(1096) A group of teachers in the Mythaca School District have agreed to stop om

Question

(1096) A group of teachers in the Mythaca School District have agreed to stop ommuting by motor vehicle. Instead, each of these teachers will choose each morming etween walking and bicycling to school, depending on the weather. The utility functions for the two non-motorized modes for these teachers are: Ua +3.0-0.5 bde 1 Where Wis a weather related variable and t is the travel time in minutes. W-0 in good weather, W-1 in bad weather. Please answer the following questions: a) When the weather is good, what is the probability that a "non-motorized" teacher with a choice between a 15-min walk and a 6-min bike ride will choose the bicycle mode? At what value of the weather coefficient c will the teacher in part a be equally likely to choose walk and bicycle in bad weather? b)

Explanation / Answer

(a) When weather is good, W = 0.

Given twalk = 15 min

tbike = 6 min

Ubike = 0.5 -0.6 tbike = 0.5 - 0.6 x 6 = -3.1

Uwalk = 3 - 0.5 twalk = 3 - 0.5 x 15 = -4.5

Probability of choosing bike mode = e-(-3.1) / (e-(-3.1) + e-(-4.5)) = 0.198

(b) When weather is bad, W = 1.

Ubike = 0.5 -0.6 tbike - c = 0.5 - 0.6 x 6 - c = -3.1 - c

Uwalk = 3 - 0.5 twalk = 3 - 0.5 x 15 = -4.5

Probability of choosing bike mode = e-(-3.1-c) / (e-(-3.1-c) + e-(-4.5))

Probability of choosing walking = e-(-4.5) / (e-(-3.1-c) + e-(-4.5))

Given that above two probabilities are equal.

So, e-(-3.1-c) / (e-(-3.1-c) + e-(-4.5)) = e-(-4.5) / (e-(-3.1-c) + e-(-4.5))

=> -3.1-c = -4.5

=> c = 1.4

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