4. Lindahl Example - Suppose there are three individuals within a neighborhood: Anne, Bob, and Cara. They form a homeowners' association (HOA) to help decide the optimal level of security through a neighborhood security guard (public good). (25 points total) They each have utility functions of the form u(x, )) = yo -(a; - x)2, where x denotes the hours of neighborhood security that is provided each week, and y; denotes the amount of money homeowner i has available for other goods. The values of their preference parameters of are CA = 27, aB = 24, ac = 19 a. What are the marginal rate of substitution functions of y for x? (5 points) Several firms will provide security services and all charge the same price, p = $40 per hour. That is, the marginal cost to homeowners per hour of security is $40. b. If homeowners contract individually, what amount of security, x, will be purchased? (5 points) C. What will be the Pareto amount of security, x? (5 points) d. Suppose the HOA sets Lindahl prices for x. What are the Lindahl prices? (5 points) e. Are the Lindahl prices Pareto efficient? Explain. (5 points)