PS13+exercises

# PS13+exercises - c q = 1 4 q 2 while the consumer has...

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Intermediate Microeconomics, 2010 Problem Set 13: Exercises 1. Taxes. Consider the quasilinear economy from the last problem set: U ( m;q ) = m + ± 15 q ± 1 2 q 2 ² c ( q ) = q 2 and Y = 100. Recall that we found the competitive allocation to be [ q ± ;q ± ± ;m ± ] = [5 ; 5 ; 25 ; 50] and p ± = 10 on a previous problem set. Now we will consider the con- sequences of a tax: What happens with a speci±c tax t = 1 : 5 which has to paid by the ±rm? What is the competitive allocation with a tax, x t = [ q t ;q t t ;m t ]. What is the tax revenue T ? What is the deadweight loss? 2. Monopoly. Until now we have assumed that the ±rm and the consumer take the price as given. What happens if the ±rm does not take prices as given and chooses its quantity to maximize pro±ts, taking into account that prices will depend on the quantity supplied? Suppose the ±rm has cost
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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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