Unformatted text preview: c ( q ) = 1 4 q 2 while the consumer has preferences U ( m;q ) = m + 10 q ± 1 4 q 2 with income Y = 100. As you know, inverse demand is given by P D ( q ) = 10 ± 1 2 q . A monopolist can choose q to maximize pro±ts ± m ( q ) = qP D ( q ) ± c ( q ) . The monopolistic allocation is x M = [ q m ;q m ;± m ;m m ] if q m maximizes qP D ( q ) ± c ( q ) ± m = q m P D ( q m ) ± c ( q m ) m m = Y ± q m P D ( q m ) (a) Find the optimal quantity supplied by the monopolist. What is the monopo-listic allocation x m ? (b) Find the competitive allocation x ± and the surplus in the competitive alloca-tion. (c) What is the surplus in the monopolistic allocation? What is the deadweight loss? 1...
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- Summer '08