I am not quite sure how to set up and solve for the social and private optimal income. Could you please help?

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 wi(c, 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, = pdi/ I; denote the income share of driveway expenditures for person i. First, assume that 71 = 2 = y and /1 = 12 = 1. 2 1. Find the social optimal income share of driveway services, 6. (5pts) 2. Find the private optimal income share of driveway services, 6*. (5 pts) 3. Compare &* and 6. Explain intuitively why they are different. (5 pts)