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Is it possible to give , in economics, an example of a relation ( set of ordered pairs) that is not a function?

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Is it possible to give , in economics, an example of a relation ( set of ordered pairs) that is not a function?

1

$begingroup$

In mathematics, some relations ( sets of ordered pairs) are not functions.

I know economists make use of functions.

But do they also consider relations that are not functions.

In which branch of economics could "non-functional" relations be useful?

macroeconomics microeconomics mathematical-economics

share|improve this question

edited 6 hours ago

Eleonore Saint James

asked 7 hours ago

Eleonore Saint JamesEleonore Saint James

1063

New contributor

Eleonore Saint James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  In "I know mathematicians make use of functions. But do they also consider relations that are not functions.", the "they" seems to be refer to "mathematicians". Do you mean to ask whether mathematicians make use of relations that are not functions? Or more in line with you last line whether "economists" do?
  $endgroup$
  – Martin Van der Linden
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MartinVanderLinden. It was a mistake. Thanks.
  $endgroup$
  – Eleonore Saint James
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You could edit your question if it was a mistake.
  $endgroup$
  – Martin Van der Linden
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not sure how much asking this in the context of economics adds. Unless you look at really abstract example, most examples from math will have applications to economics.
  $endgroup$
  – Acccumulation
  1 hour ago
  

  
  
  
  

add a comment | 

1

$begingroup$

In mathematics, some relations ( sets of ordered pairs) are not functions.

I know economists make use of functions.

But do they also consider relations that are not functions.

In which branch of economics could "non-functional" relations be useful?

macroeconomics microeconomics mathematical-economics

share|improve this question

edited 6 hours ago

Eleonore Saint James

asked 7 hours ago

Eleonore Saint JamesEleonore Saint James

1063

New contributor

Eleonore Saint James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  In "I know mathematicians make use of functions. But do they also consider relations that are not functions.", the "they" seems to be refer to "mathematicians". Do you mean to ask whether mathematicians make use of relations that are not functions? Or more in line with you last line whether "economists" do?
  $endgroup$
  – Martin Van der Linden
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MartinVanderLinden. It was a mistake. Thanks.
  $endgroup$
  – Eleonore Saint James
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You could edit your question if it was a mistake.
  $endgroup$
  – Martin Van der Linden
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not sure how much asking this in the context of economics adds. Unless you look at really abstract example, most examples from math will have applications to economics.
  $endgroup$
  – Acccumulation
  1 hour ago
  

  
  
  
  

add a comment | 

$begingroup$

In mathematics, some relations ( sets of ordered pairs) are not functions.

I know economists make use of functions.

But do they also consider relations that are not functions.

In which branch of economics could "non-functional" relations be useful?

macroeconomics microeconomics mathematical-economics

share|improve this question

edited 6 hours ago

Eleonore Saint James

asked 7 hours ago

Eleonore Saint JamesEleonore Saint James

1063

New contributor

Eleonore Saint James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this question

edited 6 hours ago

Eleonore Saint James

asked 7 hours ago

Eleonore Saint JamesEleonore Saint James

1063

New contributor

Eleonore Saint James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

edited 6 hours ago

Eleonore Saint James

asked 7 hours ago

Eleonore Saint JamesEleonore Saint James

1063

New contributor

Eleonore Saint James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 7 hours ago

Eleonore Saint JamesEleonore Saint James

1063

New contributor

Eleonore Saint James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 7 hours ago

Eleonore Saint JamesEleonore Saint James

1063

1 Answer
1

active

oldest

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4

$begingroup$

I feel that your question might be a little broad, but there are certainly many areas of economics where non-functional relations are used. Two simple examples (there are many others):

1. One of the most fundamental models of behavior in economics relies on the idea that choices can be represented by "preferences" which mathematically are binary relations that do not have to be functions (they very often are not, e.g., $A succ B succ C$ is not a function, since $succ = (A,B), (A,C), (B,C)$.


2. Economics also relies on correspondences, or ``multivalued" functions (which, depending on the definition, can be just another way to view binary relations). Correspondences are used in a lot of subfields of economics but perhaps most notably in consumer theory, where the choice set of consumer with preference $succeq$ and budget set $B$ can be a whole subset of the consumption space $C(succ,B) subseteq X$ (where $X$ denotes the consumption space).

share|improve this answer

edited 5 hours ago

answered 6 hours ago

Martin Van der LindenMartin Van der Linden

3,7011240

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Example 1 can be represented as a function though, relating the set of alternatives $S$ to the powerset of $S$. It is not very unusual to see it represented this way. It's perfectly fine (mathematically) to have a function relate elements to sets. It's just not a function from the set to itself in that case. Example 2 has the same issue.
  $endgroup$
  – John Doucette
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sure. Every relation $R subseteq (Atimes B)$ can be somewhat "equivalently" represented as a function $f colon A rightarrow 2^B$ such that for all $a in A$ and all $b in B$, we have $b in f(a)$ if and only if $(a,b) in R$. It remains that $succ$ is not itself a function. I think it's fair to say that binary relations like $succ$ are "useful" in economics. Since the OP's question was about "relations that are not functions and are useful in economics" that hopefully provides a good example.
  $endgroup$
  – Martin Van der Linden
  1 hour ago
  

  
  
  
  

add a comment | 

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4

$begingroup$

I feel that your question might be a little broad, but there are certainly many areas of economics where non-functional relations are used. Two simple examples (there are many others):

1. One of the most fundamental models of behavior in economics relies on the idea that choices can be represented by "preferences" which mathematically are binary relations that do not have to be functions (they very often are not, e.g., $A succ B succ C$ is not a function, since $succ = (A,B), (A,C), (B,C)$.


