The choice whether or not to exercise in period 0 is made by Sarah's parents on her behalf but she will make the choice on her own behalf in periods 1 and 2. Let o {0,1} (that is, , is either 0 or 1) denote the choice Sarah's parents made in period 0 (when she was a child) on her behalf. Sarah chooses ei {0,1} in period 1 and 22 {0,1} in period 2. She has no choice regarding exercise in period 3. Sarah's unbiased preferences over her exercise choices (e1,e2) are represented by the sum of the period utilities: U1 + 2 + 3 where for t = 1, 2, u = u(er,&-1) and us = 7o (e1 + 2) + (3.1) e102. The values for uler, 4-1) are as follows: u (0, 0) tu (0, 1) u(1,0) u(1, 1) 1 5 -1 2 Sarah, however, suffers from projection bias and in period 1 she perceives that uz, her utility from exercise in period 2 will equal u(e2, 7o). For parts (a), (b) and (c) suppose g = 0, that is, she didn't exercise during her childhood. (a) [5 marks] What will be her choice of exercise in period 1 and what choice does she plan to make in period 2. (6) [1 marks) What will be her actual choice in period 2. The choice whether or not to exercise in period 0 is made by Sarah's parents on her behalf but she will make the choice on her own behalf in periods 1 and 2. Let o {0,1} (that is, , is either 0 or 1) denote the choice Sarah's parents made in period 0 (when she was a child) on her behalf. Sarah chooses ei {0,1} in period 1 and 22 {0,1} in period 2. She has no choice regarding exercise in period 3. Sarah's unbiased preferences over her exercise choices (e1,e2) are represented by the sum of the period utilities: U1 + 2 + 3 where for t = 1, 2, u = u(er,&-1) and us = 7o (e1 + 2) + (3.1) e102. The values for uler, 4-1) are as follows: u (0, 0) tu (0, 1) u(1,0) u(1, 1) 1 5 -1 2 Sarah, however, suffers from projection bias and in period 1 she perceives that uz, her utility from exercise in period 2 will equal u(e2, 7o). For parts (a), (b) and (c) suppose g = 0, that is, she didn't exercise during her childhood. (a) [5 marks] What will be her choice of exercise in period 1 and what choice does she plan to make in period 2. (6) [1 marks) What will be her actual choice in period 2