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:
|