Public goods (25 points total) Suppose there are two individuals in the economy, with a private good X and public good F. Each individual is taxed $5, with which the government provides $10 of the public good. Each individual has a utility function: Ul- = 2 - log(X1-) + log + F3 + 10) and budget constraint: XE + F: = 100 5 a. Set up the utility maximization problem for individual i. (5 points) b. Solve for the levels of each good individual i will choose to conSume. (5 points) c. Suppose the government no longer taxed and provided public good F. Solve for the levels of each good individual i will choose to consume. (5 points) d. For each of the scenarios above, is the outcome socially optimal. Explain why. (10 points)