Three Toed Sloth has a nice exposition on the difficulties of optimizing an economy, including the best explanation of convex optimization ever:
If plan A calls for 10,000 diapers and 2,000 towels, and plan B calls for 2,000 diapers and 10,000 towels, we could do half of plan A and half of plan B, make 6,000 diapers and 6,000 towels, and not run up against the constraints.
central planning is intractable (polynomial, but n is large)
Three Toed Sloth has a nice exposition on the difficulties of optimizing an economy, including the best explanation of convex optimization ever: