Competitive equilibrium with one productive asset

A competitive dividend economy specifies the joint law of total output, an information filtration, utility functions, discount factors, initial ownership shares and trading restrictions. Its derived objects are a common ex-dividend price, individually optimal consumption and share holdings satisfying ${\sum }_j{C}_t^j=d_t$ and ${\sum }_j{\theta }_t^j=1$. Each investor obeys the discrete dividend budget equation and, at an unconstrained interior optimum, marginal utility pricing in a dividend economy. A common price is required; a unique common state-price density or arbitrary contingent transfers require extra market completeness or implementability hypotheses.