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We consider exchange economies with two types of agents: one risk-averse and the other consistent with Prospect Theory. We study equilibrium properties for the economy and explore the nature of optimal decisions of the different agents. Prospect Theory agents change their optimal decision by parting from the reference point in favor of a frontier allocation depending on conditions for aggregate uncertainty and the wealth distribution of the risk-averse agents. When the aggregate endowment of the risk-averse agent is sufficiently large, the equilibrium price will induce the Prospect Theory agents to abandon the reference point and instead choose a boundary allocation. This behavior contrasts with the predictions of the endowment effect. Assuming the reference point as initial endowment, we prove the prevalence of either a non-trading equilibrium or a frontier equilibrium.