# Why do some models have a habit stock in consumer utility function?

I have searched for this on the internet and found the Columbia University.pdf file

In the first paragraph, it says

"Intuitively, the more the consumer eats today, the hungrier he wakes up tomorrow."

I cannot understand this statement.

Would anybody be able to enlighten me?

Thank you

I quote a passage of the article you linked:

Habit persistence, or ‘habit formation’ in its most common representation, is a preference specification according to which the period utility function depends on a quasi-difference of consumption. Specifically, if the utility function without habit formation is given by

$$\sum_0^\infty \beta^tU(c_t)\qquad (1)$$

where $$c_t$$ denotes consumption in period $$t$$, $$U$$ denotes the period utility function, and $$\beta \in (0,1)$$ denotes the subjective discount factor, then the utility function with habit persistence is given by $$\sum_0^\infty \beta^tU(c_t-\alpha c_{t-1}).\qquad (2)$$ The parameter $$\alpha \in (0,1)$$ denotes the intensity of habit formation and introduces non-separability of preferences over time. [emphasis mine]

To understand the meaning of habit persistence, we have to look at the different forms of the utility functions $$(1)$$ and $$(2)$$.

In the utility function $$(2)$$ the utility depends not only on the current period consumption $$c_t$$, but also on the consumption of the previous period $$c_{t-1}$$. In particular, the utility depends on the difference between current and past period consumption wheigted by a parameter $$\alpha \in (0,1)$$, which the article calls intensity of habit formation.

What does it mean? It means that, given $$\alpha$$, the more the present consumption differs from the previous period consumption, the lower will be the utility.

This, intuitively, means that a consumer considers not only the present consumption, but also how much this present consumption differs from the past: this can be interpreted as the fact that the consumer has formed habits of consumption over time, and attaches a positive utility to the fact that the amount of consumption is similar to their past habits: they doesn't want that their pattern of consumption vary too much over time.

In this sense, the difference $$c_t-\alpha c_{t-1}$$ can be seen as proxy of the unwillingness of the consumer to vary habits.

$$\alpha$$ can be seen as a measure of this attachment to habits: if $$\alpha$$ is high, for the same level of current consumption, the difference is smaller, and the result will be a lower current utility, and vice versa.

The article continues by writing:

Under habit persistence, an increase in current consumption [$$c_{t-1}$$, my note] lowers the marginal utility of consumption in the current period [$$t-1$$, my note] and increases it in the next period [$$t$$, my note]. Intuitively, the more the consumer eats today, the hungrier he wakes up tomorrow. [italics mine]

The sentence in italics says simply this fact, if I eat a lot today, tomorrow this will enter negatively in my utility function, and in order to have a given level of utility I will have the necessity to eat more tomorrow (I will be hungrier in this sense).

• Wow this was really helpful. Thank you so much @BakerStreet
– EHMJ
Commented Jun 17, 2023 at 20:22
• I'm happy having been helpful! Commented Jun 17, 2023 at 20:52

People develop habits. If someone eats more than average and becomes fat it is likely that person won't stop eating more than average tomorrow. That is what they mean by eating lot today and waking up hungrier tomorrow.

• Thank you so much for the help! @csilvia
– EHMJ
Commented Jun 17, 2023 at 20:22