Existence of an equilibrium for lower semi-continuous information acquisition functions

We consider a two period model in which a continuum of agents trade in a context of costly information acquisition and systematic heteroge- neous expectations biases. Because of systematic biases agents are sup- posed not to learn from others' decisions. In a previous work under some- how strong technical assumptions a market equilibrium was proved to exist and the supply and demand functions were proved to be strictly monotonic with respect to the price. Here we extend these results under very weak technical assumptions. We also prove that the equilibrium price maximizes the trading volume and further additional properties (such as the anti-monotonicity of the trading volume with respect to the marginal information price).