[Retric]

Ideally 100% of LED light is in the photosynthetic rage. It looks like there using white LED's which are less efficient AND not optimal for plants. Sill, assuming the 'best case' using current mass market tech.

  Sunlight > photosynthisis (45%)   = 45%.
  Sunlight > solar cell (22%) > conversion, storage, transmission (90%) 
  > LED (40%) > photosynthisis(100%) = 8%

reality is LED efficecy drops over time and LED light is not quite 100% ect but this is the optomistic best case numbers.

[idibidiart]

but what stops a structural technique for maximizing light usage by plants (like stacking or some more optimal structural pattern, such as the natural tree pattern [1] optimized by nature) from achieving 4X or more increase in efficiency of light usage?

1. http://online.wsj.com/news/articles/SB1000142405297020355030...

[Retric]

You can do the same sort of 3D arrangements with plants and sunlight. However, building a 3d structure costs money so you need to compare it with all the other ways of boosting yeild to find out the best option.

Generally, a mix of irrigation, fertilizer, better breeds, and greenhouses are the best option for boosting yield. Mix in more marginal land as needed (Note: ~68.4% of Japan is covered in forests.)

Greenhouses for example let you have a longer growing season and pack plants more closely together when their young. Which can let you have an early harvest and then use that same land for another plant or a plant with a longer growing season. Closer to the tropics you can often get 2 or 3 harvests a year. However, they have significant capital and labor costs.

PS: Now, we can try and figure out how a Dystopian future can feed say X billion people but we are a long way from needing indoor hydroponics.