In class we dealt with insurance economics and, specifically, adverse selection due to information asymmetry. As one possible solution we considered pooling contracts, i.e. the same contract for both high- and low-risk households for some average price. We showed and I understood why the high-risk households now would buy more insurance than the low-risk ones and thus everybody would act as if they were low-risk whether this is true or not. What I am not sure about is why there wouldn't be an equilibrium in a competitive market.
It's clear that the low-risk individuals have reason to go for a lesser premium and, if some other insurer would offer this, then they would go there.
Therefore, my questions are:
1) So why won't there be an equilibrium? I would think that if a new insurer appears with a better deal than the pooling contract, then there would again be the problem with adverse selection. Hence, the new insurer wouldn't appear and offer a better deal in the first place?
2) I also read that this is pareto-inefficient in that it disadvantages the low-risk households (obvious) but does not benefit the high-risk households. The latter point I do not understand since the high-risk households will have a higher demand since the pooling contract situation makes the insurance relatively cheap. Isn't that a benefit?