2

3. (10 pts) A discrete choice model of travel mode to work includes two alternatives:

driving alone (alternative 1) and taking transit (alternative 2). The model is based on

the following utility functions:

U₁= 1- t + ₁

U2 = 42- t^+

2

Probability and Discrete Choice Models

where 1 and 2 are model parameters. Both error terms 1 and 2 follow a uniform

distribution between -b and b.

(a) Develop an analytical expression for P₁ as a function of 9₁, 92, t, t^, and b.

(b) Assume that 41 - 92= 1 and plot P₁ versus t^-t for several values of b. Discuss the

effect of b on the choice probability and draw general conclusions.