3
$\begingroup$

(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.

$\endgroup$
  • $\begingroup$ You really should post this as two questions instead of one. $\endgroup$ – The Almighty Bob Apr 13 '15 at 16:39
1
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ 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., $u_{ij}= v_j-\alpha log(p_j) + \epsilon_{ij}$. $\endgroup$ – berter Apr 13 '15 at 15:51
  • $\begingroup$ 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.) $\endgroup$ – berter Apr 17 '15 at 16:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.