<p>Under Gorman's conditions, a &quot;normative representative consumer&quot; exists, a single consumer such that an allocation is Pareto efficient if and only if it maximizes the utility of the representative consumer.</p>
<p>So if one proves the first welfare theorem, the result that shows that all market equilibrium allocations are Pareto efficient in the Arrow-Debreu-McKenzie  or related models, by showing a market allocation maximizes the utility of a representative consumer, one would essentially require Gorman's condition.</p>
<p>However, the usual short and...uhm...elegant proof of the first welfare theorem does no such thing and works perfectly well without Gorman's condition. This is something that one can find in pretty much every graduate-level microeconomics textbook.</p>

CC BY-SA 4.0
2024-11-24T13:15:32.127Z
2024-11-24T13:15:32.127Z
Michael Greinecker
<p>In the book Underskud from 2024, Emma Holten claims that [G53] shows that &quot;no mathematically elegant proof exists that markets distribute and set prices in an optimal way&quot; (my translation). I guess this refers to the conditions for individuals (parallel Engels curves) that must be fulfilled for the existence of a unique aggregate utility function and demand curve for the community.</p>
<p>From a mathematical standpoint, Holten's statement makes little sense (like, why would it matter if the proof is elegant?). But is Holten right in spirit that Gorman's paper shows some fundamental limitations of markets? And do those limitations have significant practical consequences for real-world markets?</p>
<p>[G53] Gorman, Community preference fields, 1953</p>

<markets><aggregate-demand>
What are the consequences of Gorman's paper community preference fields?
Strandtomt
# What are the consequences of Gorman's paper community preference fields?

(Asked by: username_0 on 2024-11-24)

In the book Underskud from 2024, Emma Holten claims that [G53] shows that "no mathematically elegant proof exists that markets distribute and set prices in an optimal way" (my translation). I guess this refers to the conditions for individuals (parallel Engels curves) that must be fulfilled for the existence of a unique aggregate utility function and demand curve for the community.

From a mathematical standpoint, Holten's statement makes little sense (like, why would it matter if the proof is elegant?). But is Holten right in spirit that Gorman's paper shows some fundamental limitations of markets? And do those limitations have significant practical consequences for real-world markets?

[G53] Gorman, Community preference fields, 1953

**Tags:** markets, aggregate-demand


---

## 1 answers

### Answer by username_1 on 2024-11-24. Score: 1

Under Gorman's conditions, a "normative representative consumer" exists, a single consumer such that an allocation is Pareto efficient if and only if it maximizes the utility of the representative consumer.

So if one proves the first welfare theorem, the result that shows that all market equilibrium allocations are Pareto efficient in the Arrow-Debreu-McKenzie or related models, by showing a market allocation maximizes the utility of a representative consumer, one would essentially require Gorman's condition.

However, the usual short and...uhm...elegant proof of the first welfare theorem does no such thing and works perfectly well without Gorman's condition. This is something that one can find in pretty much every graduate-level microeconomics textbook.


---

