Equilibrium FOC

$\lambda^i_s$ is the multiplier for constraint $s$, $s=0,1,\ldots,S$.

for all $s$ and $l$, $D_{sl}U^i(x^i)-\lambda^i_sp_{sl}=0$.

for all $j$, $-\lambda^i_0q_j+\sum_s\lambda^i_sa^j_s=0$.

The Radner budget constraint must be satisfied.

$x^i\gg0$ and $\lambda^i\gg0$.