The Arrow-Debreu Model

At date 0 traders trade current consumption bundles and contracts promising the delivery of $x_{sl}$ units of good $l$ if state $s$ occurs in date 1.

• Prices are $\phi=(\phi_0,\ldots, \phi_S)\in\Rlp/{0}$.
• The Arrow-Debreu budget set is
\begin{equation*} B_{AD}(\phi,\omega^i)=\left\{y\in\Rlsp:\sum_{s=0}^S\phi_s(y_s- \omega^i_s)=0\right\}. \end{equation*}
• Equilibrium in the AD model is a price $\phi$ and allocation $x$ such that
  • Each trader $i$ is maximizing $U^i(x^i)$ on $B_{AD}(\phi,\omega^i)$;
  • For all $s$ and $l$, $\sum_ix^i_{sl}-\omega^i_{sl}=0$.

 

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