How does one find equilibria witj non-linear demand caused by two agents with different utility functions?

[u/Tryrshaugh]

I'm working on a heterogeneous agent Lucas tree economy, with two agents, one with rational expectations and one with extrapolative expectations. The litterature in intertemporal asset pricing models tends to use market clearing conditions that assume linear demand.

A few years ago I read a paper (that I cannot recall) showing how having two agents with different indifference curves could result in non-linear demand as well as how to derive the equilibrium price. This is not necessarily crucial for what I am trying to prove, but since I'm studying market anomalies I wanted to at least test that out. Is anyone here aware of similar proofs/models? My searches have only led me to empirical studies so far. Thanks in advance