<p>You could use the fact that <span class="math-container">$\sum_{i=1}^{n}e_i=y$</span> (adding-up property) to see which parameter values are compatible with the above specification and this identity.<br>
Before proceeding, you should replace on the RHS <span class="math-container">$\sum_{i=1}^{n}\beta_{ij}p_i$</span> by <span class="math-container">$\sum_{j=1}^{n}\beta_{ij}p_j$</span>.</p>

CC BY-SA 4.0
2019-10-19T11:22:43.023Z
Okay thank you, I'm starting to understand it a bit better but I'm still not there. I also have the answer from the back of the textbook but I don't really understand it. If you could give me a few more hints I would really appreciate it.
Jack Salvatore
CC BY-SA 4.0
2019-10-18T11:25:36.667Z
2019-10-18T11:25:36.667Z
Bertrand
<p>You plan to use the following specification for an empirical study:
<span class="math-container">$$e_i = \alpha_i + \sum_{j=1}^{n} \beta_{ij}p_i + \gamma_iy +\delta_i, 
i=1,...,n$$</span> 
where <span class="math-container">$e_i$</span> is the consumer's expenditure on good <span class="math-container">$i$</span>, <span class="math-container">$p_i$</span> is the price of good <span class="math-container">$i$</span>, <span class="math-container">$y$</span> is the income and the <span class="math-container">$\alpha_i, \beta_{ij}, \gamma_i, \delta_i$</span> are parameters.</p>

<p>You want the specification to be consistent with standard consumer theory and three friends offer the following opinions: </p>

<p>1) “the equation will work for any values of the parameters;” </p>

<p>(2) “you need to impose the  <span class="math-container">$\beta_{ij}=0,\sum_{i=1}^{n}, \delta_{i}=1$</span>";</p>

<p>(3)“you need to impose restrictions such as <span class="math-container">$\beta_ij = -\gamma_i\alpha_j, \gamma_i \geq 0,\sum_{i=1}^{n}, \gamma{i}=1,\delta_i=0 $</span></p>

<p>(a) Explain which of the friends gave sensible advice.
(b) Why should you really not listen to the advice of the other friends?</p>

CC BY-SA 4.0
2019-10-17T21:18:15.637Z
As on the LHS of the equality there is $e_i$ indexed by $i$, there should be $\sum_{j=1}^{n} \beta_{ij}p_j$ on the RHS (which depends upon $i$ not $j$).
Bertrand
CC BY-SA 4.0
2019-10-17T21:24:44.790Z
You could also give some elements of response showing us that you have thought about the question. What are the properties of Marshallian demand functions?
Bertrand
CC BY-SA 4.0
2019-10-18T09:41:22.253Z
I haven't studied the Marshallian demand functions (as this is the 1st week of consumer theory and 3rd week of university) but my thought process was that the expenditure for a good will be price times quantity of that good, so you have to assume that $\alpha$ is the quantity. That means that the first part (alpha times price) is the$e_i$, and the rest has to be zero, so the third friend is right
Jack Salvatore
<microeconomics><consumer-theory>
Consumer Theory question
Jack Salvatore
# Consumer Theory question

(Asked by: username_0 on 2019-10-17)

You plan to use the following specification for an empirical study:
$$e\_i = \alpha\_i + \sum\_{j=1}^{n} \beta\_{ij}p\_i + \gamma\_iy +\delta\_i,
i=1,...,n$$
where $e\_i$ is the consumer's expenditure on good $i$, $p\_i$ is the price of good $i$, $y$ is the income and the $\alpha\_i, \beta\_{ij}, \gamma\_i, \delta\_i$ are parameters.

You want the specification to be consistent with standard consumer theory and three friends offer the following opinions:

1) “the equation will work for any values of the parameters;”

(2) “you need to impose the $\beta\_{ij}=0,\sum\_{i=1}^{n}, \delta\_{i}=1$";

(3)“you need to impose restrictions such as $\beta\_ij = -\gamma\_i\alpha\_j, \gamma\_i \geq 0,\sum\_{i=1}^{n}, \gamma{i}=1,\delta\_i=0 $

(a) Explain which of the friends gave sensible advice.
(b) Why should you really not listen to the advice of the other friends?

**Tags:** microeconomics, consumer-theory
> **Comments:**
> **username_1**: As on the LHS of the equality there is $e_i$ indexed by $i$, there should be $\sum_{j=1}^{n} \beta_{ij}p_j$ on the RHS (which depends upon $i$ not $j$).  
> **username_1**: You could also give some elements of response showing us that you have thought about the question. What are the properties of Marshallian demand functions?  
> **username_0**: I haven't studied the Marshallian demand functions (as this is the 1st week of consumer theory and 3rd week of university) but my thought process was that the expenditure for a good will be price times quantity of that good, so you have to assume that $\alpha$ is the quantity. That means that the first part (alpha times price) is the$e_i$, and the rest has to be zero, so the third friend is right  

---

## 1 answers

### Answer by username_1 on 2019-10-18. Score: 0

You could use the fact that $\sum\_{i=1}^{n}e\_i=y$ (adding-up property) to see which parameter values are compatible with the above specification and this identity.  
Before proceeding, you should replace on the RHS $\sum\_{i=1}^{n}\beta\_{ij}p\_i$ by $\sum\_{j=1}^{n}\beta\_{ij}p\_j$.

> **Comments:**
> **username_0**: Okay thank you, I'm starting to understand it a bit better but I'm still not there. I also have the answer from the back of the textbook but I don't really understand it. If you could give me a few more hints I would really appreciate it.  

---

