HW1 - equilibrium values for prices and allocations(c...

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

View Full Document Right Arrow Icon
Graduate Macro II, Homework 1 Jonathan Heathcote Due in class on Tuesday January 31st 2006 Recall the example economy we worked through following Chapter 2 in Dirk Krueger’s notes. 1. Consider the following alternative description of preferences and endow- ments. Period utility is given by u ( c i ) = ¡ c i ¢ 1 γ 1 γ Assume both individuals are in fi nitely-lived, and discount at rate β . Sup- pose the endowment stream is e 1 t = 1 . 5 if t is even, e 1 t = 1 if t is odd e 2 t = 0 . 5 if t is even, e 2 t = 2 if t is odd (a) Characterize the set of Pareto E cient allocations in this economy, assuming β = 0 . 9 and γ = 2 . (b) For these parameter values, use Negishi’s method to fi nd a candidate competitive equilibrium for this economy. Describe the candidate
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: equilibrium values for prices and allocations (c) Verify that the prices and allocations you solved for satisfy the nec-essary conditions for equilibrium (d) Which agent enjoys higher utility in the equilibrium, and why? 2. Now revert back to the original description of preferences and endowments. Consider a Pareto e ffi cient allocation indexed by the Pareto weight α. Show that for any α ∈ (0 , 1) this e ffi cient allocation can be decentralized as a competitive sequential markets equilibrium given an appropriate choice for a 1 (where a 1 is not necessarily equal to zero). 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