Could you help with only the first three parts of the following public economics problem?

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 = dj + d2, such that ui(ci, D) = In(c) + % In(D). Price of snowplow- ing/repairing services is p in terms of the consumption good. Each person has income I;. Let 6, = pd;/I; denote the income share of driveway expenditures for person i. First, assume that 71 = 2 = y and I1 = 12 = 1. 2 1. Find the social optimal income share of driveway services, 5. (5pts) 2. Find the private optimal income share of driveway services, 5*. (5 pts) 3. Compare &* and 8. Explain intuitively why they are different. (5 pts) 4. Now suppose there is some extent of altruism. Le. ";(c, D) = In(c) + yl(D) + 5In(D). Find the private optimal income share with altruism 64. Compare 64 and 5. What happens if 9 = v. (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, w;(c, d;) = In(c) + yln(d:). Find the private optimal income share with warm glow, ". Compare 5" and 6. Explain intuitively. (10 pts)