The USA only overtook Britain in per capita GDP per capita in purchasing power parity terms early in the 20th century. Canada overtook the mother country in the post-war period.
Figure 1: British, American and Canadian GDP per capita (1990 Int. GK$PPP), 1775 – 2010
Source: The Maddison-Project, http://www.ggdc.net/maddison/maddison-project/home.htm 2013 version.
Figure 2: British, American and Canadian GDP per capita (1990 Int. GK$PPP), 1775 – 1870
Source: The Maddison-Project, http://www.ggdc.net/maddison/maddison-project/home.htm 2013 version.
Figure 3: British, American and Canadian GDP per capita (1990 Int. GK$PPP), 1870 – 2010
Source: The Maddison-Project, http://www.ggdc.net/maddison/maddison-project/home.htm 2013 version.
Utopia, you are standing in it! 
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