Please help me solve 13 a

11. 13. Suppose 20 people each have the demand (.2 = 21] Pfor streetlights, and 5 people have the demand Q = 13 2P for streetlights. The cost of building each streetlight is $10. If it is impossible to purchase a fractional number of streetlights, how many streetlights are socially optimal? Amy, Brooke, and Chelsea live in Minneapolis. Amy's demand for bike paths, a public good, is given by Q = 24 1P. Brooke's demand is Q = 14 P, and Chelsea's is Q = 5 Pf3. The marginalcost of building a bike path is ME = 13. The town government decides to use the following procedure for deciding how many paths to build. It asks each resident how many paths she wants, and it builds the largest number asked for by any resident. To pay forthese paths, it then taxes Amy, Beth, and Cathy the prices a, b, and c per path, respectively, where a. + b + e = MC. [The residents know these tax rates before stating how many paths they want.) a. If the taxes are set so that each resident shares the cost evenly {a = b = c}, hovlr many paths will get built? b. Show that the government can achieve the social optimum by settin g the correct tax prices a, b, and c. What prices should it set