I don't agree with the basic premise that Google is under-monetized. Online advertising is one of the most profitable things you could do and they own most of the market.
The guys at google are very smart. It becomes clear if you see how they have gradually progressed. Starting from search engine, gmail, blogger, youtube, chrome browser, chrome OS. And at each step they created value for users without charging them directly. They wanted to make money but they were not greedy. Most of the main page of google is still blank white space, so pleasing to the eye. Compare with Yahoo, where you have to find the search box amongst all those crowded ads.
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