In class, we analyzed the crowd out effect of a community decision to spend a given amount of funds per household on providing a public school. The decision about what amount to spend on the public school, which is assumed to determine the quality of the school services, is a community decision. The students in the community will have access to the same quality of public school, so we can analyze the decision about the common level of public school quality using our median voter model from the political economy section of the course.

Consider a community of 3 households. The marginal benefit/inverse demand for school quality (denoted as S) for each household is given below: MB1 = 250 - S MB2 = 150 - S MB3= 50 - S The marginal cost of increasing school quality is 300 per unit. Whatever school quality is chosen for the school will apply to all pupils. a. What is the efficient level of school quality for this community? b. The community government finances the school with property taxes. The share of costs per unit to a household will be equal to the proportion of community property value the household owns. Property values are distributed: Value 1 = 150,000, Value 2 = 100,000, Value 3 = 50,000. The community government will provide the largest quantity that a majority of the households will support. What is the majority voting choice? A neighboring community of 3 households also finances school quality through property taxes and selects school quality through majority voting. In the second community, the marginal benefits are:

MB1 = 300 - S MB2 = 200 - S MB3= 100 - S The marginal cost of increasing school quality is 300 per unit. Whatever school quality is chosen for the school will apply to all pupils.

Property values are distributed: Value 1 = 300,000, Value 2 = 200,000, Value 3 = 100,000. c. What is the majority voting choice in this community? d. The marginal benefit/inverse demands in the second community are higher because incomes are higher in that community. How do your results in parts b. and c. relate to the income stratification features of public school systems?