12:35 bath-prod-sss1.s3.eu-west-1.amazonaws.com 94 3. Question You are tasked with estimating the time preferences for chocolate and biscuit consumption of two subjects, Adam and Beth. Both subjects have the same instantaneous utility function for the consumption of x units of chocolate and y biscuits at a given day: u(x, y) = x¹/2 . y¹/2¸ (a) Today (Monday), Adam tells you he is indifferent between consuming 1 piece of chocolate with 9 biscuits today (Monday) and 4 pieces of each, chocolate and biscuits, tomorrow (Tuesday). Determine the exponential discount factor ♪ that is implied by Adam's statement. (b) Today (Monday), Adam also tells you that he is indifferent between con- suming 9 pieces of chocolate with 1 biscuit tomorrow (Tuesday) and 3 pieces of chocolate with 3 biscuits in two days (Wednesday). What is the exponential discount factor & that is implied by this statement? Can the exponential discounting model explain both of Adam's statements from questions (a) and (b) together? (c) In what sense can the hyperbolic discounting model be a better fit to explain Adam's preferences? Derive the implied discount factors (ẞ, 5) that are consistent with the indifference relations in (a) and (b). (d) Considering Beth, she predicts today (Monday) that when asked tomor- row she will be indifferent between consuming 2 pieces of chocolate with 8 biscuits on Tuesday and 5 pieces of chocolate with 5 biscuits on Wednes- day. Moreover, she predicts today when asked tomorrow that she will be indifferent between 4 pieces of chocolate with 4 biscuits on Tuesday and 4 pieces of chocolate with 9 biscuits on Thursday. Determine whether Beth is an exponential, naive or sophisticated hyperbolic discounter and determine the corresponding discount factors. (e) Suppose that it is possible to perfectly monitor Beth's daily chocolate and biscuit intake. You offer the following contract to Beth: Whenever she eats more than an amount x of chocolate and biscuits that she can specify freely today, a fine of 100 GBP is subtracted from her account (the monetary equivalent of consuming any amount of chocolate and biscuits is always lower than the fine). Is she going to accept the contract on Monday? Would she regret on Tuesday having accepted the contracted on Monday? Justify your responses based on your answer to question (d). Page 4 of 5 ES30037