Based on the wikipedia summary, Girard's mimesis seems similar to Veblen's conspicuous consumption. But Girard generally doesn't go too much into the economic details of any specific era - he is more focused on traditional religion. I may need to read Veblen.

I'd also be curious to see a modern update of it - Veblen's theory of a leisure class driving conspicuous consumption and a worker class partaking of it doesn't reflect modern reality at all (these days the poor form the leisure class). Yet the consumption/Girardian mimetic behavior persists.