Draw the profit maximizing equilibrium for a monopolist with a standard U-shaped average cost curve

Draw the profit maximizing equilibrium for a monopolist with a standard U-shaped average cost curve where the monopolist would be make and economic loss when charging a single price. Would we expect this good to be produced in equilibrium in this case? Now show the profit maximizing quantity assuming that this monopolist can perfectly price discriminate. Is it possible that perfect price discrimination can allow this good to be produced? With reference to your graph, how can you tell if price discrimination allows the monopolist to now make at least a zero profit?

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