We consider a general equilibrium model of a private ownership economy with consumption and production externalities. Utility functions and production technologies may be affected by the consumption and production activities of all other agents in the economy. We use homotopy techniques to show that the set of competitive equilibria is non-empty and compact. Fixing the externalities, the assumptions on utility functions and production technologies are standard in a differentiable framework. Competitive equilibria are written in terms of first-order conditions associated with agents' behavior and market clearing conditions, following the seminal paper of Smale (1974). The work of adapting the homotopy approach to economies with externalities on the production side is non trivial and it requires some ingenious adjustments, because the production technologies are not required to be convex with respect to the consumption and production activities of all agents.
We study the testability implications of public versus private consumption in collective models of group consumption. The distinguishing feature of our approach is that we start from a revealed preference characterization of collectively rational behavior. Remarkably, we find that assumptions regarding the public or private nature of specific goods do have testability implications, even if one only observes the aggregate group consumption. In fact, these testability implications apply as soon as the analysis includes three goods and four observations. This stands in sharp contrast with existing results that start from a differential characterization of collectively rational behavior. In our opinion, our revealed preference approach obtains stronger testability conclusions because it focuses on a global characterization of collective rationality, whereas the differential approach starts from a local characterization.
We consider a pure exchange economy with externalities. We adopt a cooperative approach to equilibrium analysis, allowing each individual to cooperate with others and to form coalitions. Individual preferences are affected by the consumption of all other agents in the economy, and the consumption set of each agent is affected by the coalition to which he/she belongs. Following Montesano (2002), we introduce a measure of social loss with respect to the γ-core and α-core of the economy which completely characterizes the corresponding core allocations.
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