<p>Thaler's acquisition/transaction utility and Fehr-Schmidt's inequity averse utility apply in very different contexts, and the arguments to the two utility functions are different as well. </p>

<p>Thaler's acquisition/transaction utility function is used to evaluate purchasing decisions. Say an individual has value <span class="math-container">$\bar p$</span> for an object that sells for <span class="math-container">$p$</span>, and the reference price for the object is <span class="math-container">$p^*$</span>, then her acquisition utility for the object would be <span class="math-container">$U_A(\bar p, p)=\bar p-p$</span>, her transaction utility would be <span class="math-container">$U_T(p^*,p)=p^*-p$</span>, and her total utility would be <span class="math-container">$$U(\bar p,p,p^*)=U_A+U_T=(\bar p-p)+(p^*-p).$$</span> Three arguments go into this utility function: <span class="math-container">$\bar p$</span>, <span class="math-container">$p$</span>, and <span class="math-container">$p^*$</span>. The terms <em>acquisition utility</em> and <em>transaction utility</em> are commonly understood to refer to <span class="math-container">$U_A$</span> and <span class="math-container">$U_T$</span>, respectively. </p>

<p>Fehr-Schmidt's inequity averse utility applies when an individual <span class="math-container">$i$</span> evaluates an outcome involving payoffs to <span class="math-container">$n$</span> individuals. Individual <span class="math-container">$i$</span>'s (inequity-averse) utility over payoff outcome outcome <span class="math-container">$(x_1,\dots,x_n)$</span> has the following form: 
<span class="math-container">\begin{equation}
U_i(x_1,\dots,x_n)=x_i-\frac{\alpha_i}{n-1}\sum_{j\ne i}\max\{x_j-x_i,0\}-\frac{\beta_i}{n-1}\sum_{j\ne i}\max\{x_i-x_j,0\},
\end{equation}</span>
where <span class="math-container">$\alpha_i\ge \beta_i$</span> and <span class="math-container">$\beta_i\in[0,1]$</span>.
Fehr and Schmidt call the second term <em>disutility from disadvantageous inequity</em> and the third term <em>disutility from advantageous inequity</em>. The arguments that go into this utility function are the payoffs received by the individuals. It appears that your version of inequity-averse utility deviates quite a bit from the version Fehr and Schmidt has, even with <span class="math-container">$n=2$</span>, since the terms <span class="math-container">$\bar p,p,p^*$</span> are not properly defined. </p>

CC BY-SA 4.0
2020-05-22T20:08:58.450Z
2020-05-22T20:08:58.450Z
Herr K.
<p>Your formulas contain an undefined <span class="math-container">$p^*$</span>, and the Fehr-Schmidt utility function is wrong. The brackets should be <span class="math-container">$\max\{p^*-p,0\}$</span> and <span class="math-container">$\max\{p-p^*,0\}$</span>, respectively. Apart form that, the two additional terms are usually called the disutility from advantageous inequity and the disutility from disadvantageous inequity, respectively. Calling them "transactional (dis)utility" would not fit in this context.</p>

CC BY-SA 4.0
2020-05-26T01:20:00.077Z
@KarlA: I don't know of any general term for these kinds of additional utility components. You might call them "nonstandard utility", but I guess it would be better to come up with a model-specific name if necessary.
VARulle
CC BY-SA 4.0
2020-05-25T13:57:00.690Z
Thanks for the answer! I was a little bit sloppy, I admit. My question was not so much about how these terms are called in their respective theories but rather whether there is a term for these "additional utility components". The first part $\overline{p}-p$ is like a standard utility function. But is there a term for these different types of additional (dis-)utility
Karl A
CC BY-SA 4.0
2020-05-22T15:36:10.223Z
2020-05-22T15:36:10.223Z
VARulle
<p>I am looking for a term describing the second part of a utility function in behavioral economics and related disciplines.</p>
<p>For example, Thaler (1983) describes a utility function that could be simplified like</p>
<p><span class="math-container">$u_i=\overline{p}-p \pm v(p^*-p)$</span></p>
<p>with <span class="math-container">$\overline{p}$</span> valuation of the good, <span class="math-container">$p$</span> price of the good, and <span class="math-container">$v(p^*-p)$</span> the so-called transaction utility; the utility gain/loss from making a bargain or being ripped off.
Similarly, a simplified Fehr-Schmidt utility (1999) function consists of</p>
<p><span class="math-container">$u_i=(\overline{p}-p)-\alpha (p^*-p)-\beta (p-p^*)$</span>.</p>
<p>with the second and the third term of the utility function describing negative preferences for inequity.</p>
<p>Thaler calls the first term &quot;acquisition utility&quot; and the second term &quot;transactional utility&quot;. Is this a consensus in (behavioral) economics, i.e., could we call the second/third part of Fehr-Schmidt &quot;transactional utility&quot; or is there another, better term for this second part of utility that is added to the &quot;classical&quot; utility?</p>
<p>Do you know of a paper comparing these terms? I only do so with respect to fairness (Fehr, Schmidt, 2006; Clavien, Chapuisat, 2016).</p>
<p>...</p>
<p><em>Clavien, Christine; Chapuisat, Michel (2016): The evolution of utility functions and psychological altruism. In: Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 56, S. 24–31. DOI: 10.1016/j.shpsc.2015.10.008.</em></p>
<p><em>Fehr, Ernst; Schmidt, Klaus M. (1999): A Theory of Fairness, Competition, and Cooperation. In: Quarterly Journal of Economics 114 (3), S. 817–868. DOI: 10.1162/003355399556151.</em></p>
<p><em>Fehr, Ernst; Schmidt, Klaus M. (2006): The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories. In: Foundations, Bd. 1: Elsevier (Handbook of the Economics of Giving, Altruism and Reciprocity), S. 615–691.</em></p>
<p><em>Thaler, Richard (1983): Transaction Utility Theory. In: Advances in Consumer Research 10 (1), S. 229–32.</em></p>

<utility><behavioral-economics>
Additional components in utility functions (behavioral economics)
Karl A
# Additional components in utility functions (behavioral economics)

(Asked by: username_0 on 2020-05-22)

I am looking for a term describing the second part of a utility function in behavioral economics and related disciplines.

