Question

Question 3:4 A group of students will choose walking or bicycling to commute to a school. The utility functions for the two modes for these students are as follows: Vwalk = 2.9 -0.5 * twalk Vbike =-0.5 * thika+c*W+ where V = observable utilities, t = travel time (minutes), W = 0 in good weather and W = 1 in bad weather, and c=unknown coefficient for weather. (a) When the weather is good, what is the probability that a student will choose the bicycle mode if he/she knows that it will take 15 minutes by walk and 6 minutes by bicycle?- (b) At what value of the weather coefficient c will the student in part (a) be equally likely to choose walk and bicycle modes in bad weather?

Answer 1

Given utility functions are: Page 1 walk 2.9 -0.5 xt walk bike -0.5xt bike + C#W When weather is good, Wzo then, v 2.4-0.5 x 15 "walk =-4.6 and V. bike -0.5x6 tcxo e-3 probability that student will choose Nike bicycle walk & bike e e te -3 1) -406 te²3 probability = 0.832 probability in % = 83.2%, Answer

(b For For equal probability or equal likely to choose both modes : I walk bike in case of bad weather, W = 1 so, 2.9 -0.5x15 -0,5*6+.cxl -4.60 -37c c-4.60 + 3 .. c = -1.6 required anjeurer