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Xiaotie Denga and Li-Sha Huang (2006), “On the complexity of market equilibria with maximum social welfare” Information Processing Letters 97, 1: 4–11 [DOI] [PDF].

We consider the computational complexity of the market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard.

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