Using the new data from the OECD-WTO world network of economic activities we construct the Google matrix $G$ of this directed network and perform its detailed analysis. The network contains 58 countries and 37 activity sectors for years 1995, 2000, 2005, 2008, 2009. The construction of $G$, based on Markov chain transitions, treats all countries on equal democratic grounds while the contribution of activity sectors is proportional to their exchange monetary volume. The Google matrix analysis allows to obtain reliable ranking of countries and activity sectors and to determine the sensitivity of CheiRank-PageRank commercial balance of countries in respect to price variations and labor cost in various countries. We demonstrate that the developed approach takes into account multiplicity of network links with economy interactions between countries and activity sectors thus being more efficient compared to the usual export-import analysis. Our results highlight the striking increase of the influence of German economic activity on other countries during the period 1995 to 2009 while the influence of Eurozone decreases during the same period. We compare our results with the similar analysis of the world trade network from the UN COMTRADE database. We argue that the knowledge of network structure allows to analyze the effects of economic influence and contagion propagation over the world economy.