A firm is a natural monopoly. Its marginal cost curve is flat, and its average cost curve is downward sloping (because it has a fixed cost). The firm can perfectly price discriminate. Use a graph to show how much the monopoly pro duces, Q*. Show graphically and mathematically that a monopoly might shut down if it can only set a single price but operate if it can perfectly price discriminate.
Solution:
A monopoly profit-maximizing quantity is where: MR = MC
The price charged by a monopoly is not equal to MR or MC, but higher on the demand curve as a monopoly firm seeks to maximize its profits.
A monopoly might shut down if it can only set a single price and its profit-maximizing price is lower than its average variable cost. But it will operate if it can perfectly price discriminate because it can set different prices for different consumers depending on their willingness to pay.
This is depicted by the below graph:
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