Price Discrimination and Welfare
Tirole (p. 139)
Suppose 2 markets have different linear demand curves, and demand in
both is strong enough that under monopoly and under price
discrimination both markets will be served. Start with the monopolist
just charging one price.
If the monopolist can charge two prices, he will raise the price in
one market and reduce it in the other. Tirole shows that total output
remains the same. Efficient allocation of a fixed amount of output,
however, requires that the marginal rates of substitution be the same
across consumers, which they aren’t if prices differ. This means that
unless output strictly rises after price discrimination, total surplus
falls. Thus, in our linear-demand case, allocation has become
inefficient and welfare has fallen.