{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture12-2010 - Von Neumann-Morgenstern Proof I Lecture...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Von Neumann-Morgenstern - Proof I: Lecture XII Charles B. Moss September 16, 2010 I. A:A If u v then α < β implies (1 - α ) u + α v (1 - β ) u + β v (1) 1. The direction of the assertion is that if u v and α < β , then the preference ordering must follow. 2. To demonstrate this we start with axiom 3:B:a given 0 α 1 u v u α u + (1 - α ) v u (1 - β ) + β v (2) 3. Intuitively, this axiom states that if u is the inferior bundle, then any bundle constructed with any combination of v must be pre- ferred to u . 4. bf Axiom 3:B:b reverses this axiom by saying that if u is the pre- ferred bundle then it must also be preferred to a bundle containing any amount of v . u v u α u + (1 - α ) v (3) 5. We start from the first equation, replace with and by replacing the first in the right-hand side with preceding equation yields (1 - β ) u + β v ((1 - β ) u + β v ) + (1 - γ ) v (4) 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture XII Fall 2010 6. Next, we reverse the order of the combining in the first set of
Image of page 2
Image of page 3
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