Deriving New Model
Here, I am extending the Henderson-Chu approach in the Mun (1999) paper to include two groups of heterogeneous agents — the rich and the poor. We make the distinction between these two groups of commuters by drawing the boundary at $100,000/yr income. The goal is to set up four equations with four unknown variables.
Solving Cost Equations
In solving the cost equations derived earlier, I come to the conclusion that this nonlinear system cannot be analytically solved. Instead, we numerically simulate our results with appropriate values for our constants.