3. Suppose that the city of Philadelphia provides only one public good, education, to its residents. Education is financed through property taxes; any money left over after these taxes is spent by families on private goods. Imagine that the cost of each type of spending is $1, that the city's budget is $1 million, and that the city has the following preferences: U(E, P) = ln(E) + 2ln(P), where E is education spending and P is private goods spending. All units are in thousands. (a) Draw the city of Philadelphia's budget constraint with education spending (in thousands) on the x-axis and private goods spending (in thousands) on the y-axis. (b) What are the optimal amounts of E and P? (c) The state of Pennsylvania wants to encourage Philadelphia to spend more money on education, but at as low a cost as possible to the state. It considers the following two policies: Policy A (block grant of $50,000) and Policy B (a 1-for-1 matching grant with a $50,000 limit). i. On your graph from (a), show how each policy changes the city's budget constraint. ii. Which policy will better achieve Pennsylvania's goals and why? iii. In a perfect Tiebout world, would Pennsylvania subsidize Philadelphia public schools? Why or why not?