### Calculate the total amount of government spending on public

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Suppose that households have one child each and an income of M per year to spend on their child's education and other goods. Each year they elect to either send their children to a Public School and receive \$21,000 worth of education or to a Private School and pay \$X to receive \$14,000+\$X worth of education. For example, if a household chooses to spend X=\$5,000 on private education, then they receive \$19,000 in education.

Assume that \$ of education funding whether provided by Government Schools or Private Schools are perfect substitutes. Note that for the Private school option, the \$14,000 is effectively added to income as a voucher (V), which households can top up with their own spending X on education. Note that households cannot spend more on other goods than their income (that is they may not exchange the Government funding for cash).

a. Complete the table below by determining how much X, Y and U each of the four household types would have if they sent their child to a Public School and how much X, Y and U the four types would have if they sent their child to a Private School. Using this information determine whether each household type will choose to send their child to a Public or Private school.

b. Some advocates have proposed a pure-voucher system, where all current government education funding to both government and private schools would stop and be divided equally amongst all households. Advocates of the voucher system claim, "All households will be better off and it will result in a better level of education for all Australian students".

i. Calculate the total amount of government spending on public and private education under the current system. Calculate the size of the voucher under this pure-voucher system.

ii. Calculate the amount of education (X) and other non-essential goods (Y) for each household type and their Utility (U) for each of the four household types.

iii. Evaluate the advocates for the voucher systems claim.

c. Supporters of public education argue that all government funding to private education should cease and be invested in public schools. The public school supporters claim, "This reform would improve the quality of public education and raise the average level of education of Australian students and make all but the wealthiest household better off". Assume that the government uses all its education funding to fund an expanded public education system. Any household wishing to send their child to a private school would receive no voucher or other support.

i. Assume initially that no household switches from their current choice. Calculate the \$ of government funding per public school student under the new scheme.

ii. If Type III and IV households were still to send their children to private schools (with no support) how much would they spend on education (X) and other non-essential goods (Y) and what would be their utility (U)?

iii. Calculate the utility for household types III and IV if their child attended a public school with expanded funding as calculated in i. Would type III or IV households prefer private unsupported education or the improved public system?

iv. Given your answer in iii would there be any change in the amount of funding per student at public schools? What would be the utility of each household type under this level of funding?

v. Evaluate the claims of the supporters of the expanded public education system.

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