This paper studies the relationship between the amount of public information that stock market prices incorporate and the equilibrium behavior of market participants. The analysis is framed in a static, NREE setup where traders exchange vectors of assets accessing multidimensional information under two alternative market structures. In the first (the unrestricted system), both informed and uninformed speculators can condition their demands for each traded asset on all equilibrium prices; in the second (the restricted system), they are restricted to condition their demand on the price of the asset they want to trade. I show that informed traders incentives to exploit multidimensional private information depend on the number of prices they can condition upon when submitting their demand schedules, and on the specific price formation process one considers. Building on this insight, I then give conditions under which the restricted system is more efficient than the unrestricted system.