# Is addiction a case of increasing marginal utility?

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

• 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. Jul 15 '21 at 12:13
• Thanks for clearing my doubt! Jul 15 '21 at 14:05

To expand on @1muflon1'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").

There is quite a sizeable literature on rational addiction and rational habit formation starting with the paper of Becker and Murphy and Spinnewyn(1981).

• 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
Jul 16 '21 at 17:23
• @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
Jul 16 '21 at 18:38

It is possible for an addict to be rational. A famous work on this was done by Becker (1988) 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.