1. Inresponse to low SAT scores by high school students, politicians have decided to abolish all private provision of education and move to a purely public education system. That is, all school will be publicly funded. The government has W total resources available to divide between units of educational quality (E) and spending on all other public goods (G). Aggregate preferences within the country over E and & are given by: U=aln(G) + (1 a)in(E) wherea (0, 1). The cost of each unit of education quality is pg. a) If the country maximizes the aggregate utility function above, how many units of education quality will it provide? b) What fraction of total resources is spent on education, and what fraction of total resources is spent on other public goods? How do these fractions depend on the price p; of educational quality and total government resources W? BONUS (Give this part a try in preparation for the midterm exam. It will also be solved and explained in class, but I recommend you try it first, on your own.) Next, evaluate the impact of the federal government intervention relative to the setup in the first part of the question. Suppose the federal government provides with an extremely generous p-for-one matching grant, such that each $1 in public spending on the education program is matched by $f from the federal government. a) What is the effective price per unit of improving education quality under this proposal? b) Before solving the problem mathematically, how would you expect the quality provided to change under this proposal, relative to no federal intervention? Should this be an income etfect, a substitution ettect, or a combination of both? Provide intuition for how each price effect impacts the provided level of quality for the education program. ) Solve mathematically for the revised level of quality provided for the education program and the total size of the grant. d) How much does federal spending crowd out state spending