Problem 5: [10 points] A state government has 1000/ as total resources available to divide between units of educational quality (E) and spending on all other public goods (G). Aggregate preferences within the state over E and G are given by U = 0.251116 4- 0.751115 The cost of each unit of education quality is \"E. a. If the state of Maine maximizes the aggregate utility function above, how many units of education quality will Maine provide? Demonstrate the optimal choice graphically, using a standard budget constraint and indifference curve analysis. Suppose the union government provides the state with an extremely generous 0.75-forone matching grant, such that each 1/- in state spending on the education program is matched by 75 paise from the union government. b. What is the state's effective price per unit of improving education quality under this proposal? Present the state's revised problem graphically, as above, labeling the original and revised budget constraints as well as the original and revised level of quality provided for the education program and relevant indifference curves. Solve mathematically for the revised level of quality provided for the education program and the total size of the grant. Suppose instead that the union government is contemplating either providing the state with a block grant of equivalent size to the grant calculated in (b) or a conditional block grant whereby the grant is provided to the state with a mandate that the grant be spent only on improving the quality of the education program. c. Present the state's revised problem graphically under the two proposals, labeling the original and revised budget constraints as well as the original and revised level of quality provided for the education program and relevant indifference curves. d, Which policy works better if the main aim is to improve the quality of education in the state