# Intuitive Explanation of Convex Preference

Could you explain intuitively why the phenomena of convex preference exist in the market?

• What do markets have to do with them? Commented Oct 8, 2022 at 11:08
• @MichaelGreinecker Like, because consumers have preference convexity, a monopolist who originally sells only one product in the market can surely make more money after introducing a new product with differentiated quality. I don't know if I understand your question. Commented Oct 8, 2022 at 11:46

From an intuitive point of view, convexity of preferences can be interpreted as a 'taste for diversification', that is a consumer prefers (at least weakly) bundles more 'balanced ' with respect to the quantity of each good to 'unbalanced' bundles, heavily weighted toward one commodity.

From Mas Colell, Green, Whinston, Microeconomc Theory, 1995, p. 44:

Convexity can also be viewed as the formal expression of a basic inclination of economic agents for diversification. Indeed, under convexity, if $$x$$ is indifferent to $$y$$ , then $$\frac{1} {2} x+\frac{1} {2} y$$, the half mixture of $$x$$ and $$y$$, cannot be worse than either $$x$$ and $$y$$. [...] A taste for diversification is a realistic trait of economic life.

Therefore, for a monopolist, it could be convenient to produce two differentiated products, instead of only one.

• Hi! You quote a plausible argument, but could you please support the existence of convex preferences with empirical references? Commented Oct 8, 2022 at 20:52
• Hi Giskard! No. I tried to give an intuitive grasp of the concept of convexity of preferences, beyond formalization, as I thought the OP asked for, to understand, for instance, the logic of the behavior of a monopolist. I can’t quote experimental researches about actual existence of convex preferences. Commented Oct 9, 2022 at 15:24

Convex preferences simply exist. They are a fundamental innate feature of consumers and exist independently of markets. (Some) people can have convex preferences even in a centralized communist economy without markets. They just have these preferences.

For example, in microeconomics you could say preferences are just as fundamental as a person’s eye color, which exists regardless of circumstances.

• If your claim is more than "the existence of convex preferences is an assumption" can you please support it with some (empirical) references? Commented Oct 8, 2022 at 20:50