The first law of economics is the lone rule when it comes to commodity prices and commodity stocks. Surplus creates price drops and shortages spur price increases.

For copper miners, one side of the equation is about to sharply change. Though demand remains weaker than normal in the face of a global economy, supply is tightening.

The coming shift from oversupply  of copper to undersupply helps explain why shares of Freeport-McMoran (NYSE: FCX) rallied more than $1 on Thursday, July 19, even as the company reported second-quarter results that were far below year-ago results. Investors are appropriately looking ahead, focusing on what this company’s quarterly results could look like a year from now.

For a recap of why I think this stock is quite undervalued, please click here.

As I wrote back in April, “the supply and demand picture enables this company to generate decent profits when the global economy is under pressure and copper demand cools, and really solid profits when demand is at a more normal state.”

In the second quarter, Freeport-McMoran earned $0.80 a share, roughly half of what the company earned a year ago. Annualize the current profits, and Freeport would make around $3 a share this year, meaning shares trade for a reasonable 11-12 times depressed earnings. (That EPS figure is after one-time charges, so Freeport actually topped the consensus if you back that out).

Yet looked at in the context of a more typical results, this is one cheap stock. For example, shares trade for just seven times 2011 EPS of $4.84. And here’s the key takeaway: That’s what Freeport-McMoran is likely to earn in 2013. The projected profit rebound (from an expected $3.50 in EPS in 2012) is mostly a function of forecasts for copper prices. It’s not that demand for copper is likely to suddenly surge — the global economy won’t likely look that healthy unto 2014 or 2015. Instead, you have to focus on the supply side of the equation.

Simply put, many copper producers around the world are struggling to meet production quotas because current mined ore has a lower concentration of copper than we’ve seen in the past. Notably, that’s not the case for Freeport ‘s mines, which remain among the most productive in the world. Yet in the coming quarters, Freeport-McMoran is voluntarily reducing output by about 5% anyway, in a bid to support firmer prices.

You can already see the effects of falling output. The world had been awash in copper at the start of the year, with supply exceeding demand by more than 100,000 tons. But that figure has fallen below 20,000 tons, according to a Bloomberg survey. More to the point, it increasingly appears as if there will be greater demand than supply in 2013 as supply keeps falling. And this comes at a time of weak global economic activity. You can only imagine what the supply and demand imbalance will look like when the global economy strengthens.

My take: In coming months, futures prices for copper will strengthen as the copper shortage starts to take shape, bringing a fresh wave of buying interest to Freeport-McMoran. Right now, copper futures are flat into 2014, at around $3.50 a pound, but this defies the reality that is emerging for the economics of copper.

As I’ve noted before in columns about gold and silver miners, rising labor and extraction costs are now a fact of life. Freeport-McMoran must now spend roughly $1.50 for every pound of copper it mines —  up 50% in the past year. This trend has likely peaked and mining costs should stay flat in the periods ahead. Notably, Freeport-McMoran is still solidly profitable with copper selling at $3.50, though it’s profit spread would rise 25% (from $2 a pound to $2.50) if copper prices move up to $4, as I suspect.

Risks to Consider: The European economic crisis has not disappeared. There is still a small chance that we return to the scary investor environment that we saw back in 2008 and early 2009, which would quickly push this stock down into the $20s.

Action to Take –>  Shares of Freeport-McMoran have fallen from $55 to $35 during the past year. A year ago, investors were focusing on what could go right for the copper mining sector. In effect, the glass was half full. Paradoxically, that’s the wrong time to own a mining stock. Instead, you should be focusing when these stocks are deeply out of favor.

Shares of Freeport rallied nicely on news of production cuts and the looming transition from oversupply to undersupply of copper. Yet shares remain sharply undervalued in the context of rebounding earnings and the value of the company’s global network of mining assets. Investors who buy into the stock before the crow catches on will be better positioned to make huge gains.