The equilibrium set of economies with a continuous consumption space
The paper investigates global properties of the equilibrium set of exchange economies with a continuous consumption space \(X=C^{++}(M,R^{n})\), where \( M \), the parameter set, is a compact subset of \( R^m \). The consumption plan of agent \( i\in \{1,...,I\}\)\, is a continuous function \( x_{i}:M \to R^{n}_{++} \). Each agent \( i \) is equipped with an initial endowment \(\omega_{i}\in{X}\) and her preferences are represented by separable utilities \[ U_i(x)=\int_{M}u^i(x(t),t)dt, \] where \( u^i(x,t):R^n_{++}\times{M}\to{R} \) is a strictly monotonic, concave, \( C^2 \) function. The author shows that the equilibrium set of the corresponding exchange problem is contractible and equilibrium prices vary continuously (outside the singular) as functions of initial endowments.
scientific article; zbMATH DE number 5933147