Suppose each person gets utility on the private consumption good, c, and the driveway... (see image for the rest)

Problem V. Shared Driveway (35 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 = di + d2, such that us(c, D) = In(c) + 7In(D). Price of snowplow- ing/repairing services is p in terms of the consumption good. Each person has income I;. Let di =pd;/I; denote the income share of driveway expenditures for person i. First, assume that 71 = 12 = y and I1 = 12 = 1.1. Find the social optimal income share of driveway services, 5. (5pts) 2. Find the private optimal income share of driveway services, 8*. (5 pts) 3. Compare &* and o. Explain intuitively why they are different. (5 pts) 4. Now suppose there is some extent of altruism. Le. w;(c, D) = In(c) + yln(D) + 5 In(D). Find the private optimal income share with altruism 84. Compare 4 and 5. What happens if ~ = y. (10 pts) 5. Now, consider the case with warm glow where each person cares about his contribu- tion to the driveway rather than his consumption of driveway. Specifically, wi(ci, di) = In(c) + y In(d;). Find the private optimal income share with warm glow, 6 . Compare 5W and 5. Explain intuitively. (10 pts)