{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Macroeconomics Exam Review 174

Macroeconomics Exam Review 174 - Solutions for Foundations...

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

View Full Document Right Arrow Icon
3.226 Assume y is an efficient production plan in 𝑌 and let 𝑆 = 𝑌 𝑦 . 𝑆 is convex. We claim that 𝑆 ∩ℜ 𝑛 ++ = . Otherwise, if there exists some z 𝑆 ∩ℜ 𝑛 ++ , let y = y + z z 𝑆 implies y 𝑌 while z ∈ ℜ 𝑛 ++ implies y > y contradicting the efficiency of y . Therefore, 𝑆 is a convex set which contains no interior points of the nonnegative orthant 𝑛 + . By Exercise 3.225, there exists a price system p such that p 𝑇 x 0 for every x 𝑆 Since 𝑆 = 𝑌 𝑦 , this implies p ( y y ) 0 for every y 𝑌 or py py for every y 𝑌 𝑦 maximizes the producer’s profit at prices p . 3.227 Consider the set 𝑆 = { x ∈ ℜ 𝑛 : x 𝑆 } . 𝑆 int 𝑛 = = 𝑆 int 𝑛 + = From the previous exercise, there exists a hyperplane with nonnegative normal p 0 such that p 𝑇 x 0 for every x 𝑆 Since p 0 , this implies p 𝑇 x 0 for every x 𝑆 3.228 1. Suppose x ( x ). Then, there exists an allocation (
Image of page 1
This is the end of the preview. Sign up to access the rest of the 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