<p>Yes, a commodity space is the set of all possible commodity bundles. The simplest Micro 101 example is typically the nonnegative quadrant of <span class="math-container">$\mathbb{R}^2$</span>, but in general equilibrium theory it is often assumed to be infinite-dimensional since there are infinitely many commodities (each good is differentiated by time and space, etc.).</p>

CC BY-SA 4.0
2020-05-29T13:52:13.713Z
You write "yes" (i.e. it is a vector-space), but then you immidiatly call it a set. I can see both concepts ultimately describing the same thing, but I would just really like to have a concrete defintion, instead of just a general understanding. So, is it a vector space, a set or something else?
Andre
CC BY-SA 4.0
2020-05-29T23:14:28.283Z
Well, it's $\mathbb{R}^n_+$, which is a set and is endowed with the operations of addition between pairs of its elements and multiplication of its elements with real numbers (usually non-negative ones). So, it's a vector space over the reals (or to be precise, a subset of the vector space $\mathbb{R}^n$ with addition and scalar multiplication). Moreover, it is usually also endowed with the Euclidean norm and so, it is a normed space. The way authors view it depends on where they want to focus their attention.
pegasus
CC BY-SA 4.0
2020-05-29T12:49:15.987Z
2020-05-29T12:49:15.987Z
VARulle
<p>I have seen the concept of commodity space being used multiple times in economics, in particular within microeconomics, but I could not find a general definition of it.
Based on the examples that I have seen, I would guess that it is a vector-space of n-dimensions, in which every dimension coincides with one specific commodity. Furthermore, n is equivalent to the cardinality of the set of commodities.
Is this understanding correct? Is there even a universal understanding of a commodity space?</p>

<microeconomics><definition><decision-theory>
What is the definition of: 'commodity space'?
Andre
# What is the definition of: 'commodity space'?

(Asked by: username_0 on 2020-05-29)

I have seen the concept of commodity space being used multiple times in economics, in particular within microeconomics, but I could not find a general definition of it.
Based on the examples that I have seen, I would guess that it is a vector-space of n-dimensions, in which every dimension coincides with one specific commodity. Furthermore, n is equivalent to the cardinality of the set of commodities.
Is this understanding correct? Is there even a universal understanding of a commodity space?

**Tags:** microeconomics, definition, decision-theory


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## 1 answers

### Answer by username_1 on 2020-05-29. Score: 4 | Accepted answer

Yes, a commodity space is the set of all possible commodity bundles. The simplest Micro 101 example is typically the nonnegative quadrant of $\mathbb{R}^2$, but in general equilibrium theory it is often assumed to be infinite-dimensional since there are infinitely many commodities (each good is differentiated by time and space, etc.).

> **Comments:**
> **username_0**: You write "yes" (i.e. it is a vector-space), but then you immidiatly call it a set. I can see both concepts ultimately describing the same thing, but I would just really like to have a concrete defintion, instead of just a general understanding. So, is it a vector space, a set or something else?  
> **username_2**: Well, it's $\mathbb{R}^n_+$, which is a set and is endowed with the operations of addition between pairs of its elements and multiplication of its elements with real numbers (usually non-negative ones). So, it's a vector space over the reals (or to be precise, a subset of the vector space $\mathbb{R}^n$ with addition and scalar multiplication). Moreover, it is usually also endowed with the Euclidean norm and so, it is a normed space. The way authors view it depends on where they want to focus their attention.  

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