A market segment consists of 300 individuals. A Logit mode choice model (with pa

Question

A market segment consists of 300 individuals. A Logit mode choice model (with parameter equal to 1) has been estimated for this market resulting in the following utility function: U= beta_m - 0.40C - 0.03 T, where C is out-of-pocket cost in $ and T is travel time in min. Values of beta_m are Bus: 0.00; Rail: 0.50; Car: 1.50. For a particular origin-destination pair, the cost of a car trip is 2S and the duration 8min, a rail trip is 1.50$ and 12min, while a bus takes 20min and costs 1.25$. a. Predict the number of trips for each mode. b. An increase in the price of gas changes the cost of car to 3$, while all other parameters remain constant. What is the % increase in the share of bus and rail?

Explanation / Answer

Firstly determine the utility function

Um=m-0.40C-0.03T

C is out of pocket cost in dollars, and T is travel time, min

Min. Value m

For Bus transit 0.00

Rail transit       0.50

Auto                  1.50

For Auto, T= 8min, C=$2

For Rail, T=12 min, C=$1.50

For Bus, T=20min, C=1.25

UB=B-0.40C-0.03T = 0-0.40x1.25-0.03x20= -1.10

UR=m-0.40C-0.03T= 0.50-0.40x1.50-0.03x12= -0.46

UA=m-0.40C-0.03T= 1.50-0.40x2-0.03x8= 0.46

e-1.10=0.33,   e-0.46=0.63, e+0.42=1.58

The probability of different mode

PB=0.33/(0.33+0.63+1.58)=0.33/2.54=0.13

PR=0.63/(0.33+0.63+1.58)= = 0.245

PA=1.58/(0.33+0.63+1.58)=            =0.622

No. of trips by each mode

TB = 300*0.13= 39

TR = 300*0.245 = 73.5

TA =300*0.622=186.6

b)

UB=B-0.40C-0.03T = 0-0.40x1.25-0.03x20= -1.10

UR=m-0.40C-0.03T= 0.50-0.40x1.50-0.03x12= -0.46

UA=m-0.40C-0.03T= 1.50-0.40x3-0.03x8= 0.06

e-1.10=0.33,   e-0.46=0.63, e+0.06=1.06

The probability of different mode

PB=0.33/(0.33+0.63+1.06)=0.33/2.02=0.1633

PR=0.63/(0.33+0.63+1.06)=0.63/2.02=0.312

PA=0.06/(0.33+0.63+1.06)=0.06/2.02=0.03

No. of trips by each mode

TB = 300*0.1633= 48.99

TR = 300*0.312 = 93.6

TA =300*0.06=18

Hence, % increase in BUS = (48.99-39)100/39 = 25.61%
% increase in RAIL = (93.6-73.5)100/73.5 = 27.35%

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