Explore a comprehensive lecture from the Brooklyn Quant Experience Lecture Series featuring Kim Weston, Assistant Professor of Mathematics at Rutgers University. Delve into the topic of "Equilibrium Existence in a Limited Participation Economy" as presented at New York University's Department of Finance and Risk Engineering. Over the course of 56 minutes, gain insights into the problem's history, logarithmic preferences, and the process of writing equations. Examine exponential investors, equilibrium concepts, and the system of equations involved. Understand the key assumptions and follow the proof presented. Analyze a practical example and investigate time preference parameters before reaching the lecture's conclusion.