Everybody knows that Japan has an energy crisis. We also know that the yen has greatly depreciated, by some 20 percent in just a few weeks. It's time to put these two facts together.

"Abenomics," the shorthand for the aggressive economic strategies being pursued by Prime Minister Shinzo Abe, is the hot thing in Asia. What wonders will the weak yen work for Japan's export machine? Is a recovery just around the corner? Despite its volatility, Japan's stock market says so, and foreign investors, in particular, like the prospects.

Yet what makes exports more competitive also makes imports more expensive. After the March 11, 2011, Fukushima disaster, Japan turned off its nuclear-power plants and stepped up imports of energy. Looking just at the four biggest categories (oil, liquefied natural gas, coal and liquefied propane gas), the monthly value of Japan's energy imports jumped from ¥1.4 trillion (before March 2010) to ¥2.2 trillion in March 2013. In March, that was about $17 billion; now add 20 percent in exchange-rate shifts to get $22 billion per month. Energy imports constitute about one-third of total imports, and since Fukushima, imports have grown to account for 17 percent of gross domestic product, up from 12 percent.