The Question is attached below:

A state government has 100012 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 + 0.?51nE The cost of each unit of education quality is 11.3. a. Ifthe 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.?S-for-one matching grant, such that each 1/- in state spending on the education program is matched by 'IS 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, labejjggthe 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, Mthe 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