Madison has two residents: Sam and Ryan. Both love to drive. Each resident’sutility depends positively on the weight of his own car (Wr or Ws) and the totalamount of a public good, snow removal, purchased in the town. Speci?cally,both residents i have utility functions, (lower case letters are subscribts) Ui = 4 ln(Wi) + ln(R) The total amount of snow removal (measured in dollars) is the sum R = Rr +Rs + Rg of Ryan’s snow-removal purchase, Sam’s snow-removal purchase, andthe local government’s snow removal purchase. Sam and Ryan each have incomes of $2,500, and all cars sell for a price of $W($1 per pound). Now consider how the equilibrium outcome changes when the local gov-ernment implements a small tax of $τ per resident and uses the proceeds to spend Rg = $2τ on snow removal.
Question: Compute the market equilibrium outcome (i.e. ?nd the values of Rs and Rr that are best responses to one another). How has the total quantity of snow removal R = Rs + Rr + Rg changed? What does this result suggest about the e?ectiveness of small interventions aimed at increasing the quantity of a public good that is already provided in positive quantities privately.