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 proceedsto spend Rg = $2τ on snow removal.

Question: Write down Ryan’s and Sam’s new utility maximization problems.How have their incentives to purchase snow removal changed?