3 Public Goods - 2 points Andy and Beth live near the beach in California where the risk of tsunami is relatively high. They both offer fishing trips to the tourists in the area. Their business has two types of expenditures: motor boats (m) and tsunami alert systems (t). Tsunami alert systems are non-excludable, and therefore are a public good. In addition, these systems are not perfect: in many cases they produce false alarms. Tourists like being safe, but can get annoyed if too many boat trips are canceled because of malfunctioning alarm systems. The profits of Andy's firm are given by: The customers of Beth are less worried about tsunami threat, so her profits are: IT = In(14 | 2") | la(m") ("_m (a) Suppose 24 =0.25. Find the optimal level of investment in the tsunami alert systems by firm B, ". Mark this point in the space (tAt"). ( point) (b) Find analytically the best response function for firm B and plot it on your graph from the previous part. ( point) (c) Find the best response function for firm A. Add it to the graph. ($ point) (d) Find the (Nash) equilibrium for two firms. What is the total amount of money invested in tsunami alert systems? ( point) (e) Is the predicted outcome associated with free riding? If yes, explain which firm is free riding and why? ( point) (f) Propose a nudge that might generate more investment in tsunami alert systems. Be explicit about. how this nudge might change either or both of the two firms' profit functions ( point)