<p>Consider the following passage in Sonnenschein (1973; full citation below):</p>
<p><a href="https://i.sstatic.net/ddukx.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ddukx.png" alt="enter image description here" /></a></p>
<p>Perhaps because I do not know much about the uniform Lipschitz condition, I do not follow his exposition after the first two sentences of the proof. That is, do the definitions of <span class="math-container">$g_1^1$</span> and <span class="math-container">$g_1^2$</span> come from some standard result in mathematics? Any intuition here would be appreciated.</p>
<p>Furthermore, what is the source of <span class="math-container">$(g_1^1, I-pg_1^1)$</span> and <span class="math-container">$(g_2^1, I-pg_2^1)$</span>?</p>
<p>Thank you.</p>
<p>Citation:</p>
<p>Sonnenschein, H. 1973. &quot;Do Walras’ identity and Continuity Characterize
the Class of Community Excess Demand Functions?&quot; <em>Journal of Economic Theory</em> 6: 345-354.</p>

CC BY-SA 4.0
2020-07-15T18:30:16.063Z
Is the question what a uniform Lipschitz condition is? The functions are constructed to be demand functions for the first good. Then the demand functions for both goods must be $(g_1^1, I-pg_1^1)$ and $(g^1_2,I−pg^1_2)$ comes from the consumer satisfying the budget constraint and the price of the second good being normalized to $1$.
Michael Greinecker
CC BY-SA 4.0
2020-07-16T00:47:37.323Z
I am asking whether he is just taking the $g_1^1$ as a given (which then leads to the question of why that choice was made) or if it is derived from some standard piece of mathematics in the same way that we could write, say, the product rule in calculus using general notation.
Ryan da Silva
CC BY-SA 4.0
2020-07-16T06:05:51.867Z
The construction is chosen because it works, and that is something you see if you read on how the functions are used later in the proof.
Michael Greinecker
<general-equilibrium>
Proof of excess community demand function in Sonnenschein (1973)
Ryan da Silva
# Proof of excess community demand function in Sonnenschein (1973)

(Asked by: username_0 on 2020-07-15)

Consider the following passage in Sonnenschein (1973; full citation below):

[![enter image description here](https://i.sstatic.net/ddukx.png)](https://i.sstatic.net/ddukx.png)

Perhaps because I do not know much about the uniform Lipschitz condition, I do not follow his exposition after the first two sentences of the proof. That is, do the definitions of $g\_1^1$ and $g\_1^2$ come from some standard result in mathematics? Any intuition here would be appreciated.

Furthermore, what is the source of $(g\_1^1, I-pg\_1^1)$ and $(g\_2^1, I-pg\_2^1)$?

Thank you.

Citation:

Sonnenschein, H. 1973. "Do Walras’ identity and Continuity Characterize
the Class of Community Excess Demand Functions?" *Journal of Economic Theory* 6: 345-354.

**Tags:** general-equilibrium

> **Comments:**
> **username_1**: Is the question what a uniform Lipschitz condition is? The functions are constructed to be demand functions for the first good. Then the demand functions for both goods must be $(g_1^1, I-pg_1^1)$ and $(g^1_2,I−pg^1_2)$ comes from the consumer satisfying the budget constraint and the price of the second good being normalized to $1$.  
> **username_0**: I am asking whether he is just taking the $g_1^1$ as a given (which then leads to the question of why that choice was made) or if it is derived from some standard piece of mathematics in the same way that we could write, say, the product rule in calculus using general notation.  
> **username_1**: The construction is chosen because it works, and that is something you see if you read on how the functions are used later in the proof.  

---

## 0 answers

