We consider a private ownership production economy with consumption and production externalities. Each household is characterized by a consumption set described by a possibility function, an endowment of commodities, and preferences described by a utility function. Each firm is owned by households and it is characterized by technology described by a transformation function. The choices of all agents (households and firms) affect individual consumption sets, individual preferences, and production technologies. Describing equlibria in terms of first-order conditions and market clearing conditions, and using a homotopy approach, under differentiability and boundary conditions, we prove the non-emptiness and the compactness of the set of competitive equilibria with consumptions and prices strictly positive.

中文翻译：

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具有可能性函数的私有生产经济中的外部性。存在结果

我们考虑具有消费和生产外部性的私有生产经济。每个家庭的特征是由可能性函数描述的消费集、商品禀赋和效用函数描述的偏好。每个企业都由家庭拥有，它的特点是由转换函数描述的技术。所有代理人（家庭和企业）的选择都会影响个人消费集、个人偏好和生产技术。用一阶条件和市场出清条件描述均衡，并使用同伦方法，在可微性和边界条件下，我们证明了消费和价格严格为正的竞争均衡集的非空性和紧致性。