Consider a community that has two residents, Bill and Amanda. Bill and Amanda would both like to see streetlights installed in their community and they are busy trying to decide what the optimal amount of streetlights for their community is and what price they should each contribute for each streetlight installed. Luckily they are both willing to reveal their preferences and so we do not have to worry about the free rider problem. Bill's demand for streetlights is given by the equation Q = 10-P and Amanda's demand for streetlights is given by the equation P = 5-(1/2)Q. The marginal cost of providing a streetlight is $3. a. On your homework paper draw three graphs vertically one above the other. The first graph should be labeled "Bill's demand"; the second graph should be labeled "Amanda's demand"; and the third graph should be labeled "market demand". On each graph the horizontal axis should be labeled "Quantity of Streetlights" while the vertical axis should be labeled "Price of Streetlights". Now in each graph draw in the demand curve corresponding to your label. Remember that the market demand curve will be a vertical summation of the individual demand curves since a public good is non-rival. b. Write an equation for the market demand curve for the public good. c. What is the optimal number of streetlights for this community? Show how you found this number. d. What price per streetlight will Bill pay? What price per streetlight will Amanda pay? Why do Bill and Amanda pay different amounts for each streetlight that is produced?