2. Economics also relies on correspondences, or ``multivalued" functions (which, depending on the definition, can be just another way to view binary relations). Correspondences are used in a lot of subfields of economics but perhaps most notably in consumer theory, where the choice set of consumer with preference $succeq$ and budget set $B$ can be a whole subset of the consumption space $C(succ,B) subseteq X$ (where $X$ denotes the consumption space).

share|improve this answer

edited 5 hours ago

answered 6 hours ago

Martin Van der LindenMartin Van der Linden

3,7011240

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Example 1 can be represented as a function though, relating the set of alternatives $S$ to the powerset of $S$. It is not very unusual to see it represented this way. It's perfectly fine (mathematically) to have a function relate elements to sets. It's just not a function from the set to itself in that case. Example 2 has the same issue.
  $endgroup$
  – John Doucette
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sure. Every relation $R subseteq (Atimes B)$ can be somewhat "equivalently" represented as a function $f colon A rightarrow 2^B$ such that for all $a in A$ and all $b in B$, we have $b in f(a)$ if and only if $(a,b) in R$. It remains that $succ$ is not itself a function. I think it's fair to say that binary relations like $succ$ are "useful" in economics. Since the OP's question was about "relations that are not functions and are useful in economics" that hopefully provides a good example.
  $endgroup$
  – Martin Van der Linden
  1 hour ago
  

  
  
  
  

add a comment | 

4

$begingroup$

I feel that your question might be a little broad, but there are certainly many areas of economics where non-functional relations are used. Two simple examples (there are many others):

1. One of the most fundamental models of behavior in economics relies on the idea that choices can be represented by "preferences" which mathematically are binary relations that do not have to be functions (they very often are not, e.g., $A succ B succ C$ is not a function, since $succ = (A,B), (A,C), (B,C)$.


2. Economics also relies on correspondences, or ``multivalued" functions (which, depending on the definition, can be just another way to view binary relations). Correspondences are used in a lot of subfields of economics but perhaps most notably in consumer theory, where the choice set of consumer with preference $succeq$ and budget set $B$ can be a whole subset of the consumption space $C(succ,B) subseteq X$ (where $X$ denotes the consumption space).

share|improve this answer

edited 5 hours ago

answered 6 hours ago

Martin Van der LindenMartin Van der Linden

3,7011240

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Example 1 can be represented as a function though, relating the set of alternatives $S$ to the powerset of $S$. It is not very unusual to see it represented this way. It's perfectly fine (mathematically) to have a function relate elements to sets. It's just not a function from the set to itself in that case. Example 2 has the same issue.
  $endgroup$
  – John Doucette
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sure. Every relation $R subseteq (Atimes B)$ can be somewhat "equivalently" represented as a function $f colon A rightarrow 2^B$ such that for all $a in A$ and all $b in B$, we have $b in f(a)$ if and only if $(a,b) in R$. It remains that $succ$ is not itself a function. I think it's fair to say that binary relations like $succ$ are "useful" in economics. Since the OP's question was about "relations that are not functions and are useful in economics" that hopefully provides a good example.
  $endgroup$
  – Martin Van der Linden
  1 hour ago
  

  
  
  
  

add a comment | 

$begingroup$

I feel that your question might be a little broad, but there are certainly many areas of economics where non-functional relations are used. Two simple examples (there are many others):

1. One of the most fundamental models of behavior in economics relies on the idea that choices can be represented by "preferences" which mathematically are binary relations that do not have to be functions (they very often are not, e.g., $A succ B succ C$ is not a function, since $succ = (A,B), (A,C), (B,C)$.


2. Economics also relies on correspondences, or ``multivalued" functions (which, depending on the definition, can be just another way to view binary relations). Correspondences are used in a lot of subfields of economics but perhaps most notably in consumer theory, where the choice set of consumer with preference $succeq$ and budget set $B$ can be a whole subset of the consumption space $C(succ,B) subseteq X$ (where $X$ denotes the consumption space).

share|improve this answer

edited 5 hours ago

answered 6 hours ago

Martin Van der LindenMartin Van der Linden

3,7011240

$endgroup$

share|improve this answer

edited 5 hours ago

answered 6 hours ago

Martin Van der LindenMartin Van der Linden

3,7011240

answered 6 hours ago

Martin Van der LindenMartin Van der Linden

3,7011240

answered 6 hours ago

Martin Van der LindenMartin Van der Linden

3,7011240