(Using Discrete Choice to Forecast Movie Sales) Three new movies will be shown at a movie theater this weekend. The theater wishes to estimate the expected number of people who will come to see each movie so they can decide how many screenings to offer, how large a theater each movie should be shown in, and so on. The movie studios that produced the

three movies held "sneak peak" screenings of the films and conducted postmovie interviews of the attendees. Based on these interviews, they estimated the utility of each movie based on a viewer's age range. They also estimated the utility of not seeing any movie. These estimated utilities are denoted Vni, although here n refers not to an individual but to a type of individual (based on age range). The following table lists the Vni values, as well as the number of people who are considering seeing a movie at that theater this weekend. a) Assume that the actual utilities Uni differ from the estimated utilities Vni by an additive iid error term that has a standard Gumbel distribution. Using the multinomial logit model, calculate the expected demand for each movie. b) Now suppose the movie theater doesn't know about the multinomial logit model and assumes that Pni is simply calculated using a weighted sum of the Vni values; that is, Pni=jVnjVni What are the expected demands for each movie using this method