Google pays for the right to be the default homepage & search engine. They aren't paying to support Mozilla they are also doing it, to prevent other SE's (BING)

Google pays for the right to be the default homepage & search engine. They aren't paying to support Mozilla they are also doing it, to prevent other SE's (BING) from holding this right - Chrome is a way to reduce this cost as well as, a few other things for Google.