Traditionally, Hobbits have relied on private provision for their schooling. As the newly elected mayor of the Shire, Samwise Gamgee has decided to launch a public schooling option. The typical Hobbit family has the following budget constraint: I = S + X, where I is total family income, S is schooling expenditures, and X is expenditures on all other goods.

Samwise is concerned that the amount of schooling has declined. He therefore closes the public school and offers all students a $1,000 voucher that can be used only on education. Draw the new budget constraint. Will the voucher lead to any Hobbits receiving less education services than before the voucher program? In what case will the voucher lead Hobbits to spend exactly $1,000 more on education?