Problem A: Throughout the problem, t {1,2,3,4}, where t = 1 denotes Friday, t = 2 denotes Saturday, t = 3 denotes Sunday, and t = 4 denotes Monday. Beta's uncle owns a coffee shop. He plans a weekend trip to visit his friends in Miami and requests Beta to take care of the coffee shop during his absence on Saturday and Sunday. The uncle promises to pay Beta a wage rate of $20 per hour upon his return on Monday. Thus, if Beta works at the coffee shop for 72 hours on Saturday and 13 hours on Sunday, then he earns a total of $20(32 + 13) on Monday. But working also gives Beta disutility (perhaps he misses having fun with his friends during the weekend). If Beta works for 12 hours on Saturday, then he suffers disutility worth $(12) on Saturday. Likewise, if Beta works for 13 hours on Sunday, then he suffers disutility worth $(23)2 on Sunday. We assume that, regardless of Beta's decision, his utility on Friday is u = $0. 2. Suppose Beta's time preferences are given by exponential discounting with the dis- count factor of 8 per day. (a) Fill in the rest of the cells in Table 2. In other words, for each work schedule, find Beta's inter-temporal utility on Friday for the two cases, 8 = 0.8 and 8 = 0.5. Which work schedule does Beta choose on Friday in each case? (2.5) (b) Before setting off for work on Saturday morning, Beta looks at his weekend work schedule one more time, just to make sure that he is indeed maximizing his inter-temporal utility. Fill in the rest of the cells in Table 3. In other words, for each work schedule, find Beta's inter-temporal utility on Saturday for the two cases, 8 = 0.8 and 8 = 0.5. Which work schedule does Beta choose on Saturday in each case? (2.5) Table 2: Beta's inter-temporal utility on Friday under exponential discounting Work Schedule Inter-temporal utility on Friday o=0.8 8=0.5 22 = 8.13 = 6.4 - 6.4, C3 = 8 22 = 5.12.13 = 8 22 = 5.12, 13 = 6.4 Table 3: Beta's inter-temporal utility on Saturday under exponential discounting Work Schedule Inter-temporal utility on Saturday 8= 0.8 8 = 0.5 22 = 8,13 = 6.4 22 = 6.4,23 = 8 C2 = 5.12, x3 = 8 12 = 5.12, 13 = 6.4