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Consider a monopolist who has a cost function of ?(?)=???. This monopolist faces two consumers, the...

Consider a monopolist who has a cost function of ?(?)=???. This monopolist faces two consumers, the first having demand ??(??)=??−?? and the second having demand ??(??)=??−??.
a) Calculate the profit-maximizing price and then the optimal quantity sold to each consumer under uniform pricing, i.e. the monopolist charges the same price for both consumers. What are the monopolist’s profits?
b) Suppose now that the monopolist can engage in third degree price discrimination. Find the monopolists profit maximizing prices for consumers 1 and 2 (they should be different), and calculate the monopolist’s profits. How do they compare to the profits in part (a)?

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