9. You have a voucher to go see one movie in the cinema over the next 4 weeks. You can choose which Saturday you want to go the cinema. Let x be the outcome of watching a movie and y skipping that week instead. Assume that a time period is a week, with the current week being time 0. Assume that the instantaneous utilities are as follows: uz(y) = 0 for every t = 1,2,3,4, and Uz(x) = 3, uz(x) = 5, uz(x) = 8 and u4(x) = 13. Also suppose that your preferences can be represented by a hyperbolic discounting utility function with B = and 8 = 1. a) Suppose that you have to make an irrevocable decision today (in week 0) as to which Saturday you will go to the movie. What will you choose? b) Suppose that you cannot commit to a movie in week 0, and must choose each week whether or not to see the movie. You are fully aware of your preferences (1.e. you are a sophisticated hyperbolic discounter). When will you choose to go to the movie? c) Now suppose you are a nave hyperbolic discounter who assumes that in future periods = 1. Which week will you go to the movie? d) Provide an intuitive rationalisation for why individuals behave differently in a), b) and c). e) Explain what is meant with a "nudge and give an example. (This example need not relate to this problem of the hyperbolic discounting movie-goer.) 9. You have a voucher to go see one movie in the cinema over the next 4 weeks. You can choose which Saturday you want to go the cinema. Let x be the outcome of watching a movie and y skipping that week instead. Assume that a time period is a week, with the current week being time 0. Assume that the instantaneous utilities are as follows: uz(y) = 0 for every t = 1,2,3,4, and Uz(x) = 3, uz(x) = 5, uz(x) = 8 and u4(x) = 13. Also suppose that your preferences can be represented by a hyperbolic discounting utility function with B = and 8 = 1. a) Suppose that you have to make an irrevocable decision today (in week 0) as to which Saturday you will go to the movie. What will you choose? b) Suppose that you cannot commit to a movie in week 0, and must choose each week whether or not to see the movie. You are fully aware of your preferences (1.e. you are a sophisticated hyperbolic discounter). When will you choose to go to the movie? c) Now suppose you are a nave hyperbolic discounter who assumes that in future periods = 1. Which week will you go to the movie? d) Provide an intuitive rationalisation for why individuals behave differently in a), b) and c). e) Explain what is meant with a "nudge and give an example. (This example need not relate to this problem of the hyperbolic discounting movie-goer.)