Does globalisation lead to lower prices? Probably not, at least in the long run, as Dani Rodrick argues. Ultimately the price level is determined by the rate of growth in the money supply. So monetary policy determines the average level of prices, independent of globalisation.
So what are the benefits to globalisation, if it doesn't result in cheaper prices? Marginal Revolution argues that globalisation should lead to increased levels of world output. Overall prices may not change, but relative prices will. Cheap imports from Mainland China make all other goods relatively more expensive. Rational consumers respond by cutting back on the relatively expensive goods, and consuming more of the cheap imports. This is the price mechanism at work. Under standard assumptions of consumer behaviour and rationality, they end up consuming more and enjoying higher levels of utility as a result.
Where does this increased output come from? In a market economy, relative prices reflect the relative resource cost of production. Cheaper goods from Mainland China are less costly to produce, and use fewer resources, than more expensive goods from elsewhere. Thus the changed consumption patterns result in more efficient resource usage, allowing total global GDP to rise.
This argument assumes that prices reflect resource costs. If prices were regulated by the government, rather than being set by the market, this mechanism may fail. And to the extent that resources are not correctly priced (do Mainland firms pay for the environmental costs that result from their production?), the result may be increased global GDP, but little increase in real global welfare.