The mayor of Roytown has W dollars to split between educational quality E and other public goods G. The mayor is trying to maximize the "aggregate utility function" U = (1111(0) + (1 a) ln(E) where a is between 0 and 1. The price of each unit of E is PE and the price of each unit ofG is 1. A. Town Provision Only 1. lfthe Roytown government maximizes the aggregate utility function above, what level of E will it provide? 2. What share of total resources will it spend on E? How does that share depend on the price PE of educational quality government resources W? 3. Demonstrate the optimal choice graphically. That is, draw a graph over the two goods with a budget constraint and an appropriate indifference curve. Be sure to label the graph clearly, including the x- and y-intercepts of the budget constraint. B. State Involvement Suppose the state government wants to help. It provides Roytown a matching grant, such that each dollar the Roytown government spending on E is matched by 2 dollars from the state government. 1. With the matching grant. what is the effective price per unit of E that Roytown faces? 2. Under this proposal, how do you expect the levels of E and G Roytown chooses will change (relative to situation where there is no assistance from the state)? First explain this "intuitively" without any math. [Hintz NoL required, but your response might mention income and substitutions effects] 3. Sketch a new graph for Roytown. Include the original budget constraint (i.e., the budget constraint without state help) as well as the new budget constraint. And draw two indifference curves that show the optimal balance of goods. 4. (10 pts) Now do the math: What is the new level of education E that Roytown will choose? What is the size of the grant from the state? Is there any crowd out