<p>To expand on @1muflon1's answer. The theory of rational addiction assumes that the utility of a consumer at time instance <span class="math-container">$t$</span> depends both on current consumption of the addicitve good, say <span class="math-container">$c_t$</span>, and the consumption of the addictive good in the past. For simplicity say <span class="math-container">$c_{t-1}$</span>. So at period <span class="math-container">$t$</span> the instantaneous utility looks something like:
<span class="math-container">$$
u(c_t, c_{t-1}, y_t),
$$</span>
where <span class="math-container">$y_t$</span> is the consumption of all other goods. Over the lifetime the consumer maximizes:
<span class="math-container">$$
\sum_{t = 0}^\infty \delta^t u(c_t, c_{t-1}, y_t).
$$</span>
where <span class="math-container">$\delta$</span> is the discount rate. A crucial assumption in Becker and Murphy's paper is that marginal utility <span class="math-container">$\dfrac{\partial u}{\partial c_t}$</span>  is increasing in <span class="math-container">$c_{t-1}$</span>, so:
<span class="math-container">$$
\dfrac{\partial u}{\partial c_t \partial c_{t-1}} &gt; 0
$$</span>
In this sense, your idea that addiction causes an increase in marginal utility is not so crazy and perfectly in line which what other economists have been thinking all along (btw, Becker won the nobel prize specifically for &quot;<a href="https://www.nobelprize.org/prizes/economic-sciences/1992/becker/facts/" rel="nofollow noreferrer">having extended the domain of microeconomic analysis to a wide range of human behaviour and interaction, including nonmarket behaviour</a>&quot;).</p>
<p>There is quite a sizeable literature on rational addiction and rational habit formation starting with the paper of Becker and Murphy and <a href="https://doi.org/10.1016/0014-2921(81)90068-4" rel="nofollow noreferrer">Spinnewyn(1981)</a>.</p>

CC BY-SA 4.0
2021-07-16T17:23:07.847Z
I am not familiar with that theory. How is it capturing the fact that after a certain time, addicts need a certain amount of drug just to feel normal (as they did before starting taking them) and that they need more of the drug to feel better than that. Is that what $\frac{\delta u}{\delta c_t \delta c_{t-1} }> 0$ is saying?
BrsG
CC BY-SA 4.0
2021-07-16T18:38:59.850Z
@BRSG I think what you are referring to is tollerance, which means that the same level of consumption provides less utility when addiction is greater. This would be captured by $\frac{\partial u}{\partial c_{t-1}} < 0$. This is different to the concept of reinforcement which relates to the fact that higher consumption today leads to more consumption tomorrow. The latter is related to the complementarity as described in my answer.
tdm
CC BY-SA 4.0
2021-07-16T09:20:48.820Z
2021-07-16T18:39:14.280Z
2021-07-16T18:39:14.280Z
tdm
<p>It is possible for an addict to be rational. A famous work on this was done by <a href="https://www.jstor.org/stable/1830469" rel="nofollow noreferrer">Becker (1988)</a> Theory of Rational addiction.</p>
<p>In order for agent to have rational preferences the preferences have to satisfy the following definition (See MWG Microeconomic Theory pp 6):</p>
<blockquote>
<p><strong>Definition 1.B.1</strong>: The preference relation <span class="math-container">$\succeq$</span> is rational if it possesses the following two properties:</p>
<p>(i) Completeness: for all <span class="math-container">$x,y \in X$</span> we have that <span class="math-container">$x \succeq y$</span> or <span class="math-container">$y \succeq x$</span> (or both).</p>
<p>(ii) Transitivity: For all <span class="math-container">$x,y,z \in X$</span>, if <span class="math-container">$x\succeq$</span> and <span class="math-container">$y \succeq z$</span> then <span class="math-container">$x\succeq z$</span>.</p>
</blockquote>
<p>However, note modern scholarship on addictions nowadays goes beyond rational agent model since addiction typically involves some behavioral biases such as hyperbolic discounting (example of time inconsistent preferences that are no longer rational), so I think probably this is what your professor was referring to.</p>
<p>This being said you certainly can have model with fully rational addicts, the question is whether that's the most appropriate way of modelling addiction.</p>

CC BY-SA 4.0
2021-07-15T12:15:39.093Z
2021-07-15T12:22:06.490Z
2021-07-15T12:22:06.490Z
1muflon1
<p>I got to know that alcohol addiction is a case of increasing marginal utility. My professor refutes me bluntly stating that once a person starts consuming he no longer remains to be a 'rational consumer' (a drunk person will lose the sense of rationality). So, alcohol addiction is out of the scope of the economic model which assumes that consumers are rational. My doubt is, can't an addict be a rational consumer? If no, why? Who exactly is a rational consumer</p>

CC BY-SA 4.0
2021-07-15T12:13:36.030Z
Addictions are often modelled as time-inconsistent behavior and highly discounted future payoffs. I don't see why excessive consumption requires increasing marginal utility, and I don't believe this is the case in any addiction.
Bayesian
<microeconomics><utility><marginal><measuring-utility>
Is addiction a case of increasing marginal utility?
Dharshan Sagar
# Is addiction a case of increasing marginal utility?

