Logit Model

Given the utility expression:

UK= AK - 0.05 Ta - 0.04Tw - 0.02 Tr - 0.01 C

Where:
Ta is the access time
TW is the waiting time
Tr is the riding time
C is the out of pocket cost

a) Apply the logit model to calculate the division of usage between the automobile mode (AK = -0.005) and a mass transit mode (AK = -0.05). Use the data given in the table below for your analysis.

 Mode Ta TW Tr C Auto 5 0 30 100 Transit 10 10 45 50

b) Estimate the patronage shift that would result from doubling the bus out-of-pocket cost.

[Solution Shown Below]

Solution

Part ‘A’ is solved by substituting the given values into the utility function and solving the logit model equation. The calculations and results for part ‘A’ are shown in the table below.

Part ‘B’ is essentially identical to part ‘A’ except for the change in the out-of-pocket cost for bus travel. The preliminary calculations for part ‘B’ are shown in the table below as well, while the final calculations are located below the table.

 Part A Mode Ta TW Tr C Ak Uk e^Uk P Auto 5 0 30 100 -0.0050 -1.855 0.1565 0.621 Transit 10 10 45 50 -0.0500 -2.350 0.0954 0.379 0.2518 1.000 Part B Mode Ta TW Tr C Ak Uk e^Uk P Auto 5 0 30 100 -0.0050 -1.855 0.1565 0.730 Transit 10 10 45 100 -0.0500 -2.850 0.0578 0.270 0.2143 1.000

A significant number of bus riders are predicted to shift to the automobile.

The increase in automobile use will be: