[34 marks in total] A decision-maker needs to perform a task and can choose whether to do it in period 1, period 2 or period 3. If she does not do it in periods 1 or 2 she is forced to do it in period 3. The cost of performing the task depends on when she does it, where t = {1, 2, 3} indexes the period. The costs are c=2, c = 4 and c3 = 8, so c = (2, 4, 8). The benefit of doing it is received in period 4 and is not influenced by when the task is performed. Utility is linear in (discounted) costs and benefits. Denote costs as negative utility. Anna is time-consistent and discounts future costs and benefits exponentially with a discount factor 8 = 1. [6 marks] From the perspective of period 1, calculate the utility that Anna receives when performing the task in period 1, period 2 or period 3. [numerical text entry], 2 per correct entry Period 1: Period 2: Period 3: [2 marks] When does Anna expect to do the task and when will they actually do it? O expects 1, does it in 2 expects 2, does it in 2 expects 3, does it in 3 expects 2, does it in 3 O expects 2, does it in 1 O expects 3, does it in 1 expects 1, does it in 3 O expects 3, does it in 2 expects 1, does it in 1 O Ben is present-biased with quasi-hyperbolic (38) preferences. For him, 6 = 1 and 3 = 0.3. He is sophisticated in the sense that he is aware of his present bias. [6 marks] From the perspective of period 1, calculate the utility that Ben receives when performing the task in period 1, period 2 or period 3. Period 1: Period 2: Period 3: [4 marks] From the perspective of period 2, calculate the utility that Ben receives when performing the task in period 2 or period 3. Period 2: Period 3: [4 marks] When does Ben expect to do the task and when will they actually do it? expects 1, does it in 2 O expects 3, does it in 2 expects 1, does it in 3 expects 2, does it in 2 O expects 2, does it in 3 O expects 3, does it in 3 expects 1, does it in 1 expects 3, does it in 1 expects 2, does it in 1 O Claire is present-biased with quasi-hyperbolic (38) preferences. For her, 8 = 1 and 3 = 0.3. She is naive in the sense that she is not aware of her present bias. [3 marks] From the perspective of period 1, calculate the utility that Claire receives when performing the task in period 1, period 2 or period 3. Period 1: Period 2: Period 3: [5 marks] In period 1, when does Claire expect to do the task and when will they actually do it? O expects 3, does it in 3 O expects 2, does it in 3 O expects 1, does it in 1 O expects 3, does it in 1 O expects 2, does it in 2 O expects 1, does it in 3 O expects 3, does it in 2 expects 2, does it in 1 O expects 1, does it in 2 4 [4 marks] Anna, Ben and Claire are offered the same commitment device in period 1. If they accept, they need to pay 0.5 in period 1, and in return they will be forced to perform the task in period 2. Select all that apply. [multiple choice] 1 mark per correct, -1 for incorrect correct: Ben will not accept it because they will do the task in period 1. Ben will accept it because they knows about his present bias. Claire will not accept it because they will do the task in period 1. Ben will not accept it because it is too expensive. Anna will accept it because it helps them to do the task in period 2. Claire will accept it because it lowers their expected costs. Claire will not accept it because they are not aware of their present bias. O Anna will not accept it because the device would increase their costs. O Anna will not accept it because they will do the task in period 1. [34 marks in total] A decision-maker needs to perform a task and can choose whether to do it in period 1, period 2 or period 3. If she does not do it in periods 1 or 2 she is forced to do it in period 3. The cost of performing the task depends on when she does it, where t = {1, 2, 3} indexes the period. The costs are c=2, c = 4 and c3 = 8, so c = (2, 4, 8). The benefit of doing it is received in period 4 and is not influenced by when the task is performed. Utility is linear in (discounted) costs and benefits. Denote costs as negative utility. Anna is time-consistent and discounts future costs and benefits exponentially with a discount factor 8 = 1. [6 marks] From the perspective of period 1, calculate the utility that Anna receives when performing the task in period 1, period 2 or period 3. [numerical text entry], 2 per correct entry Period 1: Period 2: Period 3: [2 marks] When does Anna expect to do the task and when will they actually do it? O expects 1, does it in 2 expects 2, does it in 2 expects 3, does it in 3 expects 2, does it in 3 O expects 2, does it in 1 O expects 3, does it in 1 expects 1, does it in 3 O expects 3, does it in 2 expects 1, does it in 1 O Ben is present-biased with quasi-hyperbolic (38) preferences. For him, 6 = 1 and 3 = 0.3. He is sophisticated in the sense that he is aware of his present bias. [6 marks] From the perspective of period 1, calculate the utility that Ben receives when performing the task in period 1, period 2 or period 3. Period 1: Period 2: Period 3: [4 marks] From the perspective of period 2, calculate the utility that Ben receives when performing the task in period 2 or period 3. Period 2: Period 3: [4 marks] When does Ben expect to do the task and when will they actually do it? expects 1, does it in 2 O expects 3, does it in 2 expects 1, does it in 3 expects 2, does it in 2 O expects 2, does it in 3 O expects 3, does it in 3 expects 1, does it in 1 expects 3, does it in 1 expects 2, does it in 1 O Claire is present-biased with quasi-hyperbolic (38) preferences. For her, 8 = 1 and 3 = 0.3. She is naive in the sense that she is not aware of her present bias. [3 marks] From the perspective of period 1, calculate the utility that Claire receives when performing the task in period 1, period 2 or period 3. Period 1: Period 2: Period 3: [5 marks] In period 1, when does Claire expect to do the task and when will they actually do it? O expects 3, does it in 3 O expects 2, does it in 3 O expects 1, does it in 1 O expects 3, does it in 1 O expects 2, does it in 2 O expects 1, does it in 3 O expects 3, does it in 2 expects 2, does it in 1 O expects 1, does it in 2 4 [4 marks] Anna, Ben and Claire are offered the same commitment device in period 1. If they accept, they need to pay 0.5 in period 1, and in return they will be forced to perform the task in period 2. Select all that apply. [multiple choice] 1 mark per correct, -1 for incorrect correct: Ben will not accept it because they will do the task in period 1. Ben will accept it because they knows about his present bias. Claire will not accept it because they will do the task in period 1. Ben will not accept it because it is too expensive. Anna will accept it because it helps them to do the task in period 2. Claire will accept it because it lowers their expected costs. Claire will not accept it because they are not aware of their present bias. O Anna will not accept it because the device would increase their costs. O Anna will not accept it because they will do the task in period 1