For example, Thaler (1983) describes a utility function that could be simplified like

$u\_i=\overline{p}-p \pm v(p^\*-p)$

with $\overline{p}$ valuation of the good, $p$ price of the good, and $v(p^\*-p)$ the so-called transaction utility; the utility gain/loss from making a bargain or being ripped off.
Similarly, a simplified Fehr-Schmidt utility (1999) function consists of

$u\_i=(\overline{p}-p)-\alpha (p^\*-p)-\beta (p-p^\*)$.

with the second and the third term of the utility function describing negative preferences for inequity.

Thaler calls the first term "acquisition utility" and the second term "transactional utility". Is this a consensus in (behavioral) economics, i.e., could we call the second/third part of Fehr-Schmidt "transactional utility" or is there another, better term for this second part of utility that is added to the "classical" utility?

Do you know of a paper comparing these terms? I only do so with respect to fairness (Fehr, Schmidt, 2006; Clavien, Chapuisat, 2016).

...

*Clavien, Christine; Chapuisat, Michel (2016): The evolution of utility functions and psychological altruism. In: Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 56, S. 24–31. DOI: 10.1016/j.shpsc.2015.10.008.*

*Fehr, Ernst; Schmidt, Klaus M. (1999): A Theory of Fairness, Competition, and Cooperation. In: Quarterly Journal of Economics 114 (3), S. 817–868. DOI: 10.1162/003355399556151.*

*Fehr, Ernst; Schmidt, Klaus M. (2006): The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories. In: Foundations, Bd. 1: Elsevier (Handbook of the Economics of Giving, Altruism and Reciprocity), S. 615–691.*

*Thaler, Richard (1983): Transaction Utility Theory. In: Advances in Consumer Research 10 (1), S. 229–32.*

**Tags:** utility, behavioral-economics

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## 2 answers

### Answer by username_1 on 2020-05-22. Score: 5

Thaler's acquisition/transaction utility and Fehr-Schmidt's inequity averse utility apply in very different contexts, and the arguments to the two utility functions are different as well.

Thaler's acquisition/transaction utility function is used to evaluate purchasing decisions. Say an individual has value $\bar p$ for an object that sells for $p$, and the reference price for the object is $p^\*$, then her acquisition utility for the object would be $U\_A(\bar p, p)=\bar p-p$, her transaction utility would be $U\_T(p^\*,p)=p^\*-p$, and her total utility would be $$U(\bar p,p,p^\*)=U\_A+U\_T=(\bar p-p)+(p^\*-p).$$ Three arguments go into this utility function: $\bar p$, $p$, and $p^\*$. The terms *acquisition utility* and *transaction utility* are commonly understood to refer to $U\_A$ and $U\_T$, respectively.

Fehr-Schmidt's inequity averse utility applies when an individual $i$ evaluates an outcome involving payoffs to $n$ individuals. Individual $i$'s (inequity-averse) utility over payoff outcome outcome $(x\_1,\dots,x\_n)$ has the following form:
\begin{equation}
U\_i(x\_1,\dots,x\_n)=x\_i-\frac{\alpha\_i}{n-1}\sum\_{j\ne i}\max\{x\_j-x\_i,0\}-\frac{\beta\_i}{n-1}\sum\_{j\ne i}\max\{x\_i-x\_j,0\},
\end{equation}
where $\alpha\_i\ge \beta\_i$ and $\beta\_i\in[0,1]$.
Fehr and Schmidt call the second term *disutility from disadvantageous inequity* and the third term *disutility from advantageous inequity*. The arguments that go into this utility function are the payoffs received by the individuals. It appears that your version of inequity-averse utility deviates quite a bit from the version Fehr and Schmidt has, even with $n=2$, since the terms $\bar p,p,p^\*$ are not properly defined.


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### Answer by username_2 on 2020-05-22. Score: 5

Your formulas contain an undefined $p^\*$, and the Fehr-Schmidt utility function is wrong. The brackets should be $\max\{p^\*-p,0\}$ and $\max\{p-p^\*,0\}$, respectively. Apart form that, the two additional terms are usually called the disutility from advantageous inequity and the disutility from disadvantageous inequity, respectively. Calling them "transactional (dis)utility" would not fit in this context.

> **Comments:**
> **username_0**: Thanks for the answer! I was a little bit sloppy, I admit. My question was not so much about how these terms are called in their respective theories but rather whether there is a term for these "additional utility components". The first part $\overline{p}-p$ is like a standard utility function. But is there a term for these different types of additional (dis-)utility  
> **username_2**: @KarlA: I don't know of any general term for these kinds of additional utility components. You might call them "nonstandard utility", but I guess it would be better to come up with a model-specific name if necessary.  

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