We study an Arrow--Debreu economy with externalities generated by multiplex networks. Market equilibrium prices reflect not only preferences and the scarcity of goods, but also consumers' network positions induced by goods-specific externalities and the linkages across goods arising from the endogenous budget constraint. We quantify the departures of equilibrium allocations from Pareto efficiency using both a utility-based measure of efficiency loss and a coefficient of resource utilization, thereby linking network multiplexity quantitatively to equilibrium performance. These measures also identify zero-efficiency-loss cases: competitive equilibria are efficient when the relevant network-centrality vectors are parallel, a condition satisfied, in particular, when all networks are regular or when all layers share the same network structure. When competitive markets allocate goods inefficiently, a Lindahl equilibrium implemented through personalized prices can restore efficiency, although it may leave some consumers worse off.

We study price regulation for a monopolist operating in networked markets with demand spillovers. Achieving efficiency requires price reductions proportional to consumers’ Katz–Bonacich centralities, which generally cannot be implemented by commonly used price regulations. Moreover, these regulations become asymptotically welfare neutral as spillovers grow. Nevertheless, some price regulations may still benefit consumers. In particular, average-price regulation robustly increases consumer surplus. By contrast, banning price discrimination increases consumer surplus only when more central consumers have higher intrinsic willingness to pay.