<p>Your first equation is an <strong>indirect</strong> utility function. The consumer chooses only one good and we assume that he can afford it. For simplification, the indirect utility discards the budget $m$ (often assumed be the same for all $i$).
Here, your demand function is perfectly inelastic. If the individual demand would not have been perfectly inelastic, the form would have been like $V=a-s(p)$, where $s'$ is strictly concave and increasing.</p>

<p>See, for example, Palma/Anderson/Thisse.</p>

CC BY-SA 3.0
2015-04-13T15:51:03.313Z
Is there any additional assumption required that equation (1) is a valid indirect utility function. For example that the indirect utilty is linear in price $p_j$ or could it be for example also linear in log price, i.e., $u_{ij}= v_j-\alpha log(p_j) + \epsilon_{ij}$.
berter
CC BY-SA 3.0
2015-04-17T16:28:05.637Z
Thanks! I guess you answered both questions. So I won't post the issue as second question, right? @TABob

So let me reformulate your answers once again for understanding:

1. (1) results in a demand function that is in agreement with the economic theory of utility maximizing consumers.

2. This is circumstance is also true, in the more general case, when price affects the indirect utility not necessarily in a linear but in strictly concave and increasing functional form.

(Until now I could not get access to a copy of the book of Palma/Anderson/Thisse. Hope to do so soon.)
berter
CC BY-SA 3.0
2015-04-13T15:38:30.147Z
2015-04-15T21:02:56.250Z
2015-04-15T21:02:56.250Z
Yann
<p>(1) Does the following result in a "valid" (in the sense of being consistent with the economic theory) market demand function?<br>
A consumer $i$ maximizes a utility $u_{ij}$ in choosing one of J alternatives, $j=1,..,J$:<br>
$u_{ij} = v_j - \alpha p_j + \epsilon_{ij}$<br>
where $v_j$ is the utility of alternative $j$ without the effect of price (i.e. $-\alpha p_j$) and the logit error term $\epsilon_{ij}$.<br>
The market demand results then as the choices of all consumers.</p>

<p>Is in accordance with economic theory to follow (1) and <em>not</em> assume a budget constraint but let the ultility of an alternative be directly affected by price?  And additionally assume that a consumer chooses one alternative (i.e., a corner solution follows directly from this assumption).  Does (1) result a  "valid" (in the sense of being consistent with the economic theory) market demand function ?</p>

<p>(2) Typically the theory of the microeconomic foundation of logit choice model (e.g.
<a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1718571" rel="nofollow">http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1718571</a>)  assumes that consumers maximize a utility function <em>without</em> the price effect <em>but</em> subject to a budget constraint. With a linear utility function, the maximization problem results in a corner solution of a consumer choosing only one choice alternative.
This setup (as outlined in the cited paper) leads than to the market demand.</p>

CC BY-SA 3.0
2015-04-13T16:39:35.927Z
You really should post this as two questions instead of one.
The Almighty Bob
<microeconomics><utility><choice-theory>
Microeconomic foundation of discrete choice model
berter
# Microeconomic foundation of discrete choice model

(Asked by: username_0 on 2015-04-13)

(1) Does the following result in a "valid" (in the sense of being consistent with the economic theory) market demand function?  
A consumer $i$ maximizes a utility $u\_{ij}$ in choosing one of J alternatives, $j=1,..,J$:  
$u\_{ij} = v\_j - \alpha p\_j + \epsilon\_{ij}$  
where $v\_j$ is the utility of alternative $j$ without the effect of price (i.e. $-\alpha p\_j$) and the logit error term $\epsilon\_{ij}$.  
The market demand results then as the choices of all consumers.

Is in accordance with economic theory to follow (1) and *not* assume a budget constraint but let the ultility of an alternative be directly affected by price? And additionally assume that a consumer chooses one alternative (i.e., a corner solution follows directly from this assumption). Does (1) result a "valid" (in the sense of being consistent with the economic theory) market demand function ?

(2) Typically the theory of the microeconomic foundation of logit choice model (e.g.
<http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1718571>) assumes that consumers maximize a utility function *without* the price effect *but* subject to a budget constraint. With a linear utility function, the maximization problem results in a corner solution of a consumer choosing only one choice alternative.
This setup (as outlined in the cited paper) leads than to the market demand.

**Tags:** microeconomics, utility, choice-theory
> **Comments:**
> **username_1**: You really should post this as two questions instead of one.  

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## 1 answers

### Answer by username_2 on 2015-04-13. Score: 1 | Accepted answer

Your first equation is an **indirect** utility function. The consumer chooses only one good and we assume that he can afford it. For simplification, the indirect utility discards the budget $m$ (often assumed be the same for all $i$).
Here, your demand function is perfectly inelastic. If the individual demand would not have been perfectly inelastic, the form would have been like $V=a-s(p)$, where $s'$ is strictly concave and increasing.

See, for example, Palma/Anderson/Thisse.

> **Comments:**
> **username_0**: Is there any additional assumption required that equation (1) is a valid indirect utility function. For example that the indirect utilty is linear in price $p_j$ or could it be for example also linear in log price, i.e., $u_{ij}= v_j-\alpha log(p_j) + \epsilon_{ij}$.  
> **username_0**: Thanks! I guess you answered both questions. So I won't post the issue as second question, right? @TABob  So let me reformulate your answers once again for understanding:  1. (1) results in a demand function that is in agreement with the economic theory of utility maximizing consumers.  2. This is circumstance is also true, in the more general case, when price affects the indirect utility not necessarily in a linear but in strictly concave and increasing functional form.  (Until now I could not get access to a copy of the book of Palma/Anderson/Thisse. Hope to do so soon.)  

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