What does the notation \left(p,\left(x^i\right)_{i\in I}\right) mean?

[Cinitiator]

Homework Statement

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

mean
(1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3) ?

Homework Equations

The Attempt at a Solution

Googling

 

[Cinitiator]

Also, does

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?

 

[HallsofIvy]

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 $\left(x^i\right)_{i\in I}$ is the list of x's components.

$\left(p,\left(x^i\right)_{i\in I}\right)$ is p together with all the components of the vector x.

 

[Cinitiator]

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 $\left(x^i\right)_{i\in I}$ is the list of x's components.

$\left(p,\left(x^i\right)_{i\in I}\right)$ is p together with all the components of the vector x.

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..)?