Question 5) (25 points) Los Angeles is considering building a new basketball arena. Assume the city has two residents: Lebron and Davis. Los Angeles will fund the new stadium solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (yi) and total stadium-size (A), of the form: Ui(yi, A) = log(yi 10) + log(A 15) The total size of the arena is determined by the total number of seats built, A, and is the sum of the number of seats paid for by Lebron and Davis: A = a1 + ap. Lebron has an income of $120, and Davis has an income of $110. Both the private good and an arena seat have a price of $1. 1. (8 points) How many seats will be built if the government does not intervene? How many are paid for by Lebron? By Davis? 2. (7 points) What is the socially optimal number of seats? If your answer differs from (a), explain why. 3. (10 points) Suppose, starting from the situation in part (a), the government decides to provide a certain number of seats and finances the cost of these seats from elsewhere. Find the number of seats the government needs to provide to ensure that socially optimal seats are built-in equilibrium. How many seats are supplied by Lebron and by Davis? Does the government provision of seats crowd out private contributions by Lebron and Davis? Question 5) (25 points) Los Angeles is considering building a new basketball arena. Assume the city has two residents: Lebron and Davis. Los Angeles will fund the new stadium solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (yi) and total stadium-size (A), of the form: Ui(yi, A) = log(yi 10) + log(A 15) The total size of the arena is determined by the total number of seats built, A, and is the sum of the number of seats paid for by Lebron and Davis: A = a1 + ap. Lebron has an income of $120, and Davis has an income of $110. Both the private good and an arena seat have a price of $1. 1. (8 points) How many seats will be built if the government does not intervene? How many are paid for by Lebron? By Davis? 2. (7 points) What is the socially optimal number of seats? If your answer differs from (a), explain why. 3. (10 points) Suppose, starting from the situation in part (a), the government decides to provide a certain number of seats and finances the cost of these seats from elsewhere. Find the number of seats the government needs to provide to ensure that socially optimal seats are built-in equilibrium. How many seats are supplied by Lebron and by Davis? Does the government provision of seats crowd out private contributions by Lebron and Davis
