# What are some examples of goods/services whose utility functions have local maxima?

I'm a calculus teacher trying to construct a realistic example of a smooth utility function $$U(x,y)$$ that has a local maximum at some point $$(x_0,y_0)$$. This requires two goods, X and Y, such that the single-variable functions $$U(x_0,y)$$ and $$U(x,y_0)$$ have local maxima at $$y_0$$ and $$x_0$$, respectively. I can't think of a meaningful example of a good/service where, after acquiring a certain amount, the utility actually decreases as more of the good/service is acquired. This condition seems quite strange, but perhaps there are some standard examples I've never heard of given my thin background in economics.

• The quantities in the utility function are the amounts of the goods consumed, not the amounts of the goods aquired. I challenge you to name a food where you have no satiation quantity. Apr 21, 2022 at 20:16
• Also, I am not quite sure what you mean by "realistic example". Apr 21, 2022 at 20:20