Price discrimination- how much is optimal? I am of the understanding that as a general rule, price discrimination does not benefit consumers. Yet I can think of a situation where it does. Look at two countries, Australia and India. The price levels are very different. If there is no price discrimination, prices are identical. Suppose firm profits were higher if they priced out Indians and sold just to Australians.

I am of the impression consumer surplus will be higher if a firm could choose two different prices, one to India and one to Australia.

Under what conditions would partial price discrimination be beneficial?

I am thinking, for simplicity, this firm is a monopolist and there are >2 types of consumers, each with a different valuation of the good.
Varian has a paper on Price Discrimination and Social Welfare in which he gives some necessary and sufficient conditions for (third degree) price discrimination to increase welfare.

A necessary condition is that the total level of output (i.e. the total number of consumers served) increases as a result of the discrimination. 

A sufficient condition is that the profitability of the new output (i.e. after discrimination) exceeds the profitability of the old output (before discrimination) evaluated at the new prices.