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A notation question

  1. Jul 10, 2012 #1
    1. The problem statement, all variables and given/known data

    What does the following notation mean, assuming that I is a set, and i is a member of the set i, and x is an endowment of a member i, and is a vector?

    Assuming x is (1, 2, 3) for each i, and I = {1, 2, 3, 4}

    Does khWfb.png mean
    (1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3) ?


    2. Relevant equations
    khWfb.png


    3. The attempt at a solution
    Googling
     
  2. jcsd
  3. Jul 10, 2012 #2
    Also, does p5JXM.png mean (p, (1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3))?

    Or does it imply a p assigned to each xi individually?
     
  4. Jul 10, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Is "endowment" a translation from another language? I don't recognise it here.

    Given that x is a vector (of dimension the cardinality of I) then [itex]\left(x^i\right)_{i\in I}[/itex] is the list of x's components.

    [itex]\left(p,\left(x^i\right)_{i\in I}\right)[/itex] is p together with all the components of the vector x.
     
  5. Jul 10, 2012 #4
    Thanks for your help. This is from an economics paper, so by endowment I mean an endowment bundle for each consumer. The list of consumers is in the I set, and an individual consumer is i.

    The x vector is only a commodity vector - it doesn't have any information on the consumers (in the I set). Each consumer has an endowment vector associated with them, which is expressed as x with a superscript of i.



    From what I understand, it's supposed to list all the endowment vectors for each consumer from the set I. However, I don't understand how it lists them.

    Will it be listed as: (p, vector1, vector2, vector3) etc? Or will it be listed as (p, vector1component1, vector1component1, ... vector3component1 etc..)?
     
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