A cost center doesn't "run at a loss", it performs something critical to supporting the profit center. Advertising is what customers pay for; search makes that advertising worth the price. No search = no advertising. Google's core is "know everything, to maximize advertising revenue". Yahoo's core is...well, it became famous because it provided a curated index to the then-unsearchable Web, but now that's moot and Yahoo is, um, yeah seems that's the problem.