**Problem:**

Prior to the collapse, there were two modes serving the Marcytown-Rivertown corridor: driving alone (d) and carpool (c), which takes advantage of an uncongested carpool lane. The utilities of the modes are as given below.

where t is the travel time

Assuming a multinomial logit model, and

A) That the congested time by driving alone was 15 minutes and time by carpool was 5 minutes. What was the modeshare prior to the collapse?

B) How would you interpret the constant of -12 in the expression for Uc?

C) After the collapse, because of a shift in travelers from other bridges, the travel time by both modes increased by 12 minutes. What is the post-collapse modeshare?

D) The transit agency decides to run a bus to help out the commuters after the collapse. Again assuming the multinomial logit model holds, without knowing how many travelers take the bus, what proportion of travelers on the bus previously took the car? Why? Comment on this result. Does it seem plausible?

**Solution:**

A) That the congested time by driving alone was 15 minutes and time by carpool was 5 minutes. What was the modeshare prior to the collapse?

Ud = -15

Uc = -17

Pd = 0.88

Pc = 0.12

B) How would you interpret the constant of -12 in the expression for Uc?

The constant -12 is an alternative specific constant. In this example, even if the travel time for the drive and carpool modes were the same, the utility of the carpool mode is lesser than the drive alone due to the negative constant -12. This indicates that there is a lesser probability of an individual choosing the carpool mode due to its lower utility.

C) After the collapse, because of a shift in travelers from other bridges, the travel time by both modes increased by 12 minutes. What is the post-collapse modeshare?

In this question since the travel time for both modes increase by the same 12 minutes, the post-collapse mode share will be the same as before

D) The transit agency decides to run a bus to help out the commuters after the collapse. Again assuming the multinomial logit model holds, without knowing how many travelers take the bus, what proportion of travelers on the bus previously took the car? Why? Comment on this result. Does it seem plausible?

The logit model will indicate that 88% of the bus riders previously drove alone due to the underlying Independence of Irrelevant Alternatives (IIA) property. The brief implication of IIA is that when you add a new mode, it will draw from the existing modes in proportion to their existing shares. This doesnt seem plausible since the bus is more likely to draw from the carpool mode than the drive alone mode.