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Consider an industry with a sole producer, a monopolist. The latter faces cost function C(Q)= Q/2 and aggregate (inverse) demand P(Q)=1 - Q (zero for Q> 1). Illustrate all your answers in a drawing
(a) What are the equilibrium quantity QM, price PM, pro?ts ΠM, consumer surplus CSM and total welfare WM for the case of non-discriminatory (uniform) pricing.
(b) Explain why for effciency, i. e. maximal total welfare, it must be the case that price equals marginal cost. Using this, compute the effcient quantity Q*.
(c) Finally, quantify the social cost arising from the monopoly by calculating the associated deadweight loss, telling you by how much the monopoly industry falls short of effciency.
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how to solve problems using derivatives ?
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