Derive an expression for the marginal rate

Reference no: EM133425766

In modeling travel mode choices, transportation analysts commonly disaggregate travel time into different components. Assume you are building a model with the following utility specification :

uij = γj + βTCTCij + βIVTTIVTTij + βWaitTWaitTij + βWalkTWalkTij + εij (1)

where TC is travel cost [US$], IVTT is in-vehicle travel time [hr], WaitT is waiting time [hr], and WalkT is walking time in [hr].

Q1. What are the expected signs for the β parameters? How many γj parameters can one estimate if there are J alternatives?

Q2. Suppose that you assume that γSubway = 0 and after training the model you obtained γ_Bus < 0. How would you interpret that result? (Hint: Suppose that for a given individual all attributes of bus and subway take exatly the same values - according to the said result, would the individual be indifferent between bus and subway or not?)

Q3. Derive an expression for the marginal rate of substitution (MRS) between WaitT and WalkT. Discuss intuitive interpretation of this marginal rate of substitution, an explain why companies such as Uber are really interested in modeling this type of MRS.

Q4. Empirically it has been determined that it is very usual that

∂uij/∂WaitT

∂uij/∂IVTT ≈ 2

How do you interpret this result? Given this result, does it make more sense to invest in reducing waiting or in-vehicle time? Discuss.

Q5. Lay out the steps necessary to methodologically derive a confidence interval for the MRS in M1Q4 using the Delta method. Can you propose a direct way to build a confidence interval for this MRS?

Reference no: EM133425766

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