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.

Price discrimination is generally welfare ambiguous.

Basic example: A monopoly can price discriminate between two market segments. In segment A, there is one consumer with a willingness to pay of $\$1$million and there are one million consumers with a willingness to pay of$\$1$. In segment B, there is one consumer willing to pay $\$1$million and 400,000 consumers willing to pay$3. Assume MC=AC=0 and that each consumer will buy either zero or one unit of the good.

Third-Degree Price Discrimination Prices: $\$1$in A,$\$3$ in B Uniform Price: $\$1\$ million

Price discrimination increases producer and consumer surplus.

Conditions I can think of when price discrimination might be good for everyone: otherwise the monopolist drops a market or if the total revenue curve is multi-peaked (as in this example -- note multi-peaked just means it's ambiguous, this example just happened to show higher surplus for everyone).

Assuming that market power is given, discrimination is always beneficial to agents whose indifference price is smaller than the optimal non-discriminatory price.

This is because under discrimination, they will get the good at their indifference price. Without discrimination, they will not get the good at all.

• under perfect price discrimination, CS=0. Under no price discrimination, it just consumer surplus under monopoly. I am interested in maximizing consumer surplus. Also for the sake of argument, assume that the populations of different types of consumer are similar. Commented Nov 24, 2014 at 0:38
• Right, brainfart. It's late.. Commented Nov 24, 2014 at 0:39