Homework Assignment on Travel Demand Forecasting
Now suppose you are this great planner in this great town. One day, your boss came to
you and asked you to develop a model to predict how people make choices between auto
and bus. You just learned this great random utility theory and binary logit model and you
are excited about applying this model into your work.
Your boss also gave you a sample data set in excel form. The sample was collected in
real world. It consists of 25 individuals. The variables in the data set are: choice (1= auto
and 0 – bus), travel time, travel cost, and income (in $000s). You came up with such a
systematic utility function specified below:
Vi = 1Ti + 2(Ci/Y),
Where Vi is the systematic utility, 1, 2 are parameters to be estimated, Ci is the
travel cost, Y is the income in $000s, and i refers to ith individual.
Now, with the utility form in hand, your main task is to estimate 1 and 2. So, you set
the auto alternative as the base alternative, and that will imply that in the utility function
for the auto alternative, estimates of 1, 2 will be set to be equal to zero. Now, you run a
program and found out that the estimates of 1, 2 are –1.48 and –2.82 respectively.
These two estimates are related to the bus alternative. Please answer the following
questions:
a. what the two estimates of 1, 2 mean, in terms of the propensity of choosing
bus and auto with respect to travel time and travel cost.
b. using the binary logit model formula:
eVauto
1
Pr( auto)  V

V
e auto  e bus 1  eVb Va
1

1  exp[ 1 (timebus  timeauto)   2 (cos tbus / income  cos tauto / income)]
to calculate the probability of choosing auto and bus for each individual in the data base.
c. suppose five years later, all these 25 individuals’ income have been increased
10% compared to his or her original income, recalculate the probability of choosing auto
and bus for each individual.
d. now, based on the answers you obtained in c above, your boss also wants you
to give an estimate of the market share between auto and bus (he wants to know what
percentage of these 25 people will take auto and what percentage will take bus). What
aggregation method would you use to produce this market share?
Homework on Transportation Economics
1. Suppose that you take both bus and auto to work. How much you take bus and auto
respectively depends on the bus fare and cost of auto. You have about $500 per year to
allocate on transportation cost. And your utility function looks like follows:
U = X0.9Y0.1,
Where X is the number of auto trips and Y is the number of bus trips.
Currently, the bus fare is $1.5 per trip and operating cost of auto is about $2 per trip.
Determine:
a) at level of bus trips and auto trips, you will be able to maximize your utility
level, subject to your constraint.
b). marginal utility of income
X
Y
,
c).
Pauto Pbus
d). elasticity of demand for both auto and bus.
f). if the bus fare reduces to $1, how does that will change your demand?
g). what if you have $600 to allocate on transportation, how does that change your
demand?
2. suppose that you discover that between zone A and zone B, there is a demand for
transportation services. So, you want to make some money and decide to operate a bus
route between these two locations. You determine that at minimum you need to operate
100 trips per month in order to be profitable. Now, you want to minimize your operating
cost given that you have at least provided 100 trips between two zones per month. In
order to operate your bus service, you will need hire driver. Suppose labor is your only
input and you already have a few good working buses. Now, the price of labor is about
$50 per month. Your production function looks like this: y = X2.23, where y is the number
of bus trips per month and X is number of drivers (labor) you will hire per month.
Determine:
a). how many drivers you shall hire per month?
b). is your production constant, decreasing or increasing returns to scale?
c). at the optimum, what is the average cost and what is the marginal cost?
d). then you went to some fancy business school and learned a good system of
management. So now you improve your production and your production function now
looks like: y = X3.8, how does that change the number of drivers you hire per month,
average cost and marginal cost?