Problem V. Shared Driveway (55 points) Recall the textbook example where two neigh- bors share a driveway. Suppose each person gets utility on the private consumption good, c, and the driveway, D = d. + d2, such that :(,D) = ln(c) + 7 In{D). Price of snowplow- ing/repairing services is p in terms of the consumption good. Each person has income 1. Let di = pd;/1, denote the income share of driveway expenditures for person i. First, assume that 71 = 72 = 9 and 11 = 12 = 1. 2 1. Find the social optimal income share of driveway services. . (5pts) 2. Find the private optimal income share of driveway services, 8*. (5 pts) 3. Compare 8 and 8. Explain intuitively why they are different. (5 pts) 4. Now suppose there is some extent of altruism. Le ui( GD) = ln(c) + In(D) + ln(D). Find the private optimal income share with altruism 64 Compare 54 and 8. What happens if 4 = 7. (10 pts) 5. Now, consider the case with warm glow where each person cares about his contribution to the driveway rather than his consumption of driveway. Specifically, u:(.d) = ln(c) + In(d.). Find the private optimal income share with warm glow, W. Compare and .. Explain intuitively. (10 pts) 6. Now suppose I > I. Specifically, 11 = MI, but 71 = 72 = 7. Find the social and private optimal level of income share: 8 and 8;. What happens if M + . Explain intuitively. (10 pts) 7. Now suppose I = 1, but 91 = M12. Find the social and private optimal level of income share: 8 and 87. What happens if M . Explain intuitively. (10 pts) Problem V. Shared Driveway (55 points) Recall the textbook example where two neigh- bors share a driveway. Suppose each person gets utility on the private consumption good, c, and the driveway, D = d. + d2, such that :(,D) = ln(c) + 7 In{D). Price of snowplow- ing/repairing services is p in terms of the consumption good. Each person has income 1. Let di = pd;/1, denote the income share of driveway expenditures for person i. First, assume that 71 = 72 = 9 and 11 = 12 = 1. 2 1. Find the social optimal income share of driveway services. . (5pts) 2. Find the private optimal income share of driveway services, 8*. (5 pts) 3. Compare 8 and 8. Explain intuitively why they are different. (5 pts) 4. Now suppose there is some extent of altruism. Le ui( GD) = ln(c) + In(D) + ln(D). Find the private optimal income share with altruism 64 Compare 54 and 8. What happens if 4 = 7. (10 pts) 5. Now, consider the case with warm glow where each person cares about his contribution to the driveway rather than his consumption of driveway. Specifically, u:(.d) = ln(c) + In(d.). Find the private optimal income share with warm glow, W. Compare and .. Explain intuitively. (10 pts) 6. Now suppose I > I. Specifically, 11 = MI, but 71 = 72 = 7. Find the social and private optimal level of income share: 8 and 8;. What happens if M + . Explain intuitively. (10 pts) 7. Now suppose I = 1, but 91 = M12. Find the social and private optimal level of income share: 8 and 87. What happens if M . Explain intuitively. (10 pts)