Consider a community of two families A and B, who contribute EA and EB dollars to the community’s events budget. Community events are a public good and the total quality of events provided E = EA + EB. Assume each family has an annual income of $60 which it splits between the events budget and all other consumption spending X. Family utility functions are given by UA = XA^1/2 E^1/2 and UB = XB^1/2E^1/2. (a) What event budget would maximize the social welfare function W = UA + UB? (Study tip: You can either set up and solve the social planner’s problem, or recall the necessary condition for optimal public good provision. I recommend the latter.) (b) If households privately decide how much to contribute to the event budget, what will the total budget be? (Study tip: Begin by finding each household’s best response to the other, then solve. You can use the fact that the problem is symmetric to save time in this step.)

Consider a community of two families A and B, who contribute EA and EB dollars to the community’s events budget. Community events are a public good and the total quality of events provided E = EA + EB. Assume each family has an annual income of $60 which it splits between the events budget and all other consumption spending X. Family utility functions are given by UA = XA^1/2 E^1/2 and UB = XB^1/2E^1/2. (a) What event budget would maximize the social welfare function W = UA + UB? (Study tip: You can either set up and solve the social planner’s problem, or recall the necessary condition for optimal public good provision. I recommend the latter.) (b) If households privately decide how much to contribute to the event budget, what will the total budget be? (Study tip: Begin by finding each household’s best response to the other, then solve. You can use the fact that the problem is symmetric to save time in this step.)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

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