(Asked by: username_0 on 2021-07-15)

I got to know that alcohol addiction is a case of increasing marginal utility. My professor refutes me bluntly stating that once a person starts consuming he no longer remains to be a 'rational consumer' (a drunk person will lose the sense of rationality). So, alcohol addiction is out of the scope of the economic model which assumes that consumers are rational. My doubt is, can't an addict be a rational consumer? If no, why? Who exactly is a rational consumer

**Tags:** microeconomics, utility, marginal, measuring-utility

> **Comments:**
> **username_1**: Addictions are often modelled as time-inconsistent behavior and highly discounted future payoffs. I don't see why excessive consumption requires increasing marginal utility, and I don't believe this is the case in any addiction.  

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## 2 answers

### Answer by username_2 on 2021-07-16. Score: 4

To expand on @username_4's answer. The theory of rational addiction assumes that the utility of a consumer at time instance $t$ depends both on current consumption of the addicitve good, say $c\_t$, and the consumption of the addictive good in the past. For simplicity say $c\_{t-1}$. So at period $t$ the instantaneous utility looks something like:
$$
u(c\_t, c\_{t-1}, y\_t),
$$
where $y\_t$ is the consumption of all other goods. Over the lifetime the consumer maximizes:
$$
\sum\_{t = 0}^\infty \delta^t u(c\_t, c\_{t-1}, y\_t).
$$
where $\delta$ is the discount rate. A crucial assumption in Becker and Murphy's paper is that marginal utility $\dfrac{\partial u}{\partial c\_t}$ is increasing in $c\_{t-1}$, so:
$$
\dfrac{\partial u}{\partial c\_t \partial c\_{t-1}} > 0
$$
In this sense, your idea that addiction causes an increase in marginal utility is not so crazy and perfectly in line which what other economists have been thinking all along (btw, Becker won the nobel prize specifically for "[having extended the domain of microeconomic analysis to a wide range of human behaviour and interaction, including nonmarket behaviour](https://www.nobelprize.org/prizes/economic-sciences/1992/becker/facts/)").

There is quite a sizeable literature on rational addiction and rational habit formation starting with the paper of Becker and Murphy and [Spinnewyn(1981)](https://doi.org/10.1016/0014-2921(81)90068-4).

> **Comments:**
> **username_3**: I am not familiar with that theory. How is it capturing the fact that after a certain time, addicts need a certain amount of drug just to feel normal (as they did before starting taking them) and that they need more of the drug to feel better than that. Is that what $\frac{\delta u}{\delta c_t \delta c_{t-1} }> 0$ is saying?  
> **username_2**: @username_3 I think what you are referring to is tollerance, which means that the same level of consumption provides less utility when addiction is greater. This would be captured by $\frac{\partial u}{\partial c_{t-1}} < 0$. This is different to the concept of reinforcement which relates to the fact that higher consumption today leads to more consumption tomorrow. The latter is related to the complementarity as described in my answer.  

---

### Answer by username_4 on 2021-07-15. Score: 3

It is possible for an addict to be rational. A famous work on this was done by [Becker (1988)](https://www.jstor.org/stable/1830469) Theory of Rational addiction.

In order for agent to have rational preferences the preferences have to satisfy the following definition (See MWG Microeconomic Theory pp 6):

> **Definition 1.B.1**: The preference relation $\succeq$ is rational if it possesses the following two properties:
>
> (i) Completeness: for all $x,y \in X$ we have that $x \succeq y$ or $y \succeq x$ (or both).
>
> (ii) Transitivity: For all $x,y,z \in X$, if $x\succeq$ and $y \succeq z$ then $x\succeq z$.

However, note modern scholarship on addictions nowadays goes beyond rational agent model since addiction typically involves some behavioral biases such as hyperbolic discounting (example of time inconsistent preferences that are no longer rational), so I think probably this is what your professor was referring to.

This being said you certainly can have model with fully rational addicts, the question is whether that's the most appropriate way of modelling addiction.


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