We consider an infinite-horizon economy with differential awareness in the form of coarsening. Agents with limited awareness are averse to unfavorable surprises. As a result their optimal trades are measurable w.r.t. their respective awareness partitions. We define an equilibrium with differential awareness and illustrate how the obtained equilibrium allocations observationally differ from those in economies with full awareness. In particular, economies with differential awareness can exhibit (i) lack of insurance against idiosyncratic risk; (ii) partial insurance against aggregate risk; (iii) biased state prices even when beliefs are correct and (iv) overpricing of assets which pay on events with low aggregate payoffs. We next adapt the results of Guerdjikova and Quiggin (2019) to show that agents with different levels of awareness can survive and influence prices in the limit. In this sense, the characteristics identified above would persist in the long-run. Moreover, differential awareness can lead to belief heterogeneity even in the limit. This is in contrast with the classical result of Blume and Easley (2006) stating that only agents with beliefs closest to the truth can survive. Finally, we examine the individual welfare implications of bounded awareness. If an increase in awareness comes at the cost of wrong beliefs over the larger state-space, bounded awareness can simultaneously increase individual welfare (with respect to the truth) and help avoid ruin. In this sense, heuristics which constrain agents to invest in "assets they understand" can be both ecologically rational in the sense of Gigerenzer (2007) and improve the stability of financial markets by allowing a larger set of agents to survive.