There were some really great points about changes in complexity with diminishing resources in this thread. Although complexity was discussed at length here, I don't think anyone addressed definitions of complexity, except to say that it was hard to pin down.
Biologists have a really nice, simple indicator for complexity; Simpson's Diversity Indicator.
Simpson's Diversity Indicator
So richness is measured by how many species are in a sample of 1000. Evenness is measured by the relative distribution of those species; is there a predominance of one species, or are species more evenly spread. The example given in the link is buttercups and daisies. You can take that indicator and apply it easily to human systems. Look at a sample of 1000 people in the economy, and count the number of jobs or roles that pop up. More roles/jobs equals more diversity. While a young growing economy might have less diversity/complexity due to overgrowth of successful job roles, a mature complex system would be indicated by a high amount of stable diversity. I would argue that while our current economic system in the first world is incredibly diverse, there has been some loss of diversity in the last decade, with a preponderance of new job in one or two places; service and finance, for example. It will be interesting to watch the diversity collapse in high energy places like NYC.