Cross-subsidy market separating equilibrium. Suppose that the relevant definition of equilibrium is the anticipatory equilibrium. Show that the equilibrium will always exist and will be a separating...

Cross-subsidy market separating equilibrium. Suppose that the relevant definition of equilibrium is the anticipatory equilibrium. Show that the equilibrium will always exist and will be a separating equilibrium, possibly with cross-subsidization. Does this imply that the market equilibrium is now always constrained Pareto efficient? [Hints: (i) show first that a pooling contract cannot be an anticipatory equilibrium if cross-subsidy is permitted; (ii) trace out the loci of separating cross-subsidy contracts as the amount of cross-subsidy varies and show that the locus runs from d (no cross-subsidy) to the intersection of the 45° line with the breakeven pooling contract line.]