A town has three families, each with one child, and each of which earns $100,000 per year (pre-tax). Each family is taxed $10,000 per year to finance the public school system in the town, which any family can then freely attend. Education spending is $15,000 per student in the public schools. The three families differ in their preferences for education. Though families A and B both send their children to the public school, family B places a greater value on education than family A. Family C places the greatest relative value on education and sends its child to private school.

(a) Graph the budget constraint, making sure all relevant points are correctly labelled, and draw a possible indifference curve that corresponds to the choice each family makes, providing a brief explanation.

(b) The town is considering replacing its current system with a voucher system. Under the new system, each family would receive a $15,000 voucher for education to use in either public or private schools. The voucher system is more costly and taxes need to increase to $15,000 per household to pay for it. Draw the budget constraint the families would face under the voucher system and provide an explanation.

(c) Suppose that, when the new system is introduced, family A continues to send their child to public school, but family B now sends their child to private school (along with family C's child).

(i) Explain how you know that family C is made better off and family A is made worse off by the voucher policy. Provide also a graphical illustration. (ii) Show, using diagrams, that family B could be made better or worse off by the voucher policy.