — regardless of the pie’s size.

So how do they get more pie? Only when their nation bakes a larger pie. Luckily for the poor, another bar graph suggests a good recipe.

The main ingredient is economic freedom. The poorest of the poor in the most economically free nations — those ranked in the top 25 percent in terms of freedom —earn eight times as much annual per capita income ($8,735) as those in the least free nations ($1,061). The contrast is pronounced even when the comparison pits the freest nations against those that are slightly less free. Slip from the top quartile to the second quartile of the economically free countries, and annual average per capita income drops by more than 60 percent, to $3,311.

If you’re concerned with improving the lot of the poorest of the poor, then it’s time to shelve arguments that restrict economic freedom in the name of a more equally divided pie. The only viable solution is a larger pie. Your baker’s checklist must include a healthy serving of freedom.