Equilibrium

The Radner budget set is \begin{equation*} B_R(p,q,\omega^i)=\left\{% \begin{aligned} (y,z)\in{}&\R^{L(S+1)}_+\times\R^J\mbox{ s.t.}\\ &\begin{aligned}[t] p_0y_0+qz&=p_0\omega^i_0\\[6pt] \mbox{for $s\in S$, }p_sy_s&=p_s\omega^i_s+p_{s1}A_sz \end{aligned} \end{aligned} \right\}. \end{equation*}

Equilibrium in the Radner model is a vector of spot prices $p$, asset prices $q$, a commodity allocation $x$ and an asset allocation $z$ such that

• Each trader $i$ is maximizing $U^i(x^i)$ on $B_R(p,q,\omega^i)$;
• For all $s$ and $l$, $\sum_ix^i_{sl}-\omega^i_{sl}=0$;
• $\sum_jz^j=0$.