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A monopolist faces a demand curve given by $P=60-2Q$ and has total costs given by $TC=Q^2$. Now suppose that the country in which this monopolist is located decides to engage in international trade. The world price of the product produced by the monopolist is $10. What is the firm's profit-maximizing output level?

My attempt:

$P=60-2Q$

$P=10\implies 10=60-2Q\implies 2Q=50\implies Q=25$

Unfortunately, this isn't the right answer. How do I solve this problem?

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Because the monopolist is only a monopolist in its own country, it is basically in perfect competition in the international market and cannot influence the world price. Therefore, it will have to use the condition that price is equal to marginal cost. His marginal cost (MC) is the first derivative of total cost, i.e. TC'=2Q=MC. If MC=P, then 2Q=10. Therefore, Q=5.

Is that the correct answer from your solutions?

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  • $\begingroup$ Great to hear that! Good luck with your studies! $\endgroup$
    – JotHa
    Commented Apr 19, 2018 at 21:57

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