d A witness to a midnight hit and run testifies that he saw a purple car flee

# D a witness to a midnight hit and run testifies that

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(d) A witness to a midnight hit-and-run testifies that he saw a purple car flee the scene. An expert testifies that vehicle colour recognition is 80% reliable at night. The defendant drives a silver car, which is 15 times more common than purple. The defendant is acquitted. (e) A crafty lecturer bets his class of 57 students that at least two of them share a birthday. At 10:1 odds, there are many takers. The probability that two particular people share a birthday is 1-(364/365) = 0.002%. The probability that at least two people out of a class of 57 students share a birthday is > 99% (really!). 1 Problem 2. Suppose that Bilal and Salma have piecewise-linear reference-dependent preferences over mugs ( m ∈ { 0 , 1 } ) and money ( y ), with instantaneous utility: u ( m t , y t , r t ) = Mm t + y t + G · ( m t - r t ) , m t r t Mm t + y t + λ · G · ( m t - r t ) , else where the reference point for mugs is: r t = γr t - 1 + (1 - γ ) m t - 1 , γ [0 , 1) Both Bilal and Salma exhibit simple projection bias of degree α , are perfectly patient in discounting the future. Mugs last until the end of the world in period T; that is, purchasing a mug in period 0 sets m 0 = m 1 = ... = m T = 1. 1. Interpret the parameter γ . If an agent initially has r 0 = 0 and purchases a mug, what is her reference point after τ periods have elapsed r b τ ? If an agent initially has r 0

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• Spring '20
• Economics, Period, Periodic function, Mug

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