Ron Bailey looks at an article by MIT chemist Daniel Nocera.
Nocera suggests, assuming heroic conservation measures that would enable affluent American lifestyles, that "conservative estimates of energy use place our global energy need at 28-35 TW in 2050." This means that the world will need an additional 15-22 TW of energy over the current base of 13.5 TW.
...Biomass could supply 7-10 TW of energy, but that is the equivalent of harvesting all current crops solely for energy. Nuclear could produce 8 TW which implies building 8000 new reactors over the 45 years at a rate of one new plant every two days. Wind would generate 2.1 TW if every site on the globe with class 3 winds or greater were occupied with windmills. Winds at a class 3 site blow at 11.5 miles per hour at 33 feet above the ground.
By process of elimination, Nocera's arguments suggest that only solar power will be able to meet our energy needs in 2050. That sounds plausible to me (I know nothing about fusion power, which is an alternative that Bailey does not discuss). My guess is that some time in the next 15 or 20 years, the cost of solar power will be the major determinant of energy prices, just as the cost of oil is today.
If technological progress in solar power is slow over the next 20 years, then it is hard to see how we can avoid a rise in the relative price of energy. However, if progress is sustained, then once we reach the point where solar power is the marginal source of energy, I would think that the relative price of energy would start to trend downward.
My best guess, actually, is that by 2050 we will be using more energy than Nocera predicts, at a cost per watt that is at or below today's cost, adjusted for overall price changes. I think that another 40 years of improvements in solar technology ought to do that.