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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 prots 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...
View Full Document

This note was uploaded on 12/08/2010 for the course PYSCH 111 taught by Professor Malley during the Spring '08 term at University of Michigan.

Ask a homework question - tutors are online