Total welfare when a monopoly can perfectly price discriminate is at least as high as when a monopoly must set one price.

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When a monopoly can perfectly price discriminate, it charges each consumer the maximum price they are willing to pay, resulting in a higher quantity sold compared to setting a single price for all consumers. This leads to a higher total welfare as more consumers are able to purchase the good/service at a price closer to their own valuation. Therefore, total welfare is at least as high (if not higher) than when a monopoly sets a single price.

Total Welfare When a Monopoly Can Perfectly Price Discriminate Is