$(9$ points total$)$ Multinomial Logit Model

A mode choice model was developed with the observable utility functions for auto, bus and

train shown below:

$V_{\text{a}\text{u}\text{t}\text{o}}=0\mathrm{.}10-0\mathrm{.}3$ IVTT $-0\mathrm{.}5$ OVTT $-0\mathrm{.}6C$

$V_{\text{b}\text{u}\text{s}}=-0\mathrm{.}20-0\mathrm{.}3$ IVTT $-0\mathrm{.}5$ OVTT $-0\mathrm{.}6C$

$V_{\text{t}\text{r}\text{a}\text{i}\text{n}}=,-0\mathrm{.}3$ IVTT $-0\mathrm{.}5$ OVTT $-0\mathrm{.}6C$

Where

IVTT $=in-$vehicle travel time $(min)$

OVTT $=$ out$-of-$vehicle travel time $(min)$

$C=cost($$$)$

The table below contains average travel times and average travel costs in a small city:

a$.(3$ points$)$ Estimate the expected population mode shares using the multinomial logit model.

Express your answers in percentage form $($i$.$e$.,$ percent choosing auto, percent choosing

bus, and percent choosing train$).$

b$.(3$ points$)$ The city transportation department is considering a new policy to raise parking

prices, which would increase the cost of auto from $$5$ to $$10.$ Again, estimate the expect

mode shares using the multinomial logit model for auto, bus, and train.

c$.(1$ point$)$ Briefly discuss the differences between your answers to part a and part $b.$ If the

city is trying to reduce car trips and increase transit use, is this policy effective?

d$.(1$ point$)$ Briefly discuss why the coefficient of the cost $($C$)$ variable is negative in the utility

functions $($one sentence is sufficient$).$

e$.(1$ point$)$ Briefly discuss the meaning of the alternative specific constant $($i$.$e$.,$ the modal

bias parameter$)$ for bus. How does it compare to train? One sentence is sufficient$\mathrm{.}1.(9$ points total$)$ Multinomial Logit Model

A mode choice model was developed with the observable utility functions for auto, bus and train shown below:

V$\_$auto $=0\mathrm{.}10-0\mathrm{.}3$ IVTT $-0\mathrm{.}5$ OVTT$-0\mathrm{.}6$ C

V$\_$bus $=-0\mathrm{.}20-0\mathrm{.}3$ IVTT$-0\mathrm{.}5$ OVTT$-0\mathrm{.}6$ C

V$\_$train$=-0\mathrm{.}3$ IVTT $-0\mathrm{.}5$ OVTT$-0\mathrm{.}6$ C

Where

IVTT $=$ in$-$vehicle travel time $($min$)$

OVTT $=$ out$-$of$-$vehicle travel time $($min$)$

C $=$ cost $($$$)$

The table below contains average travel times and average travel costs in a small city:

IVTT $($min$)$ OVTT $($min$)$ Cost $($$$)$

Auto $1105$

Bus $2032$

Train $1243$

$(3$ points$)$ Estimate the expected population mode shares using the multinomial logit model. Express your answers in percentage form $($i$.$e$.,$ percent choosing auto, percent choosing bus, and percent choosing train$).$

$(3$ points$)$ The city transportation department is considering a new policy to raise parking prices, which would increase the cost of auto from $$5$ to $$10.$ Again, estimate the expect mode shares using the multinomial logit model for auto, bus, and train.

$(1$ point$)$ Briefly discuss the differences between your answers to part a and part b$.$ If the city is trying to reduce car trips and increase transit use, is this policy effective?

$(1$ point$)$ Briefly discuss why the coefficient of the cost $($C$)$ variable is negative in the utility functions $($one sentence is sufficient$).$

$(1$ point$)$ Briefly discuss the meaning of the alternative specific constant $($i$.$e$.,$ the modal bias parameter$)$ for bus. How does it compare to train? One sentence is sufficient.