Consider a local government with preferences represented by U=C 0.75 E 0.25 where C stands for expenditure on local private goods and E stands for expenditure on locally provided education. The local income absent any federal government grant is $100 million. The federal government is considering 3 alternative grant programs: (1) a \$40 million block grant; (2) a \$40 million categorical grant. where the designated category is locally provided education; and (3) a matching grant for locally provided education on a dollar-fordollar basis.

(a) How much does the locality spend on local private goods and locally provided education in the absence of any federal government grant? Provide a graphical representation. 

(b) How much does the locality spend on local private goods and locally provided education under each of the alternative grans programs? Provide a graphical representation for each grant program.

(c) Which type of grant results in a larger expenditure on locally provided education? Which type of grant yields a higher level of local social welfare? Justify your answer.