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

Info icon This 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
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 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...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern