If we plot the number of patents granted in the USA against the GDP for the last 200 years, the following graph emerges:
Well there is a clear correlation between the number of patents granted and the GDP/capita.
Do patents contribute to prosperity? YES THEY DO!
 Gap Minder: http://www.gapminder.org/data/ Data on GDP/cap in PPP US$ 2005: Gross Domestic Product per capita by Purchasing Power Parities (in international dollars, fixed 2005 prices). The inflation and differences in the cost of living between countries has been taken into account.
 Statistical website of the USPTO: http://www.uspto.gov/web/offices/ac/ido/oeip/taf/us_stat.htm
 Federico, P. J., 1964: Historical Patent Statistics 1791 – 1961, in: Journal of the Patent Office Society (46), No. 2, S. 112